theorems of Euclid

This is a list of theorems contained in Euclid’s The Elements.At present, the list is incomplete, but as time goes on, more theorems willsystematically be added until it is complete. Note that boththeorems and constructions are combined together in the elements; for a listingof the constructions, please see http://planetmath.org/node/9531their entry.

• I 4 SAS theorem

• I 5 (the pons asinorum) The base angles of anisosceles triangle are equal to each other. Moreover, the angles underthe bases are also equal.

• I 6 If two angles of a triangle are equal, then that triangle isisosceles. (converse of the preceding proposition)

• I 7 Given a line segment, it is not possible to constructupon it two distinct triangles which lie upon the same side of the segmentwhose remaining sides are equal to each other pairwise.

• I 8 SSS theorem