From 2e77300d975c0e939f381aa18293f2bf26674dc6 Mon Sep 17 00:00:00 2001 From: guyotv Date: Fri, 4 Jan 2019 21:55:58 +0100 Subject: [PATCH] Un exercice avec deux masse en plus. --- Annexe-Exercices/Annexe-Exercices.aux | 9 +- Annexe-Exercices/Annexe-Exercices.log | 5281 +++++++++++++++++++ Annexe-Exercices/Annexe-Exercices.tex | 72 +- Annexe-Exercices/Annexe-Exercices.tex.bak | 82 +- Annexe-Exercices/Images/incline.svg | 90 +- Annexe-Incertitudes/Annexe-Incertitudes.aux | 6 +- CoursMecaniqueOSDF.dvi | Bin 1475996 -> 1483184 bytes CoursMecaniqueOSDF.log | 50 +- CoursMecaniqueOSDF.pdf | Bin 12252813 -> 12259349 bytes CoursMecaniqueOSDF.ps | 351 +- SolutionsOS.tex | 65 + 11 files changed, 5826 insertions(+), 180 deletions(-) create mode 100644 Annexe-Exercices/Annexe-Exercices.log diff --git a/Annexe-Exercices/Annexe-Exercices.aux b/Annexe-Exercices/Annexe-Exercices.aux index 2b7f475..1fa0c77 100644 --- a/Annexe-Exercices/Annexe-Exercices.aux +++ b/Annexe-Exercices/Annexe-Exercices.aux @@ -24,6 +24,7 @@ \newlabel{poulie}{{L.2}{212}} \@writefile{lof}{\contentsline {figure}{\numberline {L.3}{\ignorespaces Masse pendante}}{212}} \newlabel{pendante}{{L.3}{212}} +\newlabel{planinclinesimple}{{2}{212}} \@writefile{toc}{\contentsline {subsection}{\numberline {L.1.9}Relatifs aux forces}{212}} \newlabel{massedelaterre}{{48}{212}} \@writefile{toc}{\contentsline {subsection}{\numberline {L.1.10}Relatifs \IeC {\`a} l'\IeC {\'e}nergie}{213}} @@ -39,9 +40,9 @@ \@writefile{lof}{\contentsline {figure}{\numberline {L.5}{\ignorespaces Plan inclin\IeC {\'e}}}{221}} \newlabel{incline}{{L.5}{221}} \@setckpt{Annexe-Exercices/Annexe-Exercices}{ -\setcounter{page}{222} +\setcounter{page}{223} \setcounter{equation}{0} -\setcounter{enumi}{3} +\setcounter{enumi}{4} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} @@ -75,7 +76,7 @@ \setcounter{lstnumber}{1} \setcounter{Solution}{26} \setcounter{exc}{71} -\setcounter{Solution OS}{3} -\setcounter{exosc}{3} +\setcounter{Solution OS}{4} +\setcounter{exosc}{4} \setcounter{lstlisting}{0} } diff --git a/Annexe-Exercices/Annexe-Exercices.log b/Annexe-Exercices/Annexe-Exercices.log new file mode 100644 index 0000000..143553d --- /dev/null +++ b/Annexe-Exercices/Annexe-Exercices.log @@ -0,0 +1,5281 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=latex 2018.12.20) 4 JAN 2019 17:51 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**Annexe-Exercices.tex +(./Annexe-Exercices.tex +LaTeX2e <2017/01/01> patch level 3 +Babel <3.9r> and hyphenation patterns for 12 language(s) loaded. +! 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Undefined control sequence. +l.11 ...\unit{4,238}{AL} de nous. Combien de \kilo + \metre cela fait-il ? Expr... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.11 ...4,238}{AL} de nous. Combien de \kilo\metre + cela fait-il ? Exprimez l... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.11 ...rsec} (pc) cela fait-il ? Réponse : \unit + {1,33}{pc}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment sol undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.12 \begin{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.13 Comme le nombre de \kilo + \metre est 1000 fois plus petit que le nombr... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.13 Comme le nombre de \kilo\metre + est 1000 fois plus petit que le nombr... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 13. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 13. +! Undefined control sequence. +l.13 ...it que le nombre de mètres et que \(\unit + {1}{AL}=\unit{9,46\cdot 10... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.13 ...bre de mètres et que \(\unit{1}{AL}=\unit + {9,46\cdot 10^{15}}{\metre... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.13 ...nit{1}{AL}=\unit{9,46\cdot 10^{15}}{\metre + }\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +! LaTeX Error: Environment align* undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.14 \begin{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.15 \unit + {4,238}{AL}&=4,238\cdot 9,46\cdot 10^{15}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 4 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +! Misplaced alignment tab character &. +l.15 \unit{4,238}{AL}& + =4,238\cdot 9,46\cdot 10^{15}\\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +Missing character: There is no = in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing $ inserted. + + $ +l.15 \unit{4,238}{AL}&=4,238\cdot + 9,46\cdot 10^{15}\\ +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Misplaced alignment tab character &. + & + +l.16 & + =4\cdot 10^{16}\,m=\unit{4\cdot 10^{13}}{\kilo\metre} +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Undefined control sequence. +l.16 &=4\cdot 10^{16}\,m=\unit + {4\cdot 10^{13}}{\kilo\metre} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.16 ...dot 10^{16}\,m=\unit{4\cdot 10^{13}}{\kilo + \metre} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.16 ...^{16}\,m=\unit{4\cdot 10^{13}}{\kilo\metre + } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{align*}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.17 \end{align*} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.18 Comme \(\unit + {1}{pc}\approx \unit{3\cdot 10^{16}}{\metre}\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.18 Comme \(\unit{1}{pc}\approx \unit + {3\cdot 10^{16}}{\metre}\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.18 ...1}{pc}\approx \unit{3\cdot 10^{16}}{\metre + }\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 11--19 +[] + [] + + +Overfull \hbox (29.86111pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 1[] = + [] + + +Overfull \hbox (45.13887pt too wide) in paragraph at lines 11--19 +[][]$ + [] + + +Overfull \hbox (25.00003pt too wide) in paragraph at lines 11--19 +\OMS/cmsy/m/n/10 ^^A\OT1/cmr/m/n/10 9\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 46 \OMS +/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (18.47229pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 10[][] + [] + + +Overfull \hbox (7.7778pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (7.7778pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 4 \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (39.47456pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 10[] \OML/cmm/m/it/10 m \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (30.69443pt too wide) in paragraph at lines 11--19 +[][]$ + [] + + +Overfull \hbox (24.91434pt too wide) in paragraph at lines 11--19 +\OT1/cmr/m/n/10 1[] \OMS/cmsy/m/n/10 ^^Y + [] + + +Overfull \hbox (30.69443pt too wide) in paragraph at lines 11--19 +[][]$ + [] + +! Undefined control sequence. +l.19 \[\unit + {4\cdot 10^{16}}{\metre}\approx \frac{4\cdot 10^{16}}{3\cdot ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.19 \[\unit{4\cdot 10^{16}}{\metre + }\approx \frac{4\cdot 10^{16}}{3\cdot ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.19 ...frac{4\cdot 10^{16}}{3\cdot 10^{16}}=\unit + {1,33}{pc}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (119.25856pt too wide) detected at line 19 +[][] \OMS/cmsy/m/n/10 ^^Y [] \OT1/cmr/m/n/10 = [][] + [] + + +! LaTeX Error: \begin{document} ended by \end{sol}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.20 \end{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{ex}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 \end{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment ex undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.23 \begin{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 Q + uelle est la distance Terre-Soleil en \kilo\metre, en UA et en AL ?... