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

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Printed for A. Millar & J. Nourse, 1748 - Mathematics - 356 pages
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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 135 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Page 82 - 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 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 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 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 121 - 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 134 - 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 1 - 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 10 - ... 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.

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