12 LIMITS AND FLUXIONS 



ad hunc terminum. Igitur sensus lemmatis est, 

 ut, si quantitatum quarumcunque perpertuo motu 

 crescentium vel decrescentium A, B, C, etc. , 

 momenta, vel mutationum velocitates ^ dicantur 

 a, by e, etc. , momentum vel mutatio geniti ^ rectan- 

 guli AB fuerit aB-\-bA, et geniti ^ contenti ABC 

 momentum fuerit aVtC+bAC^cKB : . . . 



ly. '^ Cas. I. Rectangulum quodvis motu perpetuo 

 auctum AB, ubi de lateribus A & B deerant momen- 

 torum dimidia* ^a & ^b, fuit A — ^a in B — ^b, 

 seu AB — ^aB — h bA + \ab \ & quam primum latera 

 A & B alteris momentorum dimidiis aucta sunt, 

 evadit A + | ^ in B + |- b, seu AB + | ^B + J ^ A + ^ ab. 

 Uè hoc rectangulo subducatur rectangulum prius, et 

 manebit excessus ^B + ^A. Igitur laterum incre- 

 mentis totis ^ et ^ generatur rectanguli incrementum 

 aB-^bA. Q.E.D." 



English Translation by Andrew Motte : 



i8. " . . . These quantities I bere consider as 

 variable and indetermined and increasing or decreas- 

 ing as it were by perpetuai motion or flux ; and I 

 understand their momentaneous increments or 

 decrements by the name of Moments ; so that the 



^ In the second and third editions "hoc latus " takes the place of 

 "hunc terminum." 



" In the third edition " vel his proportionales mutationum veloci- 

 tates" takes the places of "vel mutationum velocitates." 



' "geniti" is left out in the first edition. 



^ In this history, the solidus ( / ) will be used sometimes in printing 

 fractions which come in the line of the text. The reader must remem- 

 ber that this notation is modem ; it occurs in none of the passaores 

 which we quote from seventeenth- and eighteenth-century books. In 

 some cases the use of the solidus has made it necessary to insert paren- 

 theses which do not occur in the originai. 