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no Q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.24 ...elle est la distance Terre-Soleil en \kilo + \metre, en UA et en AL ? E... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.24 ...st la distance Terre-Soleil en \kilo\metre + , en UA et en AL ? Entre n... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no ? in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ? in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no : in font nullfont! +! Undefined control sequence. +l.24 ... mettre cette distance ? Réponses : \unit + {1,496\cdot 10^{8}}{\kilo\... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no 6 in font nullfont! +! Missing $ inserted. + + $ +l.24 ...te distance ? Réponses : \unit{1,496\cdot + 10^{8}}{\kilo\metre}, \un... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.24 ...nce ? Réponses : \unit{1,496\cdot 10^{8}} + {\kilo\metre}, \unit{1}{UA... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.24 ...Réponses : \unit{1,496\cdot 10^{8}}{\kilo + \metre}, \unit{1}{UA}, \un... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.24 ...ses : \unit{1,496\cdot 10^{8}}{\kilo\metre + }, \unit{1}{UA}, \unit{16}... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.24 ...nit{1,496\cdot 10^{8}}{\kilo\metre}, \unit + {1}{UA}, \unit{16}{\micro ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.24 ... 10^{8}}{\kilo\metre}, \unit{1}{UA}, \unit + {16}{\micro AL} et \(268'2... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.24 ...ilo\metre}, \unit{1}{UA}, \unit{16}{\micro + AL} et \(268'228\,\times\). +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 ..., \unit{1}{UA}, \unit{16}{\micro AL} et \( + 268'228\,\times\). +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment sol undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.25 \begin{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.26 La distance Terre-Soleil vaut \unit + {1,496\cdot 10^{11}}{\metre}. On ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no 6 in font nullfont! +! Missing $ inserted. + + $ +l.26 ...istance Terre-Soleil vaut \unit{1,496\cdot + 10^{11}}{\metre}. On a do... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.26 ...erre-Soleil vaut \unit{1,496\cdot 10^{11}} + {\metre}. On a donc : +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.26 ...leil vaut \unit{1,496\cdot 10^{11}}{\metre + }. On a donc : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 \[ + \unit{1,496\cdot 10^{11}}{\metre}=\unit{1,496\cdot 10^{8}}{\kilo\m... + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.27 \[\unit + {1,496\cdot 10^{11}}{\metre}=\unit{1,496\cdot 10^{8}}{\kilo\m... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.27 \[\unit{1,496\cdot 10^{11}}{\metre + }=\unit{1,496\cdot 10^{8}}{\kilo\m... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.27 \[\unit{1,496\cdot 10^{11}}{\metre}=\unit + {1,496\cdot 10^{8}}{\kilo\m... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.27 ...1}}{\metre}=\unit{1,496\cdot 10^{8}}{\kilo + \metre}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.27 ...etre}=\unit{1,496\cdot 10^{8}}{\kilo\metre + }\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 ...e}=\unit{1,496\cdot 10^{8}}{\kilo\metre}\] + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \[ + \unit{1,496\cdot 10^{11}}{\metre}=\unit{1}{UA}\] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.29 \[\unit + {1,496\cdot 10^{11}}{\metre}=\unit{1}{UA}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.29 \[\unit{1,496\cdot 10^{11}}{\metre + }=\unit{1}{UA}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.29 \[\unit{1,496\cdot 10^{11}}{\metre}=\unit + {1}{UA}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 ...1,496\cdot 10^{11}}{\metre}=\unit{1}{UA}\] + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no à in font cmr10! +Missing character: There is no © in font cmr10! +Missing character: There is no à in font cmr10! +Missing character: There is no © in font cmr10! +Missing character: There is no 1 in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 6 in font nullfont! +! Missing $ inserted. + + $ +l.30 Finalement, avec $1\,AL=9,46\cdot + 10^{15}\,m$, on a : +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +! LaTeX Error: Environment align* undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.31 \begin{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.32 \unit + {1,496\cdot 10^{11}}{\metre}&=\frac{1,496\cdot 10^{11}}{9,46\cd... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no 6 in font nullfont! +! Missing $ inserted. + + $ +l.32 \unit{1,496\cdot + 10^{11}}{\metre}&=\frac{1,496\cdot 10^{11}}{9,46\cd... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.32 \unit{1,496\cdot 10^{11}} + {\metre}&=\frac{1,496\cdot 10^{11}}{9,46\cd... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.32 \unit{1,496\cdot 10^{11}}{\metre + }&=\frac{1,496\cdot 10^{11}}{9,46\cd... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Misplaced alignment tab character &. +l.32 \unit{1,496\cdot 10^{11}}{\metre}& + =\frac{1,496\cdot 10^{11}}{9,46\cd... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. + & + +l.33 & + =\unit{1,58\cdot 10^{-5}}{AL}\cong\unit{16}{\micro AL} +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Undefined control sequence. +l.33 &=\unit + {1,58\cdot 10^{-5}}{AL}\cong\unit{16}{\micro AL} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.33 &=\unit{1,58\cdot 10^{-5}}{AL}\cong\unit + {16}{\micro AL} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.33 ...,58\cdot 10^{-5}}{AL}\cong\unit{16}{\micro + AL} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{align*}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.34 \end{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.34 \end{align*} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.34 \end{align*} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no L in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ... Reference `centaure' on page \thepage + \space undefined\on@line . +l.35 L'exercice \ref{centaure} + nous indique que l'étoile la plus proche ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `centaure' on page undefined on input line 35. + +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +! Undefined control sequence. +l.35 ...©toile la plus proche de nous est à \unit + {4,238}{AL}. On a donc : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 4 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 24--36 +[] + [] + + +Overfull \hbox (121.3939pt too wide) in paragraph at lines 24--36 +\OMS/cmsy/m/n/10 ^^A\OT1/cmr/m/n/10 10[][]\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1[ +]\OML/cmm/m/it/10 ; [][]et\OT1/cmr/m/n/10 268[]228 \OMS/cmsy/m/n/10 ^^B$ + [] + + +Overfull \hbox (69.15915pt too wide) in paragraph at lines 24--36 +\OMS/cmsy/m/n/10 ^^A\OT1/cmr/m/n/10 10[][]\OML/cmm/m/it/10 :Onadonc \OT1/cmr/m/ +n/10 : + [] + + +Overfull \hbox (60.6944pt too wide) in paragraph at lines 24--36 +[][] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (305.97475pt too wide) in paragraph at lines 24--36 +[][]\OML/cmm/m/it/10 Parailleurs; pardfinitiondel[]unitastronomique\OT1/cmr/m/n +/10 (\OML/cmm/m/it/10 UA\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; ona \OT1/cmr/m/n/10 + : + [] + + +Overfull \hbox (60.6944pt too wide) in paragraph at lines 24--36 +[][] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (129.47456pt too wide) in paragraph at lines 24--36 +\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 Finalement; avec$$\OMS/cmsy/m/n/10 ^^A\OT1/ +cmr/m/n/10 10[] \OML/cmm/m/it/10 m$ + [] + + +Overfull \hbox (31.80559pt too wide) in paragraph at lines 24--36 +\OMS/cmsy/m/n/10 ^^A\OT1/cmr/m/n/10 10[][] = + [] + + +Overfull \hbox (38.37244pt too wide) in paragraph at lines 24--36 +[][] + [] + + +Overfull \hbox (7.7778pt too wide) in paragraph at lines 24--36 +\OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (72.26385pt too wide) in paragraph at lines 24--36 +[][] [] + [] + + +Overfull \hbox (24.30562pt too wide) in paragraph at lines 24--36 +[][]$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 24--36 +[] + [] + + +Overfull \hbox (109.2888pt too wide) detected at line 36 +[] \OT1/cmr/m/n/10 = 2\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 68 \OMS/cmsy/m/n/10 ^^ +A \OT1/cmr/m/n/10 10[] \OMS/cmsy/m/n/10 ^^B + [] + +Missing character: There is no A in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{sol}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.38 \end{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing } inserted. + + } +l.38 \end{sol} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{ex}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.39 \end{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing } inserted. + + } +l.39 \end{ex} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (42.25008pt too wide) in paragraph at lines 36--40 + $\OT1/cmr/m/n/10 268[]228 \OMS/cmsy/m/n/10 ^^B$ + [] + + +! LaTeX Error: Environment ex undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.41 \begin{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 C + ombien y a-t-il de fois la distance entre nous et Alpha du Centaure... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +! Undefined control sequence. +l.42 ...ie la Voie Lactée (\(\phi_{galaxie}=\unit + {80'000}{AL}\))? Réponse ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no ? in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no : in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment sol undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.43 \begin{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no L in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.44 Le diamètre de notre galaxie est de \unit + {80'000}{AL}. L'exercice \... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 8 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ... Reference `centaure' on page \thepage + \space undefined\on@line . +l.44 ...nit{80'000}{AL}. L'exercice \ref{centaure} + nous indique que la dista... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `centaure' on page undefined on input line 44. + +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.44 ...a distance à Alpha du Centaure vaut \unit + {4,238}{AL}. Ainsi, on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 4 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 42--45 +[] + [] + + +Overfull \hbox (43.56918pt too wide) in paragraph at lines 42--45 +\OML/cmm/m/it/10 ^^^[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (42.11122pt too wide) in paragraph at lines 42--45 +[][]$ + [] + + +Overfull \hbox (37.25006pt too wide) in paragraph at lines 42--45 +\OT1/cmr/m/n/10 18[]877 \OMS/cmsy/m/n/10 ^^B$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 42--45 +[] + [] + + +Overfull \hbox (80.78891pt too wide) detected at line 45 +[] \OT1/cmr/m/n/10 = 18[]877 \OMS/cmsy/m/n/10 ^^B + [] + +Missing character: There is no L in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{sol}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.47 \end{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{ex}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.48 \end{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (37.25006pt too wide) in paragraph at lines 45--49 + $\OT1/cmr/m/n/10 18[]877 \OMS/cmsy/m/n/10 ^^B$ + [] + + +! LaTeX Error: Environment ex undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \begin{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.51 S + ous quel angle (en \degree, en \arcminute et en \arcsecond) voit-on... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.51 Sous quel angle (en \degree + , en \arcminute et en \arcsecond) voit-on... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.51 Sous quel angle (en \degree, en \arcminute + et en \arcsecond) voit-on... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.51 ...en \degree, en \arcminute et en \arcsecond + ) voit-on le diamètre de ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no ; in font nullfont! +! Undefined control sequence. +l.51 ...25\cdot R_{Terre}$ ; $d_{Terre-Lune}=\unit + {3,84\cdot10^{8}}{\metre}$... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.51 ...{Terre-Lune}=\unit{3,84\cdot10^{8}}{\metre + }$). Réponses : \unit{0,5... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no : in font nullfont! +! Undefined control sequence. +l.51 ...4\cdot10^{8}}{\metre}$). Réponses : \unit + {0,5157}{\degree}, \unit{3... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 7 in font nullfont! +! Undefined control sequence. +l.51 ...etre}$). Réponses : \unit{0,5157}{\degree + }, \unit{31}{\arcminute} e... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +! Undefined control sequence. +l.51 ... Réponses : \unit{0,5157}{\degree}, \unit + {31}{\arcminute} et \unit{... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 3 in font nullfont! +Missing character: There is no 1 in font nullfont! +! Undefined control sequence. +l.51 ...nit{0,5157}{\degree}, \unit{31}{\arcminute + } et \unit{1860}{\arcsecond}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.51 ...}{\degree}, \unit{31}{\arcminute} et \unit + {1860}{\arcsecond}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.51 ...{31}{\arcminute} et \unit{1860}{\arcsecond + }. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment sol undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.52 \begin{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. + ...erence `relationdarc' on page \thepage + \space undefined\on@line . +l.53 ...donnée par l'équation \ref{relationdarc} + : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `relationdarc' on page undefined on input line 53. + +Missing character: There is no : in font nullfont! + +! LaTeX Error: Environment align* undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.54 \begin{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no D in font nullfont! +! Misplaced alignment tab character &. +l.55 D& + =2\cdot R_{Lune}=d\cdot \alpha\;\Rightarrow\;\alpha=\frac{2\cdot R... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +Missing character: There is no = in font nullfont! +Missing character: There is no 2 in font nullfont! +! Missing $ inserted. + + $ +l.55 D&=2\cdot + R_{Lune}=d\cdot \alpha\;\Rightarrow\;\alpha=\frac{2\cdot R... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Misplaced alignment tab character &. +l.56 \alpha& + =\frac{2\cdot 0,2725\cdot 6,371\cdot 10^6}{3,84\cdot 10^8}=\u... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Undefined control sequence. +l.56 ...dot 6,371\cdot 10^6}{3,84\cdot 10^8}=\unit + {0,009}{\rad} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.56 ...ot 10^6}{3,84\cdot 10^8}=\unit{0,009}{\rad + } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{align*}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.57 \end{align*} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.57 \end{align*} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.58 Comme \(\unit + {180}{\degree}=\unit{\pi}{\rad}\), l'angle considéré ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.58 Comme \(\unit{180}{\degree + }=\unit{\pi}{\rad}\), l'angle considéré ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.58 Comme \(\unit{180}{\degree}=\unit + {\pi}{\rad}\), l'angle considéré ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.58 ...omme \(\unit{180}{\degree}=\unit{\pi}{\rad + }\), l'angle considéré e... