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\title{\Huge Dependency Graph of Propositions in Euclid's Elements}
\author{\Huge Thomson Nguyen}
\date{\Huge \today}
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\Huge This is a dependency graph of propositions from the first book of Euclid's Elements. We say that a proposition $A$ depends on $B$ iff proposition $B$ is necessary in the proof of proposition $A$. In the dependency graph below, this will be denoted by an arrow starting at $A$ and pointing at $B$.\\ 

Figure 1 is a dependency graph of all propositions in the first book. Figure 2 is a dependency graph of all propositions that state a relation between two objects, while Figure 3 is a dependency graph of all propositions that state the existance of an unmarked straightedge and compass construction of something.\\

The dependencies were gratfully extracted from Richard Fitzpatrick's edition of Euclid's \textit{Elements}. The graph itself was written in \texttt{DOT} and converted to pslatex with \texttt{dot2tex}. The motivation for this graph was from Mariusz Wodzicki's Spring 2007 History of Mathematics course at the University of California, Berkeley. Corrections and comments are always appreciated at \texttt{thomson@ocf.berkeley.edu}.


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