Isosceles Triangles: Angle a Exceeds Angle d
A proof answering "the adversary" and citing the eighteenth proposition
The demonstration continues from the facing page: a triangle divided into three unequal parts carries the note that "a and b are equal," a claim attributed to "the adversary" and countered by an appeal "by the eighteenth." Below, two isosceles triangles are compared, one with apex a and sides 4, 4 over base 5, the other with apex d and sides 4, 4 over base 4, to conclude that "angle a is larger than d." Pen-strokes tie these figures back to the triangles on the facing folio. The leaf is numbered 26 at the top corner.
On this page
The adversary's claim that a and b are equal
A triangle is divided into three smaller, non-similar triangles with an outer vertex b and an inner vertex a. The note records the objection "a and b are equal, said by the adversary."
Rebuttal by the eighteenth proposition
The objection is answered by the citation "by the eighteenth," pointing to an established proposition used to settle the inequality of the angles.
Two isosceles triangles compared
Two isosceles triangles are lettered at their apices a and d. All four upright sides are marked 4, while the bases are marked 5 and 4 respectively, giving the conclusion "angle a is larger than d."