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 51--59 +[] + [] + + +Overfull \hbox (37.60005pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 R[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (32.22227pt too wide) in paragraph at lines 51--59 +\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2725 \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (29.33728pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (62.70642pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 d[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (41.15274pt too wide) in paragraph at lines 51--59 +[][]$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 51--59 +[] + [] + + +Overfull \hbox (40.37784pt too wide) in paragraph at lines 51--59 +\OMS/cmsy/m/n/10 ^^A\OML/cmm/m/it/10 R[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (7.98265pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 d \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (21.98947pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 \OMS/cmsy/m/n/10 ) + [] + + +Overfull \hbox (16.98955pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (48.13693pt too wide) in paragraph at lines 51--59 +[][] + [] + + +Overfull \hbox (16.98955pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (76.5669pt too wide) in paragraph at lines 51--59 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (24.44447pt too wide) in paragraph at lines 51--59 +[][]$ + [] + + +Overfull \hbox (25.55556pt too wide) in paragraph at lines 51--59 +[][] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (6.05905pt too wide) in paragraph at lines 51--59 +\OML/cmm/m/it/10 ^^Y[]$ + [] + +! Undefined control sequence. +l.59 \[\alpha=0,009\cdot \frac{180}{\pi}=\unit + {0,5157}{\degree}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.59 ...cdot \frac{180}{\pi}=\unit{0,5157}{\degree + }\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (107.16727pt too wide) detected at line 59 +\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 009 \O +MS/cmsy/m/n/10 ^^A [] \OT1/cmr/m/n/10 = [][] + [] + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no , in font nullfont! +! Undefined control sequence. +l.60 ...egré vaut soixante minutes d'arc, \(\unit + {1}{\degree}=\unit{60}{\ar... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.60 ...soixante minutes d'arc, \(\unit{1}{\degree + }=\unit{60}{\arcminute}\),... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.60 ...e minutes d'arc, \(\unit{1}{\degree}=\unit + {60}{\arcminute}\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.60 ..., \(\unit{1}{\degree}=\unit{60}{\arcminute + }\), on a : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (15.55553pt too wide) in paragraph at lines 59--61 + $\OT1/cmr/m/n/10 1[] = + [] + + +Overfull \hbox (10.00003pt too wide) in paragraph at lines 59--61 +[][]$ + [] + +! Undefined control sequence. +l.61 \[\alpha=\unit + {0,5157}{\degree}=0,5157\cdot 60=\unit{31}{\arcminute}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.61 \[\alpha=\unit{0,5157}{\degree + }=0,5157\cdot 60=\unit{31}{\arcminute}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.61 ...unit{0,5157}{\degree}=0,5157\cdot 60=\unit + {31}{\arcminute}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.61 ...egree}=0,5157\cdot 60=\unit{31}{\arcminute + }\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (128.10052pt too wide) detected at line 61 +\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = [][] = 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 + 5157 \OMS/cmsy/m/n/10 ^^A \OT1/cmr/m/n/10 60 = [][] + [] + +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! +! Undefined control sequence. +l.63 \[\alpha=\unit + {31}{\arcminute}=31\cdot 60=\unit{1860}{\arcsecond}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.63 \[\alpha=\unit{31}{\arcminute + }=31\cdot 60=\unit{1860}{\arcsecond}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.63 ...pha=\unit{31}{\arcminute}=31\cdot 60=\unit + {1860}{\arcsecond}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.63 ...cminute}=31\cdot 60=\unit{1860}{\arcsecond + }\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (99.21164pt too wide) detected at line 63 +\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = [][] = 31 \OMS/cmsy/m/n/10 ^^A \OT1/cmr/m/ +n/10 60 = [][] + [] + + +! LaTeX Error: \begin{document} ended by \end{sol}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.64 \end{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{ex}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.65 \end{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment ex undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.67 \begin{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.68 L + a matière interstellaire est constituée de gaz neutre (hydrogène... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.68 ...ité d'un nuage de gaz neutre est de \unit + {0,1\cdot 10^4}{atomes\per... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +! Missing $ inserted. + + $ +l.68 ... nuage de gaz neutre est de \unit{0,1\cdot + 10^4}{atomes\per\centi\me... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.68 ... de gaz neutre est de \unit{0,1\cdot 10^4} + {atomes\per\centi\metre\cu... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.68 ...tre est de \unit{0,1\cdot 10^4}{atomes\per + \centi\metre\cubed}. Combi... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 ...t de \unit{0,1\cdot 10^4}{atomes\per\centi + \metre\cubed}. Combien cel... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 ...unit{0,1\cdot 10^4}{atomes\per\centi\metre + \cubed}. Combien cela fait... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 ...,1\cdot 10^4}{atomes\per\centi\metre\cubed + }. Combien cela fait-il d'... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 .... Combien cela fait-il d'atomes par \metre + \cubed ? Par \litre ? Rép... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 ...ien cela fait-il d'atomes par \metre\cubed + ? Par \litre ? Réponses ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.68 ...-il d'atomes par \metre\cubed ? Par \litre + ? Réponses : \(10^9\,\te... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.68 ...\metre\cubed ? Par \litre ? Réponses : \( + 10^9\,\text{atomes}\) et \... + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.68 ...d ? Par \litre ? Réponses : \(10^9\,\text + {atomes}\) et \(10^6\,\tex... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no à in font cmr10! +Missing character: There is no © in font cmr10! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.68 ...: \(10^9\,\text{atomes}\) et \(10^6\,\text + {atomes}\). +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment sol undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.69 \begin{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no D in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +! Undefined control sequence. +l.70 Dans \unit + {1}{\metre\cubed}, on trouve \unit{1000}{\deci\metre\cubed... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +! Undefined control sequence. +l.70 Dans \unit{1}{\metre + \cubed}, on trouve \unit{1000}{\deci\metre\cubed... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 Dans \unit{1}{\metre\cubed + }, on trouve \unit{1000}{\deci\metre\cubed... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.70 ...ns \unit{1}{\metre\cubed}, on trouve \unit + {1000}{\deci\metre\cubed} ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.70 ...