Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bhascara. Transl. by Henry-Thomas Colebrooke (Paperback)

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. 1817 Excerpt: ...for the approximate root.--Sun. Repeating the operation, the root, more nearly approximated, is WO CHAPTER II. PULVERIZER.' 53--64. 1Rule: In the first place, as preparatory to the investigation of the pulverizer, the dividend, divisor, and additive quantity are, if practicable, to be reduced by some number.5 If the number, by which the dividend and divisor are both measured, do not also measure the additive quantity, the question is an ill put or impossible one.4 54--55--56. The last remainder, when the dividend and divisor are mutually divided, is their common measure/ Being divided by that common This is nearly word for word the same with a chapter in the LUdvati on the same subject. (Lil. Ch. 12.) See there, explanations of the terms. The method here taught is applicable chiefly to the solution of indeterminate problems that produce equations involving more than one unknown quantity. See ch. 6. Ten stanzas and two halves. If the dividend and divisor admit a common measure, they must be first reduced by it to their least terms; else unity will not be the residue of reciprocal division; but the common measure will; (or, going a step further, nought.)--Ga'n. on LU. Crishn. on Vij. 4 If the dividend and divisor have a common measure, the additive also must admit it; and the three terms be correspondently reduced: for the additive, unless it be nought or else a multiple of the divisor, must, if negative, equal the residue of a division of the dividend taken into the multiplier by the divisor; and, if affirmative, must equal the complement of that residue to the divisor. Now, if dividend and divisor be reducible to less terms, the residue of division of the reduced terms, multiplied by the common measure, is equal to the residue of division of the unreduced t...