% Math 370 hw1
%
\documentclass{article}
\pagestyle{empty}

\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{graphicx}

\newcommand{\coursehome}
{http://www.cs.umb.edu/~eb/370}

\title{History of Mathematics \\
Homework 1
}
\author{Ethan Bolker}

\begin{document}

\maketitle

\section*{Preliminaries}

Due Thursday

\begin{itemize}

\item Send me email (to \verb!eb at cs dot umb dot edu!) from the
  email   address you want me to use for the class mailing list. 

\item Complete the questionnaire at
\url{\coursehome/questionnaire.pdf} by editing and compiling the
\LaTeX{} source at \url{\coursehome/questionnaire.tex}. Turn in hard
copy of the pdf and the \LaTeX{} source.

Answering the questions is not hard. But I'm asking more than that. To
answer them in the form I require you'll have to begin to learn \TeX{}
-- in particular, \LaTeX. That typesetting system is the best in the
world for mathematics (and lots of other documents too) and well worth
the (sometimes substantial) effort it may take you to learn it. If you
go on in mathematics it may well be the most valuable thing you learn
in this course.

To use \TeX{} you need two kinds of software on your computer. The
first is a \TeX{} \emph{distribution}. You can find links to download
one at \url{\coursehome/tex}, where I have listed some \TeX{} resources.

The second is an editor. You can write \TeX{} with any word
processor. I use \verb!emacs!. Even Microsoft Word or Notepad would
do. But I recommend something like TexStudio
(\url{http://http://texstudio.sourceforge.net/}), which is a complete
environment for writing, compiling and previewing \TeX{} documents.

Once you get started you'll find it fun (I hope). You can ask me
\TeX{} questions, or ask them at
\url{http://tex.stackexchange.com}.

\end{itemize}

\newpage

Due next Tuesday. You'll have to read a fair amount of Euclid to do
it. There's some in the book on pages 20-23 and lots more in the links
at \url{\coursehome/euclid}.

\section*{Exercises}

\begin{enumerate}

\item Prove that in the Sacchieri quadrilateral
\footnote{Image edited from wikipedia}
the angles at $D$ and $C$ are equal. 
(This is Exercise 1.3 in the text.)
\begin{center}
\includegraphics[width=0.6\textwidth]{sacchieri} % TeX will find the png
\end{center}

Write your proof in \emph{Euclid's style}, with explicit references to
the Definitions, Postulates, Common Notions and Propositions that
justify each step. So your proof might begin this way:

Let $ABCD$ be a quadrilateral figure having right-angles at $A$ and
$B$ with equal sides $AD$ and $BC$. I say that the angles at $D$ and
$C$ are equal. 
\footnote{
Euclid uses ``I say that'' where we might write ``I must prove that''.
}

Draw the straight lines $AC$ and $BD$ [Postulate 1].
\footnote{This is a hint about how you might begin. Use Euclid's
  Proposition 4 to   prove that triangles $DAB$ and $CBA$ are equal
  (we would call them   congruent).
}
\ldots

\item Prove that with the parallel postulate, $C$ and $D$ in
  Sacchieri's quadrilateral are right angles. This is Exercise 1.4 in
  the text. The hint there suggests using Proposition 27.

\end{enumerate}
\end{document}
