Imatges de pàgina
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be glorious creatures then. Every family would be happy.

But as to Mifs Spence, this knowledge, with a faultless perfon, and a modesty more graceful than her exquifite beauty, were not the things that principally charmed me: nor was it her converfation, than which nothing could be more lively and delightful: nor her fine fortune. It was her manners. She was a Chriftian Deift, and confidered Benevolence and Integrity as the effentials of her religion. She imitated the piety and devotion of Jefus Christ, and worshipped his God and our God, his Father and our Father, as St. John expressly stiles the God of Chriftians, xx. 17. She was extremely charitable to others, and confidered confcious virtue as the greatest ornament and most valuable treasure of human nature. Excellent Maria!

The author's departure from Cleator for London, July 31

1731.

§. With this young lady, and her two fervants (her footman and her woman,) I went up to London. We fet out from Cleator the 31st day of July, and without meeting with any mifchiefs in all that long way, came safe, to London. We were nine days on the road; and as the weather was fine, and our horfes C 2 excel

excellent, we had a charming journey. My companion was fo agreeable, that had it been two thousand miles from Cleator to London, instead of 272, I should still have thought it too short. Her conversation was fo various and fine, that no way could feem tiresome and tedious to him that travelled with her. Her notions and remarks were ever lively and inftructive. It was vaft pleasure to hear her, even on the driest and most abftrufe fubjects, on account of the admiration her discourse raised, and the fine knowledge it communicated, to one who understood her. I will give an inftance.

§. 7. In riding over the mountains the firft day, we miffed the road in the evening, and instead of getting to a very good inn, where we intended to reft, we were forced to stop at a poor little public house, and right glad to get in there, as the evening was tempeftuous and wet, dark and cold. Here we got fome bacon and fresh eggs for fupper, and the ale was good, which amufed us well enough till nine o'clock. We then proposed to play at cribbage for an hour, and called for a pack of cards; but they had none in the house, and we were obliged to divert ourselves with converfation,

verfation, till it was time to retire. Mifs Spence began in the following manner.

A difcourfe on

fluxions.

Was Newton, Sir, or Leibnitz, the author of that method of calculation, which lends its aid and affiftance to all the other mathematical sciences, and that in their greatest wants and diftreffes? I have heard a foreigner affirm, that the German was the inventor of fluxions.

That cannot be (I replied.) In the year 1696, Dr. Barrow received from Mr. Newton a demonstration of the rule of the quadrature of curves, which the Doctor communicated to Mr. Collins; and as this is the foundation of fluxions, and the differential calculus, it is evident Mr. Newton had invented the method before that time.

In the beginning of the year 1673, Leibnitz was in England, again in October 1676; and the interval of this time he spent in France, during which he kept a corref pondence with Oldenburgh, and by his means with 7. Collins; and fometimes alfo with Newton, from the laft of whom he received a letter, dated June 18, 1676, wherein is taught the method of reducing quantities into infinite feries, that is, of C 3 exhi

exhibiting the increments of flowing quantities. This method was utterly unknown to Leibnitz, before he received the abovefaid letter of Newton's, as he himself acknowledges in a letter to Oldenburgh, dated August 27, 1676; for before that time, he fays in his letter, he was obliged to transform an irrational quantity into a rational fraction, and then by division, after the method of Mercator, to reduce the fraction into a feries.

It is likewife certain, that Leibnitz did not then understand these feries, because, in the fame letter, he defires Newton would explain to him the manner how he got these feries. And again in a fecond letter from Newton to Leibnitz, dated Octo-· ber 24, 1676, he gives yet clearer hints of his method, and illuftrates it by examples, and lays down a rule, by which, from the ordinates of certain curves, their areas may be obtained in finite terms, when it is poffible.

By thefe lights, and affifted by fuch examples, the acute Leibnitz might have learned the Newtonian method.

It

It is plain he did fo; for in 1684, he first published, in the Leipfic Acts, his Elements of the Differential Calculus, without pretending to have had the method before the year 1677, the year he received the two letters from Newton: and yet, when Sir Ifaac publifhed his books of the number of curves of the first kind, and of the quadrature of figures, the editors of the Acts faid Leibnitz was the first inventor of the differential calculus, and Newton had substituted fluxions for differences, just as Honoratus Faber, in his Synopfis Geometrica, had fubftituted a progreffion of motion for Cavallerius's method of indivisibles; that is, Leibnitz was the first inventor of the method, Newton had received it from him (from his Elements of the Differential Calculus,) and had fubftituted fluxions for differences; but the way of inveftigation in each is the fame, and both center in the fame conclufions.

This excited Mr. Keil to reply; and he made it appear very plain from Sir Ifaac's letters, published by Dr. Wallis, that he (Newton) was the firft inventor of the algorith, or practical rules of fluxions; and Leibnitz did no more than publish the fame, with an alteration of the name, and manner of notation. This however did not filence Leibnitz, nor fatisfy the-foreigners who admired

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