Euclid: Proposition 22

Out of three straight lines that are correlating to three straight lines, construct a triangle in which two straight lines, taken in conjunction are greater than the remaining one.

I. Construct straight line DE infinite in one way toward E.

II. Using proposition I.III, let C, A, B the placement, at extermities of the straight lines DF, FG, GH.

III. Using postulate III [to describe a circle with centre and distance] let DKL and KLH at center F, and at center G that accord to the circles.

IV. FD = FK, KF = A, GH = GK, KG= C, FG = B

V. Therefore, the three lines C, A, B a triangle in which two sides together are greater than the third. [I.20]

Q.E.F.

Leave a comment