## 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 linesPrinted for J. Nourse, W. Strahan, J. F. and C. Rivingtons, W. Johnston, T. Longman, G. Robinson, and T. Cadell, 1779 - Mathematics - 504 pages |

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abscissa adeoque angle arise arithmetical progression asymptote autem biquadratic cafe CHAP coefficient common measure conic section contrary signs Corol cube root cubic equation curvæ curvam curvature dimensions divided divisor ducantur ducta ductæ eadem recta enim equa equal erit ex puncto example exponent fame manner fame right line flexure flexus fraction give given greater greatest harmonical mean hyperbola integer last term let be drawn linea lineæ locus meet the curve meet the line metical multiplied occurrat odd number parabola parallel points of contact positive Prop proposed equation punctum quadratic equation quæ quævis quotient rectæ remainder Rule secet second term simple equations square root substitute subtract suppose surd tangents tertii ordinis Theorems third order tion touching the curve transformed unknown quantity vanish whence

### Popular passages

Page 102 - 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 146 - 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 55 - After the fame manner, the cube root of a'+x' will be found to be § 56. " The general Theorem which we gave for the Involution of binomials will ferve alfo for their Evolution ;" becaufe to extract any root of a given quantity is the fame thing as to raife that quantity to a power whofe exponent is a fraction that has...

Page 3 - ... or which, being compared with another thing of the same kind, may be said to be greater or less than it, equal or unequal to it. Mathematics is the science or doctrine of quantity, which, being made up of parts, is capable of being made greater or less. It is increased by addition, and diminished by subtraction ; which are therefore the two primