NEWTON 3 



second in 1713, the third in 1726. We give extracts 

 which bear on the theory of limits and fluxions and 

 indicate the changes in phraseology introduced in 

 the second and third editions. We give also trans- 

 lations into EngUsh based on the text of the 1726, 

 or third, edition. 



Principia, Book /, Section /, Lemma I 

 First edition : 



4. " Quantitates, ut & quantitatum rationes, quae 

 ad aequaUtatem dato tempore constanter tendunt 

 & eo pacto propius ad invicem accedere possunt 

 quam prò data quavis differentia ; fiunt ultimo 

 aequales. 



5. "Si negas, sit earum ultima differentia D. 

 Ergo nequeunt propius ad a^qualitatem accedere 

 quam prò data differentia D : contra hypothesin." 



Second and third editions : 



6. " Ouantitates, ut & quantitatum rationes, quae 

 ad aequalitatem tempore quovis finito constanter 

 tendunt, & ante finem temporis illius propius ad 

 invicem accedunt quam prò data quavis differentia, 

 fiunt ultimo xquales. 



7. "Si negas, fiant ultimò ina^quales, & sit 

 earum, etc." [As in the first edition.] 



Translation by Robert Thorp:^ 



8. "Quantities, and the ratios of quantities, which, 

 in any finite time, tend continually to equality; and 



^ Matheniatical Principles of Naturai Philosophy, by Sir Isaac 

 Newton, Knight. Trnnslated into Engiish, and illustrated with a 

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



