14 LIMITS AND FLUXIONS 



wìU remain the excess aY> + /^A. Therefore with the 

 whole increments a and b of the sides, the increment 

 aV> + ^A of the rectangle is generated. Q. E. D. " 



IL Wallis's De Algebra Tractatus 



20. The Latin edition of John Wallis's Algebra, 

 which appeared in 1693, contains on pages 390-396 

 a treatise on the "Quadrature of Curves " which 

 Newton had prepared many years before, and from 

 which he cited many things in his letter of October 

 24, 1676. In revised phraseology and with a new 

 Introduction, the "Quadrature of Curves" was 

 republished in 1704, as we shall see presently. 

 Through the researches of Rigaud ^ we know now 

 that what is given in Wallis's Algebra, p. 390, line 

 18, to p. 396, line 19, are Newton's own words, 

 except, no doubt, the word " clarissimus," as 

 applied to himself From this part we quote as 

 foUows : 2 — 



21. Page 391: ''V^x fluentes qua^ititates intelli- 

 git indeterminatas, id est quae in generatione 

 Cuvarum per motum localem perpetuo augentur vel 

 diminuuntur, & per earum fluxionem intelligit celeri- 

 tatem incrementi vel decrementi. Nam quamvis 

 fluentes quantitates & earum fluxiones prima fronte 

 conceptu difficiles videantur, (solent enim nova 

 difficilius concipi), earundem tamen notionem cito 

 faciliorem evasuram putat, quam sit notio momen- 



' S. P. Rigaud, Historical Essay on Sir Isaac Newton^ s Principia^ 

 Oxford, 1838, p. 22. 



2 Johannis Wallis, S.T.D., De Algebra Tractatus; Historicus &f 

 Practicus. Oxoniae, MDCXCIII. 



