Page:First six books of the elements of Euclid 1847 Byrne.djvu/58

24 F two triangles have two sides of the one respectively equal to two sides of the other ( to and  to ), and if one of the angles  contained by the equal sides be greater than the other, the side  which is opposite to the greater angle is greater than the side  which is opposite to the less angle.



Make =  (pr. 23.),

and =   (pr. 3.),

draw and. Because =  (ax. I. hyp. const.)

∴ =  (pr. 5.)

but <

and ∴ < ,

∴ >  (pr. 19.)

but =  (pr. 4.)

∴ >.

Q. E. D.