\documentclass{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{amssymb} %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Version=5.00.0.2570} %TCIDATA{} %TCIDATA{Created=Thursday, February 21, 2002 14:53:39} %TCIDATA{LastRevised=Monday, October 03, 2005 10:03:19} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %F=36,\PARA{038
Scientific Notebook: On Line Mathematics\dotfill \thepage} %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \begin{document} \section{Line\'{a}rne \'{u}tvary v $\mathbf{E}_{3}$} \subsection{D\^{o}kaz vety} Uhol priamky $p$ s rovinou $\gamma $ je definovan\'{y} ako uhol priamky $p$ s jej pravouhl\'{y}m priemetom do roviny $\gamma $. Priamka $q\equiv A% \overline{c}$, ktor\'{a} je kolm\'{a} na rovinu $\gamma $, zviera s $p$ uhol $\psi =\dfrac{\pi }{2}-\varphi $. Preto \[ \sin \varphi =\sin \left( \frac{\pi }{2}-\psi \right) =\cos \psi =\frac{% \left\vert \overline{u}.\overline{c}\right\vert }{\left\Vert \overline{u}% \right\Vert \left\Vert \overline{c}\right\Vert }.\blacksquare \] \begin{center} \begin{tabular}{|c|} \hline \textbf{% %TCIMACRO{\hyperref{Sp\"{a}\v{t}}{}{}{A63.tex#8}}% %BeginExpansion \msihyperref{Sp\"{a}\v{t}}{}{}{A63.tex#8}% %EndExpansion } \\ \hline \end{tabular} \end{center} \end{document}