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their fellows.

derstanding, in which they far excelled These girls were carefully instructed by Azora and Antonia, and beside being taught the fine works of the needle, learned musick, and the elements of the mathematics from the ladies. The eldeft of these girls was but twenty, and the youngest eighteen, and they all furprised me very greatly with their quickness in anfwering very hard arithmetical questions. They could not only add, fubtract, multiply, divide, find a fourth proportional, and extract roots of every kind, with exactness and readiness, and apply them upon all common occafions; but, were perfect in fractions vulgar and decimal. They had even gone as far in algebra as the refolution. of fimple equations.

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Finding them one morning at figures, I afked the youngest of them, what was the number that of it with 4 over, amounted to the fame as of it with 9 over? She immediately tranflated the question from common language into algebra 3*+4=1= +9, and quickly difcovered the unknown quantity to be x=60: Then she took it in finthetically, of 60=40+4=44: of 6035+9=44. -- (Sinthetically is tracing property from number:-Analetically is tracing number from property.) B 6

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This made me wonder very greatly. I afked another of them, if the bought 20 loaves for 16 pence, all of them two-penny, penny, and farthing ones how many would fhe have of each? She anfwered, 5 two-penny loaves, 3 penny ones, and 12 farthing loaves; for the equations were x +y+z20 and 8x+4y=x=64. From whence by fubtraction, 7x+3y=44, and of consequence, y=447*14—2+2

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I afked a third, how many ways the could pay 201. in piftoles, guineas, and moidores, at 17 s. 21s. and 27 s. the piftole, the guinea, and the moidore?

She replied in a very little time, 9 ways, to wit, 11 piftoles, 5 guineas, and 4 moidores-8 piftoles, 1 guinea, 9 moidores8 piftoles, 10 guineas, 2 moidores-17 piftoles, 4 guineas, I moidore-2 piftoles, 2 guineas, 12 moidores-2 piftoles, 11 guineas, 5 moidores-5 piftoles, 6 guineas, 7 moidores-5, 15, 0- and 14 piftolés, o guineas, 6 moidores. This was a hard operation.

I asked another of thefe young women, if her lady gave her 297 guineas and 339 piftoles, to pay 6 men a hundred pounds a-.. piece in guineas and. piftoles only, as was agreed,

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agreed, how could fhe contrive to pay them, and dispatch the thing? I will tell you, Sir, (she answered) very foon. x represents my guineas, and y my pistoles, and 21 +173 2000, of confequence, x95+172; &c. and quickly difcovered, that the first man fhould have 92 guineas and 4 pistoles :—the second man, 75 guineas and 25 pistoles:-the third, 58 guineas, 46 pistoles:the fourth, 41 guineas and 67 pistoles :-the fifth, 24 guineas and 88 piftoles:-and the fixth man, 7 guineas and 109 piftoles. This was admirable. But is there no other way, I faid, of pay-. ing 1001. in guineas and piftoles, befides the fix ways you have mentioned? There is no other way (the fine girl answered). If a seventh man was to be paid 10ol. in thefe two kinds of money, he must be paid in one of thefe fix methods. This was true. I was charmed with what I had heard.

While I was thus engaged with the maids, Azora and Antonia came into the room, and finding how I had been employed, they began to talk of problems, theorems, and equations, and foon convinced me, that I was not fuperior to them in this kind of: knowledge: though I had ftudied it for a much longer time, and had taken more pains

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pains than ever they did. Their fine understandings faw at once the things that had made me fweat many an hour, and in lefs time than I required for an operation, they could answer the most difficult queftions, and do any thing in fimple quadratic equations, and in the compofition and refolution of ratios. This I thought very wonderful; especially as they had been taught no longer than one year by Mr. Burcot; and that they had acquired the most abstruse part of their knowledge by their own application.--I note the thing down as one of the strangest and most extraordinary cafes that ever came in my way; perhaps, that ever was heard. It is fuch a fpecimen of female understanding, as must for ever knock up the pofitive affertions of fome learned men, who will not allow that women have as ftrong reafoning heads as the men.

An obfervation relative to the underftanding of

avomen.

By the way, I obferve, exclufive of these two ladies, that I have seen many of the fex who were distinguished for accuracy and comprehenfivenefs, not only in the fcience, where known and required qualities are denoted by letters, but in other fine parts of learning. I have little right to pretend to any thing extraordinary

in understanding, as my genius is flow, and fuch as is common in the lower claffes of men of letters; yet, my application has been very great: my whole life has been spent in reading and thinking: and nevertheless, I have met with many women, in my time, who, with very little reading, have been too hard for me on feveral fubjects. In juftice, I declare this; and am very certain from what I have heard numbers of them fay, and feen fome of them write, that if they had the laboured education the men have, and applied to books with all poffible attention for as many years as we do; there would be found among them as great divines as Epifcopius, Limborch, Whichcote, Barrow, Tillotson, and Clarke; and as great mathematicians, as Maclaurin, Saunderfon, and Simpson. The critics may laugh at this affertion; I know they will: and, if they please, they may doubt my veracity as to what I relate of the two ladies, and the ten young women, in Burcot-Hamlet; but what I fay is true, notwithstanding. Facts are things too ftubborn to be deftroyed by laughing and doubting.

As to the ladies I have mentioned, they both did wonders in fpecious arithmetic; but Azora was the brightest of the two,

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