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 Lines |
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Common terms and phrases
adeoque affumed afymptote alfo arife arithmetical progreffion autem becauſe biquadratic cafe cafu CHAP coefficient common meaſure confequently contactus cube root cubic equation curvæ curvam curvaturæ curve demonftrated dimenfions diſcover divide divifor ducantur ducta ductæ enim equa equal erit ex puncto expreffed expreffions fame manner fecond term feries fhall fide figns fimple equations fince firft firſt firſt term flexus fome fquare root fraction fubftitute fubtract fuch fuppofe furd give greateſt impoffible interfection laft term laſt leaft lefs linea lineæ locus metical muft multiplied muſt negative occurrat odd number parabola parallela pofed pofitive poſitive propofed equation punctum px² quadratic equation quæ quævis quotient recta rectæ refolved refult repreſent reſpect Rule ſhall ſquare ſubſtitute ſuppoſe tangentes tertii ordinis thefe theſe thofe thoſe tion unknown quantity vaniſh whofe roots whoſe
Popular passages
Page 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.
Page 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,.
Page 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...
Page 83 - ... coefficients taken from the orders in which z is not found ; and the denominator...
Page 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...
Page 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...
Page 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?
Page 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.
Page 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.
Page 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.