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Memorandums relating to Sr Isaac Newton given me by Mr Abraham Demoivre in Novr 1727 ——

Born on Xmas day 1642. Came to the University in 61.

In 63 being at Sturbridge fair bought a book of Astrology, out of a curiosity to see what there was in it.

Read in it till he came to a figure of the heavens which he could not understand for want of being acquainted with Trigonometry.

Bought a book of Trigonometry, but was not able to understand the Demonstrations.

Got Euclid to fit himself for understanding the ground of Trigonometry. –

Read only the titles of the propositions, which he found so easy to understand that he wondred how any body would amuse themselves to write any demonstrations of them. Began to change his mind when he read that Parallellograms upon the same base & between the same Parallells are equal, & that other proposition, that in a right angled Triangle the square of the Hypothenuse is equal to the squares of the two other sides.

Began again to read Euclid with more attention than he had done before & went through it.

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Read Oughtreds which he understood thou not entirely, he having some difficulties about what the Author calls Scala secundi et tertii gradus, relating to the solution of quadratick Cubick {sic} Equations. – Took Descartes's Geometry in hand, thou he had been told itt would be very difficult, read some few pages in it, then stop't began again, went a little farther than the first time, stopt again, went back again to the beginning, read on till by degrees he made himself master of the whole, to that degree that he understood Descartes's Geometry better than he had done Euclid.

Read Euclid again & then DesCartes's Geometry for a second time. Read next Dr Wallis's Arithmetica Infinitorum, & on the occasion of a certain interpolation for the quadrature of the circle found that admirable Theorem for raising a Binomial to a power given. But before that time a little after reading DesCartes Geometry, writt many things concerning the vortices Axes Diameters of Curves, which afterwards gave rise to that excellent tract de Curvis secundi generis. In 65 & 66 began to find the method of Fluxions, and writt several curious problems relating to that method bearing that date which weere {sic} seen by me above 25 year ago. In 65 being in the country in a garden, it came into his thought, that the power of gravity was not limited to a certain distance from the earth, but that this power would exert it self at any distance from it, & even would reach as far as the Moon, then he drew this conclusion that if it was true that this power reached as far as the Moon, it was very likely that this power or {sic} force of gravitation towards the earth was what contained the Moon in her orbit, whereupon he fell a calculating what would be the effect of that supposition, but he found himself disappointed for a while, the reason of which was that he took it for granted that a degree of the earth did contain 60 miles exactly, which made it that his calculation did not agree with the Theory, but he entertained a notion that with the force of gravity, there might be a mixture of that force which the Moon would have if it was carried along in a vortex, but when the Tract of Picard's of the measure of the earth came out, he began his calculations anew, & found it perfectly agreeable to the Theory. I beleive we may gather from the Transactions an account of a dispute that he had with Linus a Jesuit of Liege concerning his discovery of light <2r> & Colours wch would be very entertaining.

In 1673 Dr Hook writt to him to send him something new for the transactions, whereupon he sent him a little dissertation to confute that coon objection which is, that if it were true that the Earth moved from West to East, all falling bodies would be left to the West, & maintained on the contrary they would {sic} fall a little Eastward, & having described a curve with his hand to represent the motion of a falling body, he drew a negligent stroke with his pen, from whence Dr Hook took occasion to imagine that he meant the Curve would be a Spiral, whereupon the Dr writt to him that the Curve would be an Ellipsis & that the body would move according to Kepler's notion wch gave him an occasion to examine the thing thoroughly & for the foundation of the Calculus he intended laid down this proposition that the areas described in equal times were equal, which thou assumed by Kepler was not by him demonstrated, of which demonstration the first glory is due to Sr Isaac. In 1684 Dr Halley came to visit him at Cambridge, after they had been some time together, the Dr asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with <3r> * joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay, Sr Isaac looked among his papers but could not find it, but he promised him to renew it; & then to send it him, Sr Isaac in order to make good his promise fell to work again, but he could not come to that conclusion wch he thought he had before examined with care, however he attempted a new way which thou longer than the first, brought him again to his former conclusion, then he examined carefully what might be the reason why the calculation he had undertaken before did not prove right, & he found that having drawn an Ellipsis coursely with his own hand, he had drawn the two Axes of the Curve, instead of drawing two Diameters somewhat inclined to one another; whereby be {sic} might have fixed his imagination to any two conjugate diameters, which was requisite he should do, that being perceived, he made both his calculations agree together.

After this Dr Halley was (I think) sent down to Cambridge by the Royal Society to prevail with Sr Isaac to print his discoveries wch gave rise to the Principia —

Dr Halley has often valued himself to me for having been the Ulysses who produced this Achilles —

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in \May – Quære/ 1684 Dr Halley {illeg} Sr I.N. a visit at Cambridge & there in a conversation the Dr asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it – Sr I. replied immediately that it would be an Ellipsis the Doctor struck with *