LATER BOOKS AND ARTICLES 241 



part occasioned by the acceleration measures the 

 second fluxion. ..." 



The same article is reprinted in the second edition 

 (1779) and the third edition (1797). 



Robert Thorp, lyyy 



208. Thorp made a translation of part of New- 

 ton's Principia.'^ 



In the ** advertisement " we read : '* The doctrine 

 of prime and ultimate ratios . . . is established, so 

 as to remove the various objections which have been 

 raised against it, since it was first published. To 

 the relations of finite quantities alone the reasoning 

 on this subject is confined." The translation of 

 quantitates quam mininice, evanescentes^ ultimce^ in- 

 finite rnagnce^ and the like, has not been literal, yet 

 they are " explained in that sense under which the 

 author cautions his readers to understand them. 

 This is the more necessary, as the terms infinite^ 

 infinitesimal, least possible^ and the like, have been 

 grossly misapplied and abused." 



209. In the Commentary to Lemma i in Sect. i 

 of Bk. I in the Principia, Thorp says : * * The prime 

 and ultimate ratios of magnitudes . . . are investi- 

 gated by observing their finite increments or decre- 

 ments, and thence finding the limits of the ratios 

 of those vai'iable magnitudes ; not the ratios to 

 which the magnitudes ever actually arrive (for 



^ Mathematical Principks of Naturai Philosophy. By Sir Isaac 

 Newton, Knight. Translated into English, and illiistrated with a 

 Commentary, by Robert Thorp, M.A., voi. i, London, 1777. 



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