Algebra, with arithmetic and mensuration, from the Sansc. of Brahmegupta [the Gánitádhaya and Cuttacádhyaya] and Bháscara [the Vijagánita and Lílavatí] tr. by H.T. Colebrooke - Tapa blanda

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: ... and third; and lastly equal to the rest; the root comes out cl c2 c5 c.5. This, however, is wrong; for its square is ru 13 c 8 c 80 c 160. Defect then is imputable to those authors, who have not given a limitation to this method of finding a root. In the case of such irrational squares, the operation must be conducted by taking the approximate roots of the surd terms, and adding them to the rational terms: whence the square root is to be deduced.1 Largest is not rigidly intended (§ 40). Sometimes, therefore, the least is to be used. 52. Example. Say what is the root of a square, in which are the surds forty, eighty, and two hundred, with the rational number seventeen? Statement: ru 17 c40 c 80 c200. Subtracting the two last terms from the square of the rational number, the two portions found are c 10 cl. Again treating the smaller surd as a rational number, the result is c5 c2. Thus the root is c 10 c5 c 2. A rule of approximation for the square-root is given in the Chapter on Algebra, in the Sidd'hdnta-sundara of Jnya'na-ra'ja, cited by his son Su'ryada'sa; "The root of a near square, with the quotient of the proposed square divided by that approximate root, being halved, the moiety is a more nearly approximated root; and, repeating the operation as often as necessary, the nearly exact root is found." Example 5. This, divided by two which is first put for the root, gives § for the quotient: which added to the assumed root 2, makes-f; and this, divided by 2, yields-J for the approximate root.--Su'r. Repeating the operation, the root, more nearly approximated, is W-CHAPTER II. PULVERIZER 53--64. lRule: In the first place, as preparatory to the investigation of the pulverizer, the dividend, divisor, and additive quantity are, if practicab...