\metre\cubed}, on trouve \unit{1000}{\deci + \metre\cubed} et \unit{10^... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...\cubed}, on trouve \unit{1000}{\deci\metre + \cubed} et \unit{10^6}{\ce... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...}, on trouve \unit{1000}{\deci\metre\cubed + } et \unit{10^6}{\centi\me... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.70 ...ve \unit{1000}{\deci\metre\cubed} et \unit + {10^6}{\centi\metre\cubed}... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Missing $ inserted. + + $ +l.70 ...unit{1000}{\deci\metre\cubed} et \unit{10^ + 6}{\centi\metre\cubed}. Ai... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.70 ...it{1000}{\deci\metre\cubed} et \unit{10^6} + {\centi\metre\cubed}. Ains... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.70 ...}{\deci\metre\cubed} et \unit{10^6}{\centi + \metre\cubed}. Ainsi, dans... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...i\metre\cubed} et \unit{10^6}{\centi\metre + \cubed}. Ainsi, dans \unit... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...e\cubed} et \unit{10^6}{\centi\metre\cubed + }. Ainsi, dans \unit{1}{\m... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...^6}{\centi\metre\cubed}. Ainsi, dans \unit + {1}{\metre\cubed}, on trou... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...\metre\cubed}. Ainsi, dans \unit{1}{\metre + \cubed}, on trouve un mill... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...\cubed}. Ainsi, dans \unit{1}{\metre\cubed + }, on trouve un million de... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...llion de fois plus d'atomes que dans \unit + {1}{\centi\metre\cubed}. O... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...ois plus d'atomes que dans \unit{1}{\centi + \metre\cubed}. On a donc p... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...us d'atomes que dans \unit{1}{\centi\metre + \cubed}. On a donc par \me... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...tomes que dans \unit{1}{\centi\metre\cubed + }. On a donc par \metre\cu... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...{\centi\metre\cubed}. On a donc par \metre + \cubed : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.70 ...i\metre\cubed}. On a donc par \metre\cubed + : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.71 \[ + nb\,atomes=0,1\cdot 10^4\cdot 10^6=10^9\,\text{atomes}\] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.71 ...atomes=0,1\cdot 10^4\cdot 10^6=10^9\,\text + {atomes}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.71 ...\cdot 10^4\cdot 10^6=10^9\,\text{atomes}\] + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.72 Et par litre, c'est-à-dire par \deci + \metre\cubed : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.72 ...t par litre, c'est-à-dire par \deci\metre + \cubed : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.72 ...litre, c'est-à-dire par \deci\metre\cubed + : +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.73 \[ + nb\,atomes=0,1\cdot 10^4\cdot 10^3=10^6\,\text{atomes}\] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.73 ...atomes=0,1\cdot 10^4\cdot 10^3=10^6\,\text + {atomes}\] +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Bad math environment delimiter. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.73 ...\cdot 10^4\cdot 10^3=10^6\,\text{atomes}\] + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{sol}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.74 \end{sol} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.74 \end{sol} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no à in font cmr10! +Missing character: There is no   in font cmr10! +! Missing } inserted. + + } +l.74 \end{sol} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{ex}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.75 \end{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing } inserted. + + } +l.75 \end{ex} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 68--76 +[] + [] + + +Overfull \hbox (135.3376pt too wide) in paragraph at lines 68--76 +\OMS/cmsy/m/n/10 ^^A\OT1/cmr/m/n/10 10[][]\OML/cmm/m/it/10 :Combiencelafait \OM +S/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (132.07726pt too wide) in paragraph at lines 68--76 +\OML/cmm/m/it/10 ild[]atomespar\OT1/cmr/m/n/10 ?\OML/cmm/m/it/10 Par\OT1/cmr/m/ +n/10 ?\OML/cmm/m/it/10 Rponses \OT1/cmr/m/n/10 : + [] + + +Overfull \hbox (48.02092pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] []$ + [] + + +Overfull \hbox (48.02092pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] []$ + [] + + +Overfull \hbox (343.42133pt too wide) in paragraph at lines 68--76 +[][]\OML/cmm/m/it/10 :Ainsi; dans\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 ; ontrouve +unmilliondefoisplusd[]atomesquedans\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 :Onadonc +par \OT1/cmr/m/n/10 : + [] + + +Overfull \hbox (54.38428pt too wide) in paragraph at lines 68--76 +\OML/cmm/m/it/10 nb atomes \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (17.22223pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (17.26395pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (25.04167pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] = + [] + + +Overfull \hbox (126.68951pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] []\OML/cmm/m/it/10 Etparlitre; c[]est \OMS/cmsy/m/n/10 ^^@ + + [] + + +Overfull \hbox (7.7778pt too wide) in paragraph at lines 68--76 +\OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (38.75763pt too wide) in paragraph at lines 68--76 +\OML/cmm/m/it/10 direpar \OT1/cmr/m/n/10 : + [] + + +Overfull \hbox (54.38428pt too wide) in paragraph at lines 68--76 +\OML/cmm/m/it/10 nb atomes \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (17.22223pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (17.26395pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] \OMS/cmsy/m/n/10 ^^A + [] + + +Overfull \hbox (25.04167pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] = + [] + + +Overfull \hbox (48.02092pt too wide) in paragraph at lines 68--76 +\OT1/cmr/m/n/10 10[] []$ + [] + + +! LaTeX Error: Environment ex undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.77 \begin{ex} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.78 L + a première mesure du rayon de la Terre à été faite à Alexandri... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no   in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no ¨ in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +\@footnotetext ...tins {\reset@font \footnotesize + \interlinepenalty \interfo... +l.78 ...ann, DeBoeck Université, 1999, p. 15,16.} + . La méthode qu'il a util... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\@footnotetext ...}\color@begingroup \@makefntext + {\rule \z@ \footnotesep \i... +l.78 ...ann, DeBoeck Université, 1999, p. 15,16.} + . La méthode qu'il a util... