THE

Prefent State

OF THE

REPUBLICK

O F

LETTER S.

Giving a General VIEW of the State of
Learning throughout EUROPE ; and contain-
ing not only an early Account, but accurate
Abstracts of the most valuable Books published
in Great Britain or Foreign Parts.

Interfperfed with Differtations on feveral curious and
entertaining Subjects; mifcellaneous Reflections on
AUTHORS; and hiftorical Memoirs of the Lives of
the most eminent WRITERS in all Branches of
polite Literature.

A TABLE of the ARTICLES

ART. V.

For AUGUST, 1736.

R

Emarks on the Confiderations relating to Fluxions, &c. that were published by Philathethes Cantabrigienfis in the Republick of Letters for the laft Month, Page 87

VI. The Remainder of the Paper begun in our laft, entituled, Confiderations upon fome paffages of a Differtation concerning the Doctrine of Fluxions, published by Mr. Robins in the Republick of Letters for April laft. By Philalethes Cantabrigienfis,

III

THE

1

REMARKS on the Confiderations relating to Fluxions, &c. that were published by Philalethes Cantabrigienfis in the Republick of Letters for the last month.

I'

N thefe Remarks, for brevity, the words of Philalethes are not tranfcribed, but the Sections and Paragraphs, wherein they are contained, are particularly quoted.

The first four Sections contribute nothing to wards determining the points in question.

Se&t. V. §. 1-4. By the idea of fluxions Mr. Robins does not mean the doctrine of fluxions, but only one part of that doctrine; for it is exprefly faid in the Republick of Letters for October AUGUST 1736.

F

laft,

laft, pag. 253. that the doctrine of fluxions confifts of two parts, the form of conception there defcribed (that is the idea of fluxions) and the method of applying it to the folution of mathematical problems.

Again, Mr. Robins does not conclude, that the method of fluxions is abfolutely diftinct from that of first and last ratios, only because Sir Ifaac Newton had formed his idea of fluxions before he had invented the other method, but also because that other method is no otherwise made use of in this than for demonftrating the proportions between different fluxions.

§. 5-8. Here it is attempted to be proved, that one of thefe methods could not poffibly be invented before the other; because Sir Ifaac Newton has in his writings made ufe of that of prime and ultimate ratios in demonftrating propofitions in the other doctrine; whereas to make this a conclufive argument, it was neceffary to fhew, it were impoffible to form thefe demonftrations by any other means; but it appears in fact Sir Ifaac Newton did at first content himself with fuch demonftrations, as the method of indivifibles did afford; and Mr. Robins has fhewn, that these propofitions may be perfectly demonftrated another way by exhauftions.

§. 9. Because Philalethe's fees not the ufe of this diftinction, is that a proof it is of no importance? How could Philalethes imagine the letter S to be inferted through inadvertency, when that is to fuppofe the title page printed before the book was writ; for thefe two methods are as much diftinguished in the book itself, as in any thing Mr. Robins has fince published.

§. 11, 12. Has not Sir Ifaac Newton fufficiently diftinguished them in delivering his method of