
Re: Most theorems in Euclidean geometry are IFF theorems.
Posted:
Sep 5, 2013 12:10 PM


theorems about skew tetragona are theorems about tetrahedra; teh emphaisis is different; I think it is book 7 that is most of the numbertheory in Euclid; Langlands said that it was unfinished
thus quoth: different is Euclidean Geometry from e.g. number theory?
the development of geometry it was known that parallelograms have a certain property but later it was discovered that, more generally, quadrilaterals have that property. The second of the two results would have been what made its way into Euclid's Elements (assuming that it was known by then) but the second result (with a weaker premise) would have greater likelihood of having a true converse.

