Elements I: Proposition 4
- Ryan Hirst
(Under construction.) Euclid, The Elements, Book I Proposition IV: If two sides of two triangles are equal, respectively, and the angles contained by the equal sides are equal, the remaining sides and angles are equal. (The triangles are congruent)
To complete the proof, place DE at AB. F will coincide with C, and the triangles are identical. The construction protocol is a little rigid for clear visualization of the problem. If/when I build some transparency/masking tools I'll revisit this proposition. The segment sticking out of A's head are for fun. This is on the right track, though. In my copy of the Elements, T.L. Heath says a lot of silly things about Proposition 4. There is straightforward way to answer the question, and that way happens to be superposition. Trying the same proof with, say, Angle -Angle-Angle will fail. It will fail for any set of rules insufficient to obtain congruence.