A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules and Operations. II. The Composition and Resolution of Equations of All Degrees; and the Differents Affections of Their Roots. III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix, Concerning the General Properties of Geometrical LinesA. Millar and J. Nourse, opposite Katherine-Street in the Strand., 1756 - 432 sider |
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A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules ... Colin MacLaurin Uten tilgangsbegrensning - 1756 |
Vanlige uttrykk og setninger
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Populære avsnitt
Side 98 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Side 82 - Where the numerator is the difference of the produces of the oppofite Coefficients in the orders in which y is not found, and the denominator is the difference of the products of the oppofite coefficients taken from the orders that involve the two unknown quantities. For, from the firft equation, it is plain that ax — c — h,.
Side 133 - SS*1 — 50* + 24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Side 83 - ... coefficients taken from the orders in which z is not found ; and the denominator...
Side 18 - The divifer muft be ranged according to the dimenjions of the fame letters ; then you are to divide the firft term of the dividend by the firft term of the divifor, and to fet down the quotient* which, in this example, is a ; then multiply this quotient by the whole divifor, and...
Side 24 - Fractions ; and the dividend or quantity placed above the line is called the Numerator of the fraction, and the divifor or quantity placed under the line is called the Denominator...
Side 319 - AB, then fhall there be two values of y, as before, having contrary figns, that value which was pofitive before being now become negative, and the negative value being become pofitive. But if AD be taken ±= a, and P Comes to D, then the two values of y vanifh, becaufe da?
Side 139 - From the infpection of thefe equations it is plain, that the coefficients of the firft term is unit. The coefficient of the fecond term is the fum of all the roots (a, b, c , d, e) having their Jigns changed.
Side 142 - there are as many pofitive roots in any equation as there are changes in the figns of the terms 'from + to — , or from — to + ; and the remaining roots are negative.
Side 28 - Jhall give the numerator of the quotient. Then multiply the denominator of the dividend by the numerator of the divifor, and their produft Jhall give the denominator.