Euclid book 3 proposition 32 support

Euclids elements book i, proposition 1 trim a line to be the same as another line. The first three books of euclids elements of geometry from the text of dr. In this paper i offer some reflections on the thirtysecond proposition of book i of euclids elements, the assertion that the three interior angles of a triangle are. Euclids elements, book iii, proposition 32 proposition 32 if a straight line touches a circle, and from the point of contact there is drawn across, in the circle, a straight line cutting the circle, then the angles which it makes with the tangent equal the angles in the alternate segments of the circle. The opposite segment contains the same angle as the angle between a line touching the circle, and the line defining the segment. Proposition 32 in any triangle, if one of the sides is produced, then the exterior angle equals the sum of the two interior and opposite angles, and the sum of the three interior angles of the triangle equals two right angles. Axiomness isnt an intrinsic quality of a statement, so some. Built on proposition 2, which in turn is built on proposition 1. If a straight line touches a circle, and from the point of contact there is drawn across, in the circle, a straight line cutting the circle, then the angles. The national science foundation provided support for entering this text. It is a collection of definitions, postulates, propositions theorems and.

Avigads work has been partially supported by nsf grant. Guide now it is clear that the purpose of proposition 2 is to effect the construction in this proposition. The next two propositions depend on the fundamental theorems of parallel lines. In the first proposition, proposition 1, book i, euclid shows that, using only the. Leon and theudius also wrote versions before euclid fl. Remarks on euclids elements i,32 and the parallel postulate. Let abcbe a triangle, and let one side of it bcbe produced to d. The same theory can be presented in many different forms.