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no à in font cmr10! +Missing character: There is no © in font cmr10! +Missing character: There is no à in font cmr10! +Missing character: There is no ‰ in font cmr10! +Missing character: There is no à in font cmr10! +Missing character: There is no © in font cmr10! + +Overfull \hbox (18.36115pt too wide) in paragraph at lines 78--78 +[][]\OT1/cmr/m/n/10 Voir + [] + + +Overfull \hbox (55.00012pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 ``Mcanique'', + [] + + +Overfull \hbox (11.1389pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 ric + [] + + +Overfull \hbox (17.9167pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 Lin- + [] + + +Overfull \hbox (13.33334pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 de- + [] + + +Overfull \hbox (27.2223pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 mann, + [] + + +Overfull \hbox (15.41667pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 De- + [] + + +Overfull \hbox (26.25006pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 Boeck + [] + + +Overfull \hbox (19.1667pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 Uni- + [] + + +Overfull \hbox (16.69446pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 ver- + [] + + +Overfull \hbox (13.38892pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 sit, + [] + + +Overfull \hbox (22.77785pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 1999, + [] + + +Overfull \hbox (8.33336pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 p. + [] + + +Overfull \hbox (25.55563pt too wide) in paragraph at lines 78--78 +\OT1/cmr/m/n/10 15,16.| + [] + +Missing character: There is no . in font nullfont! 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Undefined control sequence. + ...ference `Erathostene' on page \thepage + \space undefined\on@line . +l.78 ...de la Terre (voir figure \ref{Erathostene} + ). Par ailleurs, il a mesu... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `Erathostene' on page undefined on input line 78. + +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! 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Undefined control sequence. + ...ference `Erathostene' on page \thepage + \space undefined\on@line . +l.78 ...mme le montre le schéma \ref{Erathostene} + , cet angle est l'angle au... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `Erathostene' on page undefined on input line 78. + +Missing character: There is no , in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! 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Undefined control sequence. +l.78 ...e. Connaissant cet angle (\(\alpha = \unit + {7,5}{\degree}\)) et la lo... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.78 ...t cet angle (\(\alpha = \unit{7,5}{\degree + }\)) et la longueur de l'a... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +! Undefined control sequence. +l.78 ...a longueur de l'arc de cercle (\(L = \unit + {5000}{stades}\)), il en d... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no à in font nullfont! +Missing character: There is no © in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.80 S + achant qu'un stade valait environ \unit{160}{\metre} d'aujourd'hui,... + +You're in trouble here. 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Undefined control sequence. +l.80 Sachant qu'un stade valait environ \unit + {160}{\metre} d'aujourd'hui,... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +Missing character: There is no 6 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.80 ...'un stade valait environ \unit{160}{\metre + } d'aujourd'hui, calculez ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.80 ... obtenu par Eratosthène. Réponse : \unit + {6'111,55}{\kilo\metre}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 6 in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no 5 in font nullfont! +! Undefined control sequence. +l.80 ...osthène. Réponse : \unit{6'111,55}{\kilo + \metre}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.80 ...ne. Réponse : \unit{6'111,55}{\kilo\metre + }. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 80--81 +[] + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.82 \begin{figure} + [ht] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.82 \begin{figure}[ + ht] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 82--83 +[] + [] + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.84 \caption + {Le rayon de la Terre par Eratosthène\label{Erathostene}} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.84 \caption{L + e rayon de la Terre par Eratosthène\label{Erathostene}} +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.87 \begin{center} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 87--87 +[] + [] + + +! LaTeX Error: File `Annexe-Exercices/Images/Erathostene.tex' not found. + +Type X to quit or to proceed, +or enter new name. (Default extension: tex) + +Enter file name: +! Emergency stop. + + +l.88 \input{Annexe-Exercices/Images/Erathostene} + ^^M +*** (cannot \read from terminal in nonstop modes) + + +Here is how much of TeX's memory you used: + 22 strings out of 494830 + 332 string characters out of 6176634 + 52245 words of memory out of 5000000 + 3444 multiletter control sequences out of 15000+600000 + 3948 words of font info for 15 fonts, out of 8000000 for 9000 + 36 hyphenation exceptions out of 8191 + 18i,8n,14p,1255b,117s stack positions out of 5000i,500n,10000p,200000b,80000s +No pages of output. diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index efae223..838b917 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -892,7 +892,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{solos} \end{exos} -\begin{exos} +\begin{exos}\label{planinclinesimple} On lâche, à vitesse initiale nulle, une masse m de \unit{3}{\kilo\gram}, sur un plan incliné d'un angle \(\alpha = \unit{20}{\degree}\) sans frottements. Calculez sa vitesse après un temps t de \unit{2}{\second}. Réponse~: \unit{9,72}{\metre\per\second}. \begin{solos} Deux forces agissent ici : la réaction du plan, qui lui est normale (c'est-à-dire perpendiculaire), et le poids de la masse. Comme la réaction du plan n'a aucune composante parallèlement au plan, elle ne peut être responsable de l'accélération de la masse le long de celui-ci. @@ -957,6 +957,76 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco &=3\cdot 9,81\cdot \cos(20)=\unit{27,67}{\newton} \end{align*} + \smallskip + Ensuite, le problème se résout de la même manière que précédemment. + \end{solos} +\end{exos} + +\begin{exos} + Une masse M = \unit{5}{\kilo\gram} glisse sur un plan incliné d'un angle \(\alpha=\unit{30}{\degree}\) par rapport à l'horizontale. Elle est retenue, du côté du haut du plan incliné, par une corde inextensible sans masse passant sur une poulie, puis accrochée à une autre masse m = \unit{3}{\kilo\gram}, pendant librement. + + Calculez l'accélération des masses et la tension dans la corde. Réponses~: \unit{-0,6}{\metre\per\second\squared} et \unit{27,6}{\newton}. + \begin{solos} + Le problème peut paraître complexe du fait de la présence de deux objets distincts se déplaçant selon deux axes différents. Pourtant, le fait que la corde soit inextensible fait de l'ensemble des deux masse et de la corde un système se déplaçant avec la même accélération. De plus, pour autant qu'on considère correctement l'action des forces sur chaque masse, on peut s'imaginer ce système se déplaçant d'un bloc horizontalement. + + \smallskip + Comme on ne connaît pas la tension dans la corde (on ne peut s'imaginer à priori qu'elle correspond au poids de la masse m), le choix du système comprenant les deux masses et la corde s'impose, car ainsi la tension dans la corde, en tant que force intérieure, n'apparaîtra pas dans les équations de Newton. + + \smallskip + Comme déjà dit, on peut considérer le système d'un seul tenant. On va donc imaginer un axe suivant la corde et orienté vers le bas du plan incliné, car la masse M étant plus grande que m, il est évident que le mouvement se fera dans ce sens. Ainsi, le signe de l'accélération sera positif. + + \smallskip + Reste à considérer les forces extérieures. Elles sont au nombre de quatre~: + \begin{enumerate} + \item le poids P de la masse M, + \item la réaction R du plan incliné, + \item celui p