A Treatise of Algebra: In Three Parts. ... To which is Added an Appendix, Concerning the General Properties of Geometrical Lines. By Colin Maclaurin, ...J. Nourse, W. Strahan, J. and F. Rivington, W. Johnston, T. Longman [and 3 others in London], 1771 - 432 pages |
Common terms and phrases
adeoque affumed afymptote alfo arifes arithmetical progreffion autem becauſe biquadratic cafe cafu CHAP coefficient common meaſure confequently contactus cube cube root cubic equation curvæ curvam curve demonftrated dimenfions diſcover divide divifor ducantur ducta eadem enim equa equal erit ex puncto expreffed expreffions fame manner fecet fecond term femper feries fhall fide figns fimple equations fince firft firſt flexus fome fquare root fraction fubftitute fubtract fuch fuppofe furd give greateſt impoffible interfection laft term laſt leaft lefs linea lineæ locus metical multiplied muſt negative obferve occurrat odd number parabola parallela pofed pofitive poſitive propofed equation punctum quadratic equation quæ quævis quotient recta rectæ refolved refpectively refult repreſent Rule ſhall ſquare ſubſtitute ſuppoſed tangentes tertii ordinis thefe theſe thofe thoſe tion unknown quantity vaniſh whence whofe roots whoſe
Popular passages
Page 127 - 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 befides...
Page 18 - 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 13 - If there is a remainder, you are to proceed after the fame manner till no remainder is left ; or till it appear that there will be always fome remainder. Some Examples will illuftrate this operation. EXAMPLE I.
Page 75 - Where the numerator confifts of all the different products that can be made of three oppofite coefficients taken from the orders in which z is not found ; and the denominator confifts of all the...
Page 4 - If there are more than two quantities to be added together, firft add the pofitive together into one fum, and then the negative (by Cafe I.) Then add thefe two fums together (by Cafe II.) to A TREATISE of EXAMPLE. Parti. -f 8a - 7" + 100 . — 124 Sum of the pofitive . . . + 1 8a Sum of the negative ... — iga Sum of all — a Cafe III.
Page 187 - ... will give a positive result. But if the degree be odd, the result will be negative. 246. The substitution of the natural series, 0, 1, 2, 3, &c., taken negatively as well as positively, will enable us to discover the position, and determine, in general, the initial figure of the real roots. Ex. 1. Let it be required to find one of the roots of the equation x* — 4.x2 — Gz-f- 8— 0.
Page 22 - Rule. Multiply the numerator of the dividend by the denominator of the divifor, their produit ¡hall give the numerator of the quotient. 'Then multiply t be denominator of the' dividend by the numerator of the divifor, and their predu£f jhall give the denominator.
Page 74 - Where the numerator is the difference of the products of the opposite coefficients in the order in which y is not found, and the denominator is the difference of the products of the opposite coefficients taken from the orders that involve the two unknown quantities. Coefficients are of the same order which either affect no unknown quantity, as c anil ci ; or the same unknown quantity in the different equations, as a and o'.