Euclid's Elements Book 3 - Proposition 35

Cross product rule for two intersecting lines in a circle

[@derekpoon5308]

Using preposition 21, book 3 (angle in same segment), it can be proved that triangle ABE ~ triangle DCE. The result is followed from proportionality.

[@arielhernandez1638]

This was a tedious proof. Wonderful twist at the end there. Thank you.

[@darw1nev0lved]

Oh man, that was so helpful. I'd been banging my head against the slightly embarrassing wall of 'where are the rectangles' which neither Euclid nor any other commentator till you, had made clear. Thank you again.

[@liznagy625]

Thank you! You are a life saver!!!

[@laurentd2773]

Merci pour cette démonstration si claire qu'on peut la comprendre à l'aide des figures et des égalités algébriques.

[@flyingjudgement]

Your explaintions are great, Thank you!

[@brendanward2991]

Pythagoras.