[42] Whiston asserts that this cause was supposed by Newton to be something analogous to the vortices of Descartes.—See Whiston’s _Memoirs of himself_, p. 231. [43] Waller’s _Life of Hooke_, p. 22. [44] _Ibid._ [45] July 27, 1686, _Biog. Brit._ p. 2662. [46] _Commercium Epistolicum_, No. 7. [47] This Scholium is added to Prop. iv. lib. i. coroll. 6. [48] In writing to Flamstead, Newton requests from him the long diameters of the orbits of Jupiter and Saturn, that he “_may see how the sesquialteral proportion fills the heavens_.” [49] Whiston’s _Memoirs of his own Life_. [50] “Dr. Reid states, that James Gregory, Professor of Philosophy at St. Andrew’s, printed a thesis at Edinburgh in 1690, containing twenty-five positions, of which twenty-two were a compend of Newton’s Principia.” [51] Nichols’s Literary Anecdotes, vol. iii. p. 322. Cotes states in his preface to the second edition of the Principia, that copies of the first edition could only be obtained at an immense price. [52] Preface to Desaguliers’s _Experimental Philosophy_. Dr. Desaguliers states that he was told this anecdote several times by Sir Isaac Newton himself. [53] _The Life of John Locke_, p. 209–215, Lond. 1829. [54] _Principia_, lib. i. prop. i. [55] _Ib._ lib. i. prop. xi. [56] “On peut regarder Fermat,” says Lagrange, “comme le premier inventeur des nouveaux calculs;” and Laplace observes, “Il paraitque Fermat le veritable inventeur du calcul differentiel, l’ait envisagé comme un cas particulier de celui des differences,” &c. [57] Art. _Mathematics_, in the _Edinburgh Encyclopædia_, volume xiii. p. 365. [58] These facts are mentioned in Newton’s letter to Oldenburgh, October 24, 1676. [59] Dr. Pemberton informs us that he had prevailed upon Sir Isaac to publish this treatise during his lifetime, and that he had for this purpose examined all the calculations and prepared part of the figures. But as the latter part of the treatise had never been finished, Sir Isaac was about to let him have other papers to supply what was wanting, when his death put a stop to the plan.—Preface to Pemberton’s _View of Sir Isaac Newton’s Philosophy_. [60] Isaci Newtoni Opera quæ extant omnia, vol. i. p. 388–519. [61] “Acutissimis qui toto orbe florent Mathematicis.”