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. 1855 Excerpt: ...frequently occur, in which it is required to determine under what circumstances the result of certain arithmetical operations performed upon numbers will be the greatest or least possible. We shall resolve a few questions of this kind the solutions of which depend upon equations of the second degree. 1. To divide, a ...
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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. 1855 Excerpt: ...frequently occur, in which it is required to determine under what circumstances the result of certain arithmetical operations performed upon numbers will be the greatest or least possible. We shall resolve a few questions of this kind the solutions of which depend upon equations of the second degree. 1. To divide, a number, 2a, into two parts such, that the product of these parts may be a maximum. Let x be one of the parts, then 2 a--x will be the other, and their product will be x(2a--x). By assigning different values to x, the product x(2a--x) will vary in magnitude, and the question is to assign to x a value such, that this product may be the greatest possible. Let m be the maximum sought, we have by the question x (2a--x) = m. Regarding for the moment m as known, and deducing from this equation the value of x, we have x = a /ai--m. '.' From this result it appears, that in order that x may be real, m must not exceed a3; the greatest value of m will therefore be a2, in which case we have x = a. Thus to obtain the greatest possible product, the proposed must be divided into two equal parts, and the maximum obtained will be equal to the square of one of these parts. In the equation x(2a--x) = m, the expressions x (2 a--x) is called a function of x. This function is itself a variable, the value of which depends upon that given to the first variable or x. 2. To divide a number, 2a, into two parts such, that the sum of the square roots of these parts may be a maximum. Let x1 be one of the parts, then 2a--x will be the other, and the sum of the square roots will be x-j-2 a--x. Let m be the maximum sought, we" have by the question x ] /2a--? = --; X-'Mc:: from which we obtain--L-X ' "-m / m2. 2a--To3 x==2 V T + or simplifying x = ...
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Seller's Description:
Good. 1861 edition. Ex-library copy with usual markings. Rebacked spine, cover shows heavy wear and tear, edgewear and rubbing. Some writing in the prelims. Pages with minor scattered staining. Very Clean Copy-Over 500, 000 Internet Orders Filled.
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Seller's Description:
Fair. Book Significant age wear, including dampstaining, warping and waving. A reference copy only. Author was contemporary professor at Bowdoin College with Civil War General Joshua Chamberlain.
