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be glorious creatures then. Every family would be happy.

me :

But as to Miss Spence, this knowledge, with a faultless person, and a modesty more graceful than her exquisite beauty, were not the things that principally charmed

nor was it her conversation, than which nothing could be more lively and delightful: nor her fine fortune. It was her manners.

She was a Christian Deift, and considered Benevolence and Integrity as the essentials of her religion. She imitated the piety and devotion of Jesus Christ, and worshipped his God and our God, his Father and our Father, as St. John expressly stiles the God of Christians, xx. 17. She was extremely charitable to others, and confidered conscious virtue as the greatest ornament and most valuable treasure of human nature, Excellent Maria!

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8. With this young lady, The author's de and her two servants (her parture from footman and her woman,) I Cleator for. Lonwent up to London. We set don, July 31

17313 out from Cleator the 31st day of July, and without meeting with any milchiefs in all that long way, came safe to London. We were nine days on the road; and as the weather was fine, and our horses

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excellent, we had a charming journey. My companion was so 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 seem tirefore and tedious to him that travelled with her. Her notions and remarks were ever lively and instructive. It was

vast pleasure to hear her, even on the driest , and most abstruse subjects, on account of

the admiration her discourse raised, and the fine knowledge it communicated, to one who understood her. I will give an instance.

$. 7. In riding over the mountains the first day, we missed the road in the evening, and instead of getting to a very good inn, where we intended to rest, we were forced to stop at a poor little public house, and right glad to get in there, as the evening was tempestuous and wet, dark and cold. Here we got some bacon and fresh eggs for supper, and the ale was good, which amused 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 con.

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versation, till it was time to retire.' Miss Spence began in the following manner.

Was Newton, Sir, or Leib

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fluxions. thod of calculation, which lends its aid and assistance to all the other mathematical sciences, and that in their greatest wants and distresses ? 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.

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In the beginning of the year 1673, Leibnitz was in England, again in O&tober 1676; and the interval of this time he spent in France, during which he kept a correspondence with Oldenburgh, and by his means with 7. Collins, and sometimes also with Newton, from the last of whom he received a letter, dated June 18, 1676, wherein is taught the method of reducing quantities into infinite series, that is, of

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exhibiting the increments of flowing, quantities. This method was utterly unknown to Leibnitz, before he received the abovesaid letter of Newton's, as he himself acknowledges in a letter to Oldenburgh, dated August 27, 1676; for before that time, he says 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 series.

It is likewise certain, that Leibnitz did not then understand these series, because, in the same letter, he desires Newton would explain to him the manner how he got these series. And again in a second letter from Newton to Leibnitz, dated O&to- · ber 24, 1676, he gives yet clearer hints of his method, and illustrates 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 these lights, and assisted by such examples, the acute Leibnitz might have learned the Newtonian method.

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It is plain he did fo ; for in 1684, he first published, in the Leipfic Asts, 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 Isaac published his books of the number of curves of the first kind, and of the quadrature of figures, the editors of the Aets said Leibnitz was the first inventor of the differential calculus, and Newton had substituted fluxions for differences, just as Honoratus Faber, in his Synopsis Geometrica, had substituted a progression 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 substituted fuxions for differences; but the way of investigation in each is the same, and both center in the same conclusions.

This excited Mr. Keil to reply; and he made it appear very plain from Sir Isaac's letters, published by Dr. Wallis, that he (Newton) was the first inventor of the algorith, or practical rules of Auxions; and Leibnitz did no more than publish the same; with an alteration of the name, and manner of notation. This however did not silence Leibnitz, nor satisfy the foreigners who ad

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