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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. 1761 Excerpt: ...he travels over a series of miles in arithmetical progress1on, whereof the number of terms is 3, the greatest term 3, and the least term 1 j in four four days he travels over a series whereof the number of terms is 4, the greatest term 4., and the least 1; therefore univerfally, in any number x of days, he must travel over a series of miles in arithmetical progreffion, whereof the number or terms is x, the greatest term, and the least term 1; but the sum of the extremes of this series is x+1, which multiplied by x the number of terms, gives xx+x, the half vv---x whereof is;therefore by the lemma foregoing, xx--x will be the sum of this series, and consequently the miles travelled by A before he was overtaken: again, if A travels x days, B must have travelled x--5 days, which at the rate of 12 miles a day, gives 12--60 for the miles travelled by B when he overtook A; but as they both set out from the fame place, and are now got together, they must have travelled the fame number of miles; whence we have XX.-x this equation, -=12--60; therefore xx+xzz 24x--120; therefore xxzzzx--120; compare this equation with the general one in art. 103, and yqu w1ll have A--1, Bzz2C----120, = 529, 4AC B+s-B--s =--480, -=4o, j = 7, ----=15----zz8;there %A 2/t fore x--8, or 15: now for the better application of these roots to the solution of this problem, it must be observed, that the problem is mere limited than the equation deduced from it; just as if, in translating out of one language into another, the terms of the latter, instead of being adequate to those of the former, should be found to be of a more extensive signification: in the problem it is only suppofed that B pvertakes A, whereas in the equation it is supposed that A and B are got both together by...

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