## 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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### Common terms and phrases

adeoque æqualis alſo arife aſſumed autem becauſe Biquadratic Cafe cafu CHAP Coefficient common Meaſure Conic Section conſequently contactus contingentes Corol Cube Root Cubic Equation curvæ curvam curvaturæ Curve demonſtrated deſcribe Dimenſions diſcover divided Diviſor ducantur ducta ductæ eadem recta enim Equa equal erit eritque eſt ex puncto Exponent expreſſed Expreſſions fame Manner fince firſt Term flexus flexus contrarii Fraction fubtract funt give greater hæc impoſſible integer Interfections itſelf laſt Term leſs Linea Lineæ tertii Ordinis Locus multiplied muſt mutuo negative Number obſerve occurrat Parabola parallela poſed poſitive Power Product Progreſſion propoſed Equation punctis punctum Quadratic Equations quæ Quotient recta quævis rectæ rectis refolved repreſent reſpect Reſult Rule ſame ſecond Term ſemper ſhall Signs ſimple ſince ſome Square ſquare Root ſtrait Line ſubſtituting ſuch ſuppoſe Surd tangentes theſe thoſe tion unknown Quantity Value vaniſh whence whoſe Roots

### Popular passages

Page 94 - 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 131 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...

Page 78 - 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'.

Page 20 - 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 15 - 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 140 - 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 117 - B, the Sum of the Terms in the even Places, each of which involves an odd Power of y will be a rational Number multiplied into the Quadratic Surd I/?2.

Page 130 - And after the same manner any other equation admits of as many solutions as there are simple equations multiplied by one another that produce it, or as many as there are units in the highest dimensions of the unknown quan tity in the proposed equation.

Page xi - BRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpofe, and found convenient. It is called an UNIVERSAL ARITHMETICK, and proceeds by Operations and Rules fimilar to thofe in Common A* rithmetick, founded upon the fame Principles.

Page 6 - ... 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.