When we turn to the other field of thought with which the name of Thales is associated--namely, geometry--we again find evidence of the Oriental influence. The science of geometry, Herodotus assures us, was invented in Egypt. It was there an eminently practical science, being applied, as the name literally suggests, to the measurement of the earth's surface. Herodotus tells us that the Egyptians were obliged to cultivate the science because the periodical inundations washed away the boundary-lines between their farms. The primitive geometer, then, was a surveyor. The Egyptian records, as now revealed to us, show that the science had not been carried far in the land of its birth. The Egyptian geometer was able to measure irregular pieces of land only approximately. He never fully grasped the idea of the perpendicular as the true index of measurement for the triangle, but based his calculations upon measurements of the actual side of that figure. Nevertheless, he had learned to square the circle with a close approximation to the truth, and, in general, his measurement sufficed for all his practical needs. Just how much of the geometrical knowledge which added to the fame of Thales was borrowed directly from the Egyptians, and how much he actually created we cannot be sure. Nor is the question raised in disparagement of his genius. Receptivity is the first prerequisite to progressive thinking, and that Thales reached out after and imbibed portions of Oriental wisdom argues in itself for the creative character of his genius. Whether borrower of originator, however, Thales is credited with the expression of the following geometrical truths: 1. That the circle is bisected by its diameter. 2. That the angles at the base of an isosceles triangle are equal. 3. That when two straight lines cut each other the vertical opposite angles are equal. 4. That the angle in a semicircle is a right angle. 5. That one side and one acute angle of a right-angle triangle determine the other sides of the triangle.