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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.
Interspersed with Dissertations on several curious and

entertaining Subjects; miscellaneous Reflections on
AUTHORS; and historical Memoirs of the Lives of
the most eminent WRITERS in all Branches of
polite Literature.

For August, 1736.

VOL. XVII.

LONDON:
Printed for W. INNYS and R. MANBY, at
the West End of St. Paul's. MDCCXXXVI.

Price One Shilling

A TABLE of the ARTICLES

For AUGUST, 1736.

ART. V. Emarks on the Considerations re

lating to Fluxions, 36. that were published by Philathethes Cantabrigiensis in the Republick of Letters for the last Month, Page 87

VI. The Remainder of the Paper begun in our

lalt, entituled, Considerations upon some palfages of a Dissertation concerning the Doctrine of Fluxions, published by Mr. Robins in the Republick of Letters for April last. By Pbilalethes Cantabrigienfis,

III

THE

Τ Η Ε

PRESENT STATE

OF THE

Republick of Letters.

For AUGUST 1736.

A R TICLE V. REMARKS on the Confiderations relating to

Fluxions, &c. that were published by Philalethes Cantabrigiensis in the Republick of Letters for the last month.

IN

N these Remarks, for brevity, the words of

Philalethes are not transcribed, but the Sečtions and Paragraphs, wherein they are contained, are particularly quoted.

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

Sect. V. §. 1-4. By the idea of Auxions Mr. Robins does not mean the doctrine of Auxions, but only one part of that doctrine; for it is ex. presly said in the Republick of Letters for October AUGUST 1736.

F

last,

3

last, pag. 253. that the doctrine of fluxions consists of two pårts, the form of conception there described (that is the idea of Auxions) and the method of applying it to the solution of mathematical problems.

Again, Mr. Robins does not conclude, that the method of fluxions is absolutely diftina from that of first and last ratios, only because Sir Isaac 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.

S. 5–8. Here it is attempted to be proved, that one of these methods could not possibly be invented before the other, because Sir Isaac Newton has in his writings made use of that of prime and ultimate ratios in demonstrating propofitions in the other doctrine; whereas to make this a conclusive argument, it was necessary to Thew, it were impossible to form these demonstrations by any other means; but it appears in fact Sir Isaac Newton did at first content himself with such demonstrations, as the method of indivisibles did afford; and Mr. Robins has shewn, that these propositions may be perfectly demonstrated another way by exhaustions.

$. 9. Because Philalethes sees not the use of this distinction, is that a proof it is of no importance? How could Philalethes imagine the letter S to be inserted through inadvertency, when that is to suppose the title page printed before the book was writ; for these two methods are as much diftinguished in the book itself, as in any thing Mr. Robins has since published.

S: 11, 12. Has not Sir Isaac Newton sufficiently distinguished them in delivering his method of

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