4 1 Greek mathematics 1 1) Mathematics (1) Mathematics Mathematics <--- Mathematica (Greek word): any subject of instruction or study Plato s inscription over the door of his academy Let no man ignorant of geometry enter here
5 1 Greek mathematics 1 1) Mathematics (1) Aristotle (Metahpysics) When all the inventions had been discovered, the sciences which are not concerned with the pleasures and necessities of life were developed first in the lands where men began to have leisure. This is the reason why mathematics originated in Egypt, for there the priestly class was able to enjoy leisure.
6 1 Greek mathematics 1 2) Demonstrative Geometry--Thales (2) Abstract Thought - An angle inscribed in a semicircle is a right angle. - A circle is bisected by its diameter. - The base angles of an isosceles triangle are equal. - If two straight lines intersect, the opposite angles are equal.
7 1 Greek mathematics 1 2) Demonstrative Geometry--Thales (2) Abstract Thought - The sides of similar triangles are proportional. - Two triangles are congruent if they have one side and two adjacent angles, respectively, equal.
8 1 Greek Mathematics 1 3) Measurement using geometry (2) Similar triangle h/h =s/s
9 1 Greek Mathematics 1 4) Isosceles (2) Angles of Isosceles triangle Pons asinorum (bridge of asses)
10 1 Greek Mathematics 1 4) Isosceles (2) Angles of Isosceles triangle Let ABC be an isosceles triangle with AB =AC. Consider the triangles ABC and ACB, where ACB is co nsidered a second triangle with vertices A, C and B co rresponding respectively to A, B and C in the original triangle. Angle A is equal to itself, AB=AC and AC=AB, so by si de-angle-side, triangles ABC and ACB are congruent. In particular angle B = angle C.