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THE

PREFACE.

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NOrder to the making any considerable Pro

ficiency in the Mathematick Sciences, there I

seem to be requisite these Four Things ift, A Good Natural Genius, as the Basis and Foundation. 2dly, A Sufficiency of vacant Time, too frequent Avocations

breaking the Intention of the Mind from the Subje&t contemplated ; and (as it generally happens in the Mathematicks) if ihe Matter under Consideration have a great many preparatory Steps, it interrupts the whole Design. 3dly, Industry and Application, without which no good Fruit is to be expected in any Sort of Literature. 4!hly, Exrernal Helps and Asistances, either immediately from Persons themselves, or by their Writings And indeed this is not only lawful, but absolutely necesSary, since the Obje&t of our Confideration is no less than The Universe itself

' : And whoever considers duly the vast Industry, Sagacity, Multitude of observations and Experiments, and other intrinsick Things necesary to compleat a System of the Mathematicks will readily believe that it is not the Work of one Man, or of one Age.

And we cannot sufficiently wonder at the Industry of the MathemaTicians, and the Power of Numbers and Geometry w:ll apply'd, when we reflett 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 mall briefly enumerate some of the most eminent Authors, who have

treated

treated upon the several Branches of the Mathematicks :
And first,
Writers on Vulgar Arithmetick, and Specious, or Algebra,
Dr. WALLIS's

ALGEBBA.
Mr. KERSEY's Š
WAR D's Young Mathematician's Guide,
RONAYNE's Algebra,
STURMIUS's Mathefis Enucleata.
JONE's Synopfis Palmariorum Matheseos.
Sir ISAAC NEWTON's Arithmetica Universalis,

On G E O M E T R Y.

TACQUET.

COMMANDINE.
Euclid's Elements, by

Dr. BARROW.
Dr. GREGORY.

2

On CONIC K-SECTIONS.
Dr. MILNES's
M. Del HOSPITAL's

Conics.
Dr. HALLEY's Appollonius.

2

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On TRIGONOMETRI
Mr. CASWELL's
Dr. K EIL's

Trigonometry
Mr. NEWTON's

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On D I ALLING.
Mr. W. LEYBOURN's Dialling.

On ASTRONOMY.
Dr. GREGOR Y's

Aftronomical Lectures, Dr. KEIL's

012 OPTICKS and PERSPECTIV E. Mr. MOLINEU,X's Dioptricks. Dr. B. TAYLOR's Linear Perspective.

ASTRONOMICAL

ASTRONOMICAL TABLES for the Calculation of ECLIPS E s, and the PLANET's Places,

STREET's Aftronomia Carolina.
LEAD BETTER's Tables.
CASSINI's Tables.
De la HIRE's Tables.

On F LUXION S.
DITTON's Institution of Fluxions.
STONE's Translation of De L' Hospital.
H A Y E's Introduction to Fluxions.
B. TAYLOR's Methodus Incrementorum.

On MECHANICS and
MATHEMATICAL PHILOSOPHY
KIEL's Physical Lectures.
DITTON's Laws of Nature and Motion.
Sir ISAAC NEWTON's Principia.
JACOBI HERMANNI Pboronómia.
SYSTEMS or Bodies of the MATHEMATICKS.
OZANA M's Cursus Mathematicus.
WOLFIl Corpus Mathematicum.
LEYBOURN's Cursus Mathematicus.
Befides in the Philosophical Tranfa&tions may be found

several Things relating to the Laws of Chance, Inf

nite Series, Hydrostaticks, Logarithms, &c. But I must now hasten to other Matters, intending to finish what relates to the Dispute concerning the Invention of the Method of Fluxions in the present Book.

JUNE the 14th, 1735.

AD

ADVERTISEMENT To all LOVERS of

INGENUITY.

The Editor intending to publish the next Quarterly Book

in SEPTEMBBR ensuing, desires that such Gentlemen and Ladies, &c. as think fit to encourage this Undertaking, either by promoting and recommending the sale thereof, or by sending such Subjects either in Verse or Proje, as are suitable to this Design, would please to direet their Letters to Mr. Tho. Gent, Printer, near the Star in StoneGate, YORK, Post paid, before the End of August next, where they will be carefully forwarded to the Author.

Whoever send either Enigmas, or Arithmetical Questions, are desired to give the Solution along with them, to prevent all Mistakes, or Ambiguity in the Terms: And I do assure 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, Astronomical, Algebraical, and in Fluxions, together with exponential Equations; and the Constru&tion of Algebraic Equations, and finding their Loci i to suit the Tastes of all Persons, and render the Work generally usefull.

Omne tulit punctum, qui miscuit utile dulci.

Miscellanea

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The OPINION of the COMMITTEE appointed

to examine the Original Letters and Coppy-Books of Letters in the Custody 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 consulted the Letters and Letter-Books EW in the Custody of the Royal SOCIETY, and

those found among the Papers of Mr. John

Collins, dated between the Years 1669 and 1677 inclusive ; and shewed them to such as knew and avouched the Hands of Mr. Barrow, Mr. Collins, Mr. Oldenburgh, and Mr. Leibnitz; and compared those of Mr. Gregory with one another, and with Copies of some 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 here with delivered to you, we believe to be genuine and authentick; and by these Letters and Papers we find,

1. That Mr. Leibnitz was in London in the Beginnir.g of the Year 2073, and went thence, in or about March, to Paris, where he kept a Correspondence with Mr. Collins, by means of Mr. Oldenburgh, till about September 1676, and then returned by London and Amferdam to Hanover;

and

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