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These being turned into Numbers, and those duly collected, according as the Signs of the Equation direct, they will become 50680 — 223742 +223241 =1513, which being all divided by 2232 the Co-efficient of el, will be 106-ol=22D ,

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By what hath been already done about the Solution of these few Equations (being carefully observed) I presume the Learner will easily conceive how to proceed in the Solution of all kinds of Equations, be they never so high, or adfected ; therefore I shall not here propose many various Examples, but only take them as they fall in Course, when I come to the next Part, wherein you will (per haps) find fuch Equations with their Solutions as are not common.

in Cour faany various or adfected of all kinds

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Of Simple Interest, annuities, or Penfions, &c.

INTEREST, or the Use paid for the Loan of Money, is

either Simple; or Compound.

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SIMPLE Interest, is that which is paid for the Loan of any

Principal or Sum of Money, lent out for some Time, at any Rate per Cent : agreed on between the Borrower and the Lender; which, according the late Laws of England, ought to be fix Pounds for the Use of 100 l, for one Year, and twelve Pounds for the Ufe of 100 l. for two Years: and fo on for a greater, or leffer Sum, proportionable to the Time proposed.

There are several Ways of computing (or answering Questions about) Simple Intereft ; as by the single and double Rule of Three (See Page 96, &c.) others make Ufe of Tables composed at several Rates per Cent, as Sir Samuel Moreland, in his Doctrine of Interest, both simple and compound, all performed by Tables; wherein he hath detected feveral material Errors committed by Sir Ifaac Newton, Mr Kersey upon Wingate, and Mr Clavil, &c. in the Business of computing Interest, &c. by their Tables, too tedious to be here repeated. But I shall in this Tract take other Methods, and fbew that all Computations relating to Simple Interest are grounded upon Arithmetick Progreffion; and from thence raise such general Theorems, as will suit with all Cases. In order to that

P= any Principal or Sum put to Interest. Let

R= the Ratio of the Rate, per Cent, per Annum. a t = the Time of the Principal's Continuance at Intereit.

LA = the Amount of the Principal, and it's Interest, Note, The Ratio of the Rate, is only the Simple Interest of il. for one Year, at any given Rate; and is thus found. Viz. 100: 6 :: 1:0,06 = the Ratio at 6 per Cent. per Annum. Or 100: 7 :: 1:0,07 = the Ratio at 7 per Cent. &c. Again 100: 7,5:: 1:0,075 = the Ratio at 7 and į per Cent.

And if the given Time be whole Years; then t = the Num. ber of whole Years: but if the Time be given, be either pure Parts of a Year, or Parts of a Year mixed with Years; those Parts must be turned into Decimals; and then t = those Decimals, &c.

Now

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