the error which arifes from the construction and pofition of the glafs is above five thousand times lefs than the error which arifes from the refrangibility: And therefore, that the fhape or figure of the glaffes is not the cause why telescopes cannot be carried to a greater perfection, but arises wholly from the nature of light.

FOR this reafon he invented a telescope, which discovers objects by reflexion and not by refraction. Telescopes of this new kind are very hard to make, and their use is not eafy. But according to the English, a reflective telescope of but five feet has the fame effect as another of an hundred feet in length.

LET

LETTER XVII.

ΟΝ

INFINITES in GEOMETRY,

AND

Sir Ifaac Newton's

CHRONOLOGY.

T

HE labyrinth and abyss of infinity is also a new course Sir Ifaac Newton has gone through, and we are oblig'd to him for the clue, by whofe affiftance we are enabled to trace its various windings.

DES CARTES got the start of him alfo in this astonishing invention. He advanc'd with mighty steps in his geometry, and was arriv'd at the very borders of infinity, but went no farther. Dr. Wallis, about the middle of the laft century, was the first who reduc'd a fraction, by a perpetual divifion, to an infinite feries.

G

THE

THE lord Brounker employ'd this feries to fquare the hyperbola.

MERCATOR publifh'd a demonstration of this quadrature, much about which time Sir Ifaac Newton, being then twenty-three years of age, had invented a general method to perform, on all geometrical curves, what had just before been try'd on the hyperbola.

'Tis to this method of fubjecting every where infinity to algebraical calculations, : that the name is given of differential calculations or of fluxions, and integral calculation. 'Tis the art of numbering and measuring exactly a thing whofe existence cannot be conceiv'd.

AND, indeed, would you not imagine that a man laugh'd at you, who fhould declare that there are lines infinitely great which form an angle infinitely little?

THAT a right line, which is a right line fo long as it is finite, by changing infinitely little its direction, becomes an infinite curve, and that a curve may become infinitely less than another curve?

THAT there are infinite squares, infinite cubes, and infinites of infinites, all greater than one another, and the laft but one of which, is nothing in comparison of the last ?

ALL these things which at firft appear to be the utmost excefs of frenzy, are in reality an effort of the fubtilty and extent of

the

the human mind, and the art of finding truths which till then had been unknown.

THIS fo bold edifice is even founded on fimple ideas. The bufinefs is to measure the diagonal of a fquare, to give the area of a curve, to find the fquare root of a number, which has none in common arithmetic. After all, the imagination ought not to be startled any more at so many orders of infinites, than at the fo well known propofition, viz. that curve lines may always be made to pass between a circle and a tangent; or at that other, namely that matter is divifible in infinitum. These two truths have been demonftrated many years, and are no lefs incomprehenfible than the things we have been speaking of.

FOR many years the invention of this famous calculation was denied Sir Ifaac Newton. In Germany Mr. Leibnitz was confider'd as the inventor of the differences or moments, call'd * Fluxions, and Mr. Bernouilli claim'd the integral calculation. However, Sir Ifaac is now thought to have first made the difcovery, and the other two have the glory of having once made the world doubt whether 'twas to be afcrib'd to him or them. Thus fome contefted with Dr. Harvey the invention of the circulation of the blood, as others difputed with

By Sir jaac Newton.

G 2

Mr.

Mr. Perrault that of the circulation of the fap.

HARTSOCHER and Lewenhoeck disputed with each other the honour of having first feen the Vermiculi of which mankind are form'd. This Hartfocher alfo contested with Huygens the invention of a new method of calculating the distance of a fix'd ftar. 'Tis not yet known to what philofopher we owe the invention of the cycloid.

BE this as it will, 'tis by the help of this geometry of infinites that Sir Isaac Newton attain'd to the most fublime difcoveries. I am now to fpeak of another work, which tho' more adapted to the capacity of the human mind, does neverthelefs difplay fome marks of that creative genius with which Sir Ifaac Newton was inform'd in all his refearches. The work I mean is a chronology of a new kind; for what province foever he undertook, he was fure to change the ideas and opinions receiv'd by the rest of men.

ACCUSTOM'D to unravel and difintangle chaos's, he was refolv'd to convey at least fome light into that of the fables of antiquity, which are blended and confounded with hiftory, and fix an uncertain chronology. 'Tis true, that there is no family, city or nation, but endeavours to remove its original as far backward as poffible. Befides, the firft hiftorians were the most negligent