Articles liés à An Elementary Treatise on Conic Sections and Algebraic...
Présentation de l'éditeur
Position of a point on a plane. Loci. Equations. 1. THE first and most obvious purpose for which Algebra may be applied toG eometry is the investigation of problems which concern the magnitude of lines or areas. The ordinary operations ofT rigonometry, in which lines are represented by algebraic symbols, will have already rendered the reader familiar with such investigations. It is not, however, to problems of this nature that we are now about to direct our attention. It was shewn by Descartes, that Algebra might be applied to express the position of points, and the form of curves and geometrical figures. It is upon this branch of the subject that we are now about to enter, and we shall confine ourselves to such points, lines, c. as may be supposed to lie in one plane, viz. that of the paper. 2. In ordinary A lgebra, we have been in the habit of considering the symbols +and as symbols of the reverse operations of addition and subtraction. But we may conceive of them in a much more general sense, as symbols of exactly opposite affections, and the use of them in elementary algebra will not be an exception to this definition, but a particular instance of it, inasmuch as a quantity to be added is exactly opposite in quality to one which is to be subtracted. We might easily multiply instances, in which it would be convenient to denote, by such symbols, opposite qualities which we have frequent occasion to express. Thus, let a mans property be a and his debts b; then we should say that the man is actually worth +a -b. If a be greater than 6, the p. c. s.
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