A HISTORY OF SCIENCE 



knowledge which added to the fame of Thales was bor- 

 rowed directly from the Egyptians, and how much he 

 actually created we cannot be sure. Nor is the ques- 

 tion raised in disparagement of his genius. Recep- 

 tivity is the first prerequisite to progressive thinking, 

 and that Thales reached out after and imbibed por- 

 tions of Oriental wisdom argues in itself for the crea- 

 tive character of his genius. Whether borrower or 

 originator, however, Thales is credited with the ex- 

 pression 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 tri- 

 angle determine the other sides of the triangle. 



It was by the application of the last of these princi- 

 ples that Thales is said to have performed the really 

 notable feat of measuring the distance of a ship from 

 the shore, his method being precisely the same in prin- 

 ciple as that by which the guns are sighted on a modern 

 man-of-war. Another practical demonstration which 

 Thales was credited with making, and to which also his 

 geometrical studies led him, was the measurement of 

 any tall object, such as a pyramid or building or tree, 

 by means of its shadow. The method, though simple 

 enough, was ingenious. It consisted merely in ob- 

 serving the moment of the day when a perpendicular 

 stick casts a shadow equal to its own length. Ob- 

 viously the tree or monument would also cast a shadow 



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