A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and operations. The composition and resolution of equations of all degrees; and the different affections of their roots. The application of algebra and geometry to each other. To which is added, an appendix, concerning the general properties of geometrical lines. I.. II.. III. |
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abfciffa adeoque affumed afymptote alfo arife autem becauſe biquadratic cafe cafu coefficient confequently conic fection contactus Corol cube cubic equation curvæ curvam curvaturæ demonftrated dimenfions divifor ducantur ducta ductæ enim equa equal erit eritque ex puncto expreffed fame manner fecet fecond term fegments femper feries fhall fide figns fimple equations fince firft firſt flexus fome fquare fubftituting fubtract fuch funt fuppofe furd greateſt harmonical mean hyperbola impoffible interfections laft term laſt lefs linea locus meaſure metical multiplied muſt negative occurrat parabola parallel pofitive progreffion PROP propofed equation punctum quadratic equation quæ quotient recta rectæ refpect refult right line roots ſhall ſubſtitute ſuppoſe tangentes tertii ordinis thefe theſe thofe tion touching the curve vaniſh whence whofe whoſe
Popular passages
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 4 - Hence it is, that any quantity may be fuppoled to enter into algebraic computations two different ways which have contrary effects ; either as an increment or as a decrement -, that is, as a quantity to be added or as a quantity to be fubtrafted.
Page 86 - ... fquare. 4. Extraft the fquare root from both fides of the equation ; which you will find, on one fide, always to be the unknown quantity with half the forefaid coefficient...
Page 49 - ... be the firft member of the root required. Then raife this root to a dimenfion lower by unit than the number that denominates the root required, and multiply the power that arifes by that number itfelf. Divide the fécond term of the given quantity by the product, and the quotient mail give the fécond member of the root required.
Page 114 - When the square root of a surd is required, it may be found, nearly, by extracting the root of a rational quantity that approximates to its value. Thus, to find the square root of 3 + 2^/2, first calculate v/ 2 = 1,41421.
Page 172 - ... m is fuppofed to furpafs all the values of x, and confequently m — x (— y} muft always be affirmative. And by this means, any equation may be changed into one that jkall have all its roots affirmative...
Page 144 - Xx + bXx+cxx + d, &c. = o, will exprefs the equation to be produced ; all whofe terms will plainly be pofitive ; fo that " -when all the roots of an equation are negative, it is plain there will be no changes in the Jigns of the iermt of that equation
Page 135 - 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 19 - 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 438 - And by fimilar equations geometrical lines of fuperior orders are defined. ^2. A geometrical line may meet a right line in as many points as there are units in the number which denotes the order of the equation or line, and never in more. The number of times that any curve will meet its...