NEWTON. 183 



erected to the memory of Newton in Westminster Abbey, the Campo 

 Santo of England. The monument is inscribed with a Latin epitaph, 

 of which the translation runs thus : "Here lies Sir Isaac Newton, knight, 

 who by the almost supernatura 1 powers of his mind first demonstrated 

 the motions and figures of the planets, the paths of the comets, and 

 the tides of the ocean. He diligently investigated the different refran- 

 gibilities of the rays of light, and the properties of the colours to which 

 they give rise. An assiduous, sagacious, and faithful interpreter of 

 nature, antiquity, and Holy Scripture, he asserted in his philosophy 

 the majesty of God. and exhibited in his conduct the simplicity of the 

 Gospel. Let mortals rejoice that there has existed such and so great 

 an ornament of human nature. Born 25th. December, 1642; died 

 2oth March, 1727." 



We have already referred to the attraction which the problem of the 

 area of the circle presented to the minds of mathematicians, and the 

 attention which has been bestowed upon it from ancient times. The 

 first step towards the solution of this and similar problems was the 

 method of exhaustions, as it was termed. The circle was supposed to 

 be inscribed and circumscribed by polygons, and as the number of 

 sides of the polygons was increased, their areas would obviously ap- 

 proach nearer to that of the circle, which would always be greater than 

 the area of the inscribed and less than that of the circumscribed polygon. 

 As the number of sides on the inner and outer polygons was increased, 

 their areas would more and more approximate, and thus the area to 

 the circle could be determined with any required degree of exactness. 

 Kepler, in consequence of a dispute concerning the capacity of a cask 

 of wine, entered upon a general investigation, in the course of which he 

 found it convenient to conceive a circle to be formed of an infinite 

 number of triangles, having their vertices at the centre, and their bases 

 infinitely small, ranged together in the circumference of the circle. The 

 ideas of infinitely great and infinitely small quantities were in this way 

 made familiar to mathematicians, and formed the origin of the vast 

 improvements which were effected in the science during the seventeenth 

 century. An ingenious Italian geometer named CAVALIERI, who was 

 born at Milan in 1598, and was appointed professor of mathematics in 

 1629, published in 1635 a work he called "A Treatise on Indivisi- 

 bles," in which he explained a method of dealing more easily with the 

 problems to which the method of exhaustions had generally been applied. 

 He considers lines as made of an infinite number of points, surfaces 

 of an infinite number of lines, and solids of an infinite number of sur- 

 faces. Though this is a mode of speaking at variance with the first 

 definitions of geometry, it was adopted for convenience and to avoid 

 prolixity, instead of the more correct expression of what is really the 

 same idea, namely, that a line may be conceived as made up of an in- 

 finite number of infinitely short lines, a surface of an infinite number 

 of infinitely narrow parallelograms, and a solid of an infinite number 