de la masse et + \item la force exercée sur la corde par la poulie. + \end{enumerate} + + La dernière est toujours perpendiculaire à la corde et ne participe donc pas au mouvement des masses. La troisième est toujours parallèle à la corde. La seconde est toujours perpendiculaire au plan incliné et ne participe elle aussi pas au mouvement. La première à une composante perpendiculaire au plan incliné et ne participe pas au mouvement, mais aussi une composante parallèle à ce plan et doit être considérée. + Avec l'angle \(\alpha\) défini, on peut reprendre le raisonnement évoqué au problème \ref{planinclinesimple}, évoquant le triangle rectangle formé par le poids de la masse M et se composantes et affirmant que l'angle \(\alpha\) est celui entre le poids et sa composante perpendiculaire au plan, pour écrire que la composante parallèle au plan vaut~: + \[P_{//}=M\cdot g\cdot \sin(\alpha)\] + + \smallskip + À partir de là, on peut écrire l'équation du mouvement du système (des deux masse et de la corde)~: + \[\sum F^{ext}=M\cdot g\cdot \sin(\alpha)-m\cdot g=(M+m)\cdot a\] + et calculer l'accélération~: + \begin{align*} + a&=\frac{M\cdot g\cdot \sin(\alpha)-m\cdot g}{M+m}\\ + &=\frac{5\cdot 9,81\cdot \sin(30)-3\cdot 9,81}{5+3}\\ + &=\unit{-0,6}{\metre\per\second\squared} + \end{align*} + Le signe négatif signifie que la masse M monte vers le haut du plan incliné. + + \medskip + Pour calculer la tension dans la corde, il est indispensable de changer de système pour la faire apparaître en tant que force extérieure dans l'équation de Newton. + + Trois éléments peuvent prétendre servir de système. + + La corde en premier lieu. Si on la considère seule, à l'une de ses extrémités la masse m exerce sur elle une force \(T_m\) et à l'autre la masse M exerce une tension à priori différente \(T_M\). La force exercée par la poulie reste perpendiculaire et ne contribue pas au mouvement. On peut donc écrire~: + \[T_M-T_m=\mu\cdot a\] + où \(\mu\) est la masse de la corde. Or, si cette masse est nulle, indépendamment de l'accélération, le deux tensions sont égales. Cela est évidemment valable pour tous les éléments de la corde dont on dira donc qu'elle exerce une force \(T\) à déterminer. + + Le système corde ne permet donc pas de la trouver. + + Restent les deux masses. Pour la masse M interviendra dans l'équation du mouvement un sinus qu'on va éviter en considérant m. + + Sur m, avec un axe pointant toujours vers le haut, l'équation de Newton devient très simple~: + \begin{align*} + \sum F{ext}&=T-m\cdot g=m\cdot a\;\Rightarrow\\ + T&=m\cdot (a+g)=3\cdot (-0,6+9,81)\\ + &=\unit{27,6}{\newton} + \end{align*} + + \medskip + Pour vérifier ce résultat, choisissons l'autre masse (M) pour système. On écrira alors~: + \begin{align*} + \sum F^{ext}&=-T+M\cdot g\cdot \sin(\alpha)=M\cdot a\;\Rightarrow\\ + T&=M\cdot g\cdot \sin(\alpha)-M\cdot a\\ + &=5\cdot 9,81\cdot \sin(30)-5\cdot (-0,6)\\ + &=\unit{27,6}{\newton} + \end{align*} \end{solos} \end{exos} diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index e274016..838b917 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -892,7 +892,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{solos} \end{exos} -\begin{exos} +\begin{exos}\label{planinclinesimple} On lâche, à vitesse initiale nulle, une masse m de \unit{3}{\kilo\gram}, sur un plan incliné d'un angle \(\alpha = \unit{20}{\degree}\) sans frottements. Calculez sa vitesse après un temps t de \unit{2}{\second}. Réponse~: \unit{9,72}{\metre\per\second}. \begin{solos} Deux forces agissent ici : la réaction du plan, qui lui est normale (c'est-à-dire perpendiculaire), et le poids de la masse. Comme la réaction du plan n'a aucune composante parallèlement au plan, elle ne peut être responsable de l'accélération de la masse le long de celui-ci. @@ -934,29 +934,99 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \smallskip Si on considére l'angle \(\alpha\), en s'imaginant le plan incliné horizontal, on comprends qu'il se reporte entre le vecteur poids \(\overleftarrow{P}\) et sa compostante selon y \(P_y\). - Avec le triangle rectangle formé par le poids et ses composantes et un peu de trigonométrie, on peut en déduire : + Avec le triangle rectangle formé par le poids et ses composantes et un peu de trigonométrie, on peut en déduire~: \begin{align*} P_x &= P\cdot \sin(\alpha)\\ P_y &= P\cdot \cos(\alpha) \end{align*} - Comme par ailleurs on sait que \(P=m\cdot g\), on peut réécrire les équations de Newton sur les axes comme : + Comme par ailleurs on sait que \(P=m\cdot g\), on peut réécrire les équations de Newton sur les axes comme~: \begin{align*} \sum F^{ext}_x&=m\cdot g\cdot \sin(\alpha)=m\cdot a_x\\ - \sum F^{ext}_y&=R-m\cdot g\cdot \cos(\alpha)=m\cdot a_y=0} + \sum F^{ext}_y&=R-m\cdot g\cdot \cos(\alpha)=m\cdot a_y=0 \end{align*} - La première de ces équations permet de trouver l'accélération du bloc selon le plan incliné : + La première de ces équations permet de trouver l'accélération du bloc selon le plan incliné~: \begin{align*} a=a_x&=g\cdot \sin(\alpha)\\ &=9,81\cdot\sin(20)=\unit{3,36}{\metre\per\second\squared} \end{align*} \smallskip - Mais une information supplémentaire nous est donnée par la seconde équation, c'est la valeur de la réaction R au plan : + Mais une information supplémentaire nous est donnée par la seconde équation, c'est la valeur de la réaction R au plan~: \begin{align*} R&=m\cdot g\cdot \cos(\alpha)\\ &=3\cdot 9,81\cdot \cos(20)=\unit{27,67}{\newton} \end{align*} + \smallskip + Ensuite, le problème se résout de la même manière que précédemment. + \end{solos} +\end{exos} + +\begin{exos} + Une masse M = \unit{5}{\kilo\gram} glisse sur un plan incliné d'un angle \(\alpha=\unit{30}{\degree}\) par rapport à l'horizontale. Elle est retenue, du côté du haut du plan incliné, par une corde inextensible sans masse passant sur une poulie, puis accrochée à une autre masse m = \unit{3}{\kilo\gram}, pendant librement. + + Calculez l'accélération des masses et la tension dans la corde. Réponses~: \unit{-0,6}{\metre\per\second\squared} et \unit{27,6}{\newton}. + \begin{solos} + Le problème peut paraître complexe du fait de la présence de deux objets distincts se déplaçant selon deux axes différents. Pourtant, le fait que la corde soit inextensible fait de l'ensemble des deux masse et de la corde un système se déplaçant avec la même accélération. De plus, pour autant qu'on considère correctement l'action des forces sur chaque masse, on peut s'imaginer ce système se déplaçant d'un bloc horizontalement. + + \smallskip + Comme on ne connaît pas la tension dans la corde (on ne peut s'imaginer à priori qu'elle correspond au poids de la masse m), le choix du système comprenant les deux masses et la corde s'impose, car ainsi la tension dans la corde, en tant que force intérieure, n'apparaîtra pas dans les équations de Newton. + + \smallskip + Comme déjà dit, on peut considérer le système d'un seul tenant. On va donc imaginer un axe suivant la corde et orienté vers le bas du plan incliné, car la masse M étant plus grande que m, il est évident que le mouvement se fera dans ce sens. Ainsi, le signe de l'accélération sera positif. + + \smallskip + Reste à considérer les forces extérieures. Elles sont au nombre de quatre~: + \begin{enumerate} + \item le poids P de la masse M, + \item la réaction R du plan incliné, + \item celui p de la masse et + \item la force exercée sur la corde par la poulie. + \end{enumerate} + + La dernière est toujours perpendiculaire à la corde et ne participe donc pas au mouvement des masses. La troisième est toujours parallèle à la corde. La seconde est toujours perpendiculaire au plan incliné et