

THE SQUARING OF THE CIRCLE. 123 



tion of the circumference. The Babylonian mathematicians had 

 discovered, that if the radius of a circle be successively inscribed 

 as a chord within its circumference, after the sixth inscription we 

 arrive at the point from which we set out, and they concluded from 

 this that the circumference of a circle must be a little larger than a 

 line which is six times as long as the radius, that is three times as 

 long as the diameter. A trace of this Babylonian method of com- 

 putation may even be found in the Bible ; for in i Kings vii. 23, 

 and 2 Chron. iv. 2, the great laver is described, which under the 

 name of the "molten sea" constituted an ornament of the temple 

 of Solomon ; and it is said of this vessel that it measured ten cubits 

 from brim to brim, and thirty cubits round about. The number 3 

 as the ratio of the circumference to the diameter is still more plainly 

 given in the Talmud, where we read that "that which measures 

 three lengths in circumference is one length across." 



With regard to the earlier Greek mathematicians as Thales 

 and Pythagoras we know that they acquired their elementary 

 mathematical knowledge in Egypt. But nothing has been handed 

 down to us which shows that they knew of the old Egyptian quad 

 rature, or that they dealt with the problem at all. But tradition 

 says, that, subsequently, the teacher of Euripides and Pericles, the 

 great philosopher and mathematician Anaxagoras, whom Plato so 

 highly praised, "drew the quadrature of the circle" in prison, in the 

 year 434 B. C. This is the account of Plutarch in the seventeenth 

 chapter of his work De Exilio. The method is not told us in which 

 Anaxagoras is supposed to have solved the problem, and it is not 

 said whether, knowingly or unknowingly, he gave an approximate 

 solution after the manner of Ahmes. But at any rate, to Anaxago- 

 ras belongs the merit of having called attention to a problem that 

 was to bear rich fruit by inciting Grecian scholars to busy them- 

 selves with geometry, and thus more and more to advance that 

 science. 



Again, it is reported that the mathematician Hippias of Elis 

 invented a curved line that could be made to serve a double pur- 

 pose : first, to trisect an angle, and second to square the circle. 

 This curved line is the Terpaywvt^ovo-a so often mentioned by the 



