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THE

PREFACE.

NOrder to the making any confiderable Proficiency in the Mathematick Sciences, there feem to be requifite thefe Four Things. Ift, A Good Natural Genius, as the Bafis and Foundation. 2dly, A Sufficiency of vacant Time, too frequent Avocations breaking the Intention of the Mind from the Subject contemplated; and (as it generally happens in the Mathematicks) if the Matter under Confideration have a great many preparatory Steps, it interrupts the whole Defign. 3dly, Industry and Application, without which no good Fruit is to be expected in any Sort of Literature. 4thly, External Helps and Affiftances, either immediately from Perfons themselves, or by their Writings: And indeed this is not only lawful, but abfolutely neceffary, fince the Object of our Confideration is no less than the Universe itself: And whoever confiders duly the vast Industry, Sagacity, Multitude of Obfervations and Experiments, and other intrinfick Things neceflary to compleat a Syftem of the Mathematicks will readily believe that it is not the Work of one Man, or of one Age. And we cannot fufficiently wonder at the Industry of the Mathematicians, and the Power of Numbers and Geometry well apply'd, when we reflect upon the vast Progress they have made in this Art. Now as the Writings of Others are the best and general Way of improving herein, I shall briefly enumerate fome of the most eminent Authors, who have treated

treated upon the feveral Branches of the Mathematicks And first,

Writers on Vulgar Arithmetick, and Specious, or Algebra,

Dr. WALLIS's

Mr. KERSEY'S

}

ALGEBRA.

WARD's Young Mathematician's Guide.
RONAYNE's Algebra,

STURMIUS's Mathefis Enucleata.
JONE's Synopfis Palmariorum Mathefeos.
Sir ISAAC NEWTON's Arithmetica Univerfalis,

On GEOMETRY

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On TRIGONOMETRY.

Mr. CASWELL'S

Dr. K EIL's

Mr. NEW TON's

} Trigonometry.

On DIALLING.

Mr. W. LEY BOURN's Dialling.

ASTRONOMY.

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Dr. GREGORY's

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Aftronomical Lectures.

Dr. KEIL's

On OPTICKS and PERSPECTIVE.
Mr. MOLINEUX's Dioptricks.

Dr. B. TAYLOR's Linear Perfpective.

ASTRONOMICAL

ASTRONOMICAL TABLES for the Calculation of ECLIPSES, and the PLANET's Places, STREET's Aftronomia Carolina. LEADBETTER's Tables.

CASSINI's Tables.

De la HIRE's Tables.

On FLUXIONS.

DITTON's Inftitution of Fluxions.
STONE's Tranflation of De L' Hofpital.
HAYE's Introduction to Fluxions.
B. TAYLOR's Methodus Incrementorum.

On MECHANICS and
MATHEMATICAL PHILOSOPHY

KIEL's Phyfical Lectures.

DITTON's Laws of Nature and Motion.
Sir ISAAC NEWTON's Principia!
JACOBI HERMANNI Phoronomia.

SYSTEMS or BODIES of the MATHEMATICKS.
OZANA M's Curfus Mathematicus.
WOLFII Corpus Mathematicum.
LEYBOURN's Curfus Mathematicus.

Befides in the Philofophical Transactions may be found
feveral Things relating to the Laws of Chance, Infi-
nite Series, Hydrostaticks, Logarithms, &c.

But I must now haften to other Matters, intending to finish what relates to the Dispute concerning the Invention of the Method of Fluxions in the prefent Book.

JUNE the 14th, 1735.

A D

ADVERTISEMENT

To all LOVERS of INGENUITY.

THE Editor intending to publish the next Quarterly Book in SEPTEMBBR enfuing, defires that fuch Gentlemen and Ladies, &c. as think fit to encourage this Undertaking, either by promoting and recommending the Sale thereof, or by fending fuch Subjects either in Verfe or Proje, as are Suitable to this Defign, would please to direct their Letters to Mr. THO. GENT, Printer, near the Star in StoneGate, YORK, Poft paid, before the End of Auguft next, where they will be carefully forwarded to the Author.

Whoever fend either Enigmas, or Arithmetical Queftions, are defired to give the Solution along with them, to prevent all Mistakes, or Ambiguity in the Terms: And I do affure the Buyers of this Treatise, that, in Process of Time, they shall have Questions in all the Branches of Mathematicks, viz. Arithmetical, Nautical, Geographical, Mechanical, Trigonometrical, Aftronomical, Algebraical, and in Fluxions, together with exponential Equations, and the Conftruction of Algebraic Equations, and finding their Loci; to fuit the Taftes of all Perfons, and render the Work generally usefull.

Omne tulit punctum, qui mifcuit utile dulci.

Mifcellanea

Of the INVENTION of the METHOD of FLUXIONS.

The OPINION of the COMMITTEE appointed to examine the Original Letters and Coppy-Books of Letters in the Cuftody of the ROYAL SOCIETY, relating to the Dispute between Sir ISAAC NEWTON and Mr. LEIBNITZ, concerning the Invention of the Method of Fluxions.

*****E have confulted the Letters and Letter-Books W

in the Cuftody of the ROYAL SOCIETY, and thofe found among the Papers of Mr. John Collins, dated between the Years 1669 and 1677 inclufive; and fhewed them to fuch as knew and avouched the Hands of Mr. Barrow, Mr. Collins, Mr. Oldenburgh, and Mr. Leibnitz; and compared thofe of Mr. Gregory with one another, and with Copies of fome of them taken in the Hands of Mr. Collins and have ex tracted from them what relates to the Matter referr'd to us: All which Extracts herewith delivered to you, we believe to be genuine and authentick; and by these Letters and Papers we find,

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1. THAT Mr. Leibnitz was in London in the Beginning of the Year 1673, and went thence, in or about March, to Paris, where he kept a Cortefpondence with Mr. Collins, by means of Mr. Oldenburgh, till about September 1676, and then returned by London and Amfterdam to Hanover;

and

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