ne participe elle aussi pas au mouvement. La première à une composante perpendiculaire au plan incliné et ne participe pas au mouvement, mais aussi une composante parallèle à ce plan et doit être considérée. + Avec l'angle \(\alpha\) défini, on peut reprendre le raisonnement évoqué au problème \ref{planinclinesimple}, évoquant le triangle rectangle formé par le poids de la masse M et se composantes et affirmant que l'angle \(\alpha\) est celui entre le poids et sa composante perpendiculaire au plan, pour écrire que la composante parallèle au plan vaut~: + \[P_{//}=M\cdot g\cdot \sin(\alpha)\] + + \smallskip + À partir de là, on peut écrire l'équation du mouvement du système (des deux masse et de la corde)~: + \[\sum F^{ext}=M\cdot g\cdot \sin(\alpha)-m\cdot g=(M+m)\cdot a\] + et calculer l'accélération~: + \begin{align*} + a&=\frac{M\cdot g\cdot \sin(\alpha)-m\cdot g}{M+m}\\ + &=\frac{5\cdot 9,81\cdot \sin(30)-3\cdot 9,81}{5+3}\\ + &=\unit{-0,6}{\metre\per\second\squared} + \end{align*} + Le signe négatif signifie que la masse M monte vers le haut du plan incliné. + + \medskip + Pour calculer la tension dans la corde, il est indispensable de changer de système pour la faire apparaître en tant que force extérieure dans l'équation de Newton. + + Trois éléments peuvent prétendre servir de système. + + La corde en premier lieu. Si on la considère seule, à l'une de ses extrémités la masse m exerce sur elle une force \(T_m\) et à l'autre la masse M exerce une tension à priori différente \(T_M\). La force exercée par la poulie reste perpendiculaire et ne contribue pas au mouvement. On peut donc écrire~: + \[T_M-T_m=\mu\cdot a\] + où \(\mu\) est la masse de la corde. Or, si cette masse est nulle, indépendamment de l'accélération, le deux tensions sont égales. Cela est évidemment valable pour tous les éléments de la corde dont on dira donc qu'elle exerce une force \(T\) à déterminer. + + Le système corde ne permet donc pas de la trouver. + + Restent les deux masses. Pour la masse M interviendra dans l'équation du mouvement un sinus qu'on va éviter en considérant m. + + Sur m, avec un axe pointant toujours vers le haut, l'équation de Newton devient très simple~: + \begin{align*} + \sum F{ext}&=T-m\cdot g=m\cdot a\;\Rightarrow\\ + T&=m\cdot (a+g)=3\cdot (-0,6+9,81)\\ + &=\unit{27,6}{\newton} + \end{align*} + + \medskip + Pour vérifier ce résultat, choisissons l'autre masse (M) pour système. On écrira alors~: + \begin{align*} + \sum F^{ext}&=-T+M\cdot g\cdot \sin(\alpha)=M\cdot a\;\Rightarrow\\ + T&=M\cdot g\cdot \sin(\alpha)-M\cdot a\\ + &=5\cdot 9,81\cdot \sin(30)-5\cdot (-0,6)\\ + &=\unit{27,6}{\newton} + \end{align*} \end{solos} \end{exos} diff --git a/Annexe-Exercices/Images/incline.svg b/Annexe-Exercices/Images/incline.svg index 258304a..9868e4d 100644 --- a/Annexe-Exercices/Images/incline.svg +++ b/Annexe-Exercices/Images/incline.svg @@ -111,9 +111,9 @@ borderopacity="1.0" inkscape:pageopacity="0.0" inkscape:pageshadow="2" - inkscape:zoom="2.9083205" - inkscape:cx="298.60998" - inkscape:cy="874.98007" + inkscape:zoom="3.4571089" + inkscape:cx="289.95818" + inkscape:cy="885.15592" inkscape:document-units="mm" inkscape:current-layer="layer1" showgrid="false" @@ -140,10 +140,10 @@ id="layer1"> + sodipodi:nodetypes="ccc" /> axe x + x="78.11998" + y="68.607101" + style="font-size:4.23333311px;fill:#000000;fill-opacity:1;stroke-width:0.26458332">axe x - R P Px Py axe y + 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Pourtant, le fait que la corde soit inextensible fait de l'ensemble des deux masse et de la corde un système se déplaçant avec la même accélération. De plus, pour autant qu'on considère correctement l'action des forces sur chaque masse, on peut s'imaginer ce système se déplaçant d'un bloc horizontalement. + + \smallskip + Comme on ne connaît pas la tension dans la corde (on ne peut s'imaginer à priori qu'elle correspond au poids de la masse m), le choix du système comprenant les deux masses et la corde s'impose, car ainsi la tension dans la corde, en tant que force intérieure, n'apparaîtra pas dans les équations de Newton. + + \smallskip + Comme déjà dit, on peut considérer le système d'un seul tenant. On va donc imaginer un axe suivant la corde et orienté vers le bas du plan incliné, car la masse M étant plus grande que m, il est évident que le mouvement se fera dans ce sens. Ainsi, le signe de l'accélération sera positif. + + \smallskip + Reste à considérer les forces extérieures. Elles sont au nombre de quatre~: + \begin{enumerate} + \item le poids P de la masse M, + \item la réaction R du plan incliné, + \item celui p de la masse et + \item la force exercée sur la corde par la poulie. + \end{enumerate} + + La dernière est toujours perpendiculaire à la corde et ne participe donc pas au mouvement des masses. La troisième est toujours parallèle à la corde. La seconde est toujours perpendiculaire au plan incliné et ne participe elle aussi pas au mouvement. La première à une composante perpendiculaire au plan incliné et ne participe pas au mouvement, mais aussi une composante parallèle à ce plan et doit être considérée. + Avec l'angle \(\alpha\) défini, on peut reprendre le raisonnement évoqué au problème \ref{planinclinesimple}, évoquant le triangle rectangle formé par le poids de la masse M et se composantes et affirmant que l'angle \(\alpha\) est celui entre le poids et sa composante perpendiculaire au plan, pour écrire que la composante parallèle au plan vaut~: + \[P_{//}=M\cdot g\cdot \sin(\alpha)\] + + \smallskip + À partir de là, on peut écrire l'équation du mouvement du système (des deux masse et de la corde)~: + \[\sum F^{ext}=M\cdot g\cdot \sin(\alpha)-m\cdot g=(M+m)\cdot a\] + et calculer l'accélération~: + \begin{align*} + a&=\frac{M\cdot g\cdot \sin(\alpha)-m\cdot g}{M+m}\\ + &=\frac{5\cdot 9,81\cdot \sin(30)-3\cdot 9,81}{5+3}\\ + &=\unit{-0,6}{\metre\per\second\squared} + \end{align*} + Le signe négatif signifie que la masse M monte vers le haut du plan incliné. + + \medskip + Pour calculer la tension dans la corde, il est indispensable de changer de système pour la faire apparaître en tant que force extérieure dans l'équation de Newton. + + Trois éléments peuvent prétendre servir de système. + + La corde en premier lieu. Si on la considère seule, à l'une de ses extrémités la masse m exerce sur elle une force \(T_m\) et à l'autre la masse M exerce une tension à priori différente \(T_M\). La force exercée par la poulie reste perpendiculaire et ne contribue pas au mouvement. On peut donc écrire~: + \[T_M-T_m=\mu\cdot a\] + où \(\mu\) est la masse de la corde. Or, si cette masse est nulle, indépendamment de l'accélération, le deux tensions sont égales. Cela est évidemment valable pour tous les éléments de la corde dont on dira donc qu'elle exerce une force \(T\) à déterminer. + + Le système corde ne permet donc pas de la trouver. + + Restent les deux masses. Pour la masse M interviendra dans l'équation du mouvement un sinus qu'on va éviter en considérant m. + + Sur m, avec un axe pointant toujours vers le haut, l'équation de Newton devient très simple~: + \begin{align*} + \sum F{ext}&=T-m\cdot g=m\cdot a\;\Rightarrow\\ + T&=m\cdot (a+g)=3\cdot (-0,6+9,81)\\ + &=\unit{27,6}{\newton} + \end{align*} + + \medskip + Pour vérifier ce résultat, choisissons l'autre masse (M) pour système. On écrira alors~: + \begin{align*} + \sum F^{ext}&=-T+M\cdot g\cdot \sin(\alpha)=M\cdot a\;\Rightarrow\\ + T&=M\cdot g\cdot \sin(\alpha)-M\cdot a\\ + &=5\cdot 9,81\cdot \sin(30)-5\cdot (-0,6)\\ + &=\unit{27,6}{\newton} + \end{align*} + +\end{Solution OS} +\begin{Solution OS}{4} Un corrigé de test. \end{Solution OS}