1/8 LIMITS AND FLUXIONS 



of variable base and altitude AEIF with the vertex 

 I moving along the curve through B has the fluxion 



In a footnote Rowe expressed the belief that this 

 mode of deriving the rule is not open to criticism as 

 was the method of using increments vvhich in 1 734was 

 **smartly attacked by the late acute Dr. Berkeley." 



Rowe proves by a geometrical method similar to 

 the above that the fluxion of a pyramid of fixed 

 vertex and slant edges, whose variable base xy 

 moves parallel to itself and whose variable altitude 

 is z^ is xyz. Taking a parallelopipedon as equal to 

 three pyramids, he finds the fluxion of xyz to be 

 xyz-\-xyz-\-xyz. This new way of deriving the 

 fluxion of xyz was copied by *'his friend" Benjamin 

 Martin in the MatJwnatical Institutions. 



At the end of the third edition of Rowe's Fluxions 

 is a bibliography of English works on this subject, 

 and he **particularly refers to the Works of his two 

 celebrated Friends, Mr. Emerson and the late Mr. 

 Simpson." 



Berkeley Ten Years After 

 i6i. Berkeley, in his Siris ^ of 1744, expressed 

 himself as follows : " Concerning absolute space, 

 that phantom of the mechanic and geometrical 

 philosophers (§ 250), it may sufiìce to observe that 

 it is neither perceived by any sense, nor proved by 

 any reason, and was accordingly treated by the 

 greatest of the ancients as a thing merely visionary. 



^ George Bcrkelcy's Works. Edition by A. C. l'raser, voi. ii, 

 Oxford, 1871, p. 468 and note. 



