Euclid's "Elements" - Book 1, Proposition 22

/ mathoma
Heath's translation of Euclid's "Elements"
www.perseus.tufts.edu/hopper/t...
This series is part of a larger project, part of which covers geometry

[@rdbury507]

As with Prop. 1, Euclid assumes there will be a point of intersection, and that if there is a point of intersection that it will not be on the line DE. In fact if the triangle inequality does not hold for A, B and C then this won't be the case. It's a bad sign when the proof does not appear to use all the assumptions, but may be false if not all assumptions are used. By invoking the principle of continuity, one only has to show that F is inside DKL and H is outside DKL, this is straightforward but it does require the using the unused assumptions.