Synopsis
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. 1787 Excerpt: ...Ans. 10100 yds. or 5 miles, 1300 yds. PART II. THE ARITHMETIC)-ALGEBRAICAL LANGUAGE. C HAPTER L THE NATURE OF THIS LANGUAGE, AND DIVISION OF QUESTIONS BELONGING TO IT. I. The Nature of the Aritbmetico-Algebraical Language. TH E arithmetico-algebraical language is an appli cation of the analytical art to the resolution of those questions where the quantities are expressed by numbers, and their magnitude alone is to be considered. The The tmatyticai art, rtfihttim, Ot anulysis, generally speaking, is the method of proceeding from the thing fought or taken for granted through its consequences to something that is really granted: but here it is strictly considered as a method of investigating quantities that are unknown, from certain given relations to each other, and to such as are known; which relations being almost universally either that of equality, or such as may be reduced to that of equality, are expressed by equations representing more conveniently and more distinctly the conditions of the question when tranflated out of common language into the arithmetico-algebraical; and because these equations must contain one or more unknown quantities, the principal business of this language will be the deducing final equations containing only one unknown quantity and resolving them. Hence the nature of this language is all comprehend ed in the following General Principle. The unknown quantities in the question proposed must be expressed by letters-, and the relations of the known and unknown quantities contained in it, or the conditions of it as they are called, must be expressed by equations. These-equations being resolved by their proper rules, will give the answer of the question. II. Division of Questions.. The division of questions arises from four differen...
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