A Mathematical and Philosophical Dictionary; Containing an Explanation of the Terms, and an Account of the Several Subjects, Comprized Under the Heads Mathematics, Astronomy, and Philosophy Both Natural and Experimental Volume 1
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1795 edition. Excerpt: ...ratio. Hence Hence also, in a series of continual proportionals, -the ratio of the first term to the third is double of the ratio of the first to the second, and the ratio of the ist to the 4th is triple of it, . and the ratio of the ill to the 5th is quadruple of it, and so on; that is, the exponents are double, triple, quadruple, &C, of the first exponent: as in the series 1, a, ar, a, a, &c; where the ratio 1 to az is double, of I to a3 ti iple, &c, of the ratio of 1 to a; or the exponent of a'-, a3, a, &c, double, triple, quadruple, &c, .of a. COMPOUND Intf.rit, called also Interest ujion Inteirjl, 13 that which is reckoned not only upon the principal, but upon the interest itself for bom, which thus becomes a soit of secondary principal. Ifbe the amount os I pound for 1 year, that is the sum of the principal and interest together for one year; then is /; the amount for 2 years, and r3 the amount for 3 years, and in general r% the amount for / years; that is r' is the sum or total amount os all the principals and interests together of 1 1. for the whole time or number of years t; consequently, if p be any other principal sum, forborn for / years, then its amount in that tiiiic at compound interest, is a = pi. 'The Rule therefore in words is this, to one pound add its interest for one year, or half year, or for the first time at which the interest is reckoned; raise the sum r to the power denoted by the time or number of terms; "then this power multiplied by the principal, or suit sum lent, will produce the whole amount. For example, To find how much 50I. will amount to in c years at 5 per cent, per annum, compound interest. Here the interest of 1 1. for 1 year is-cj, and therefore r = i-oc;hence the 5th power-of it for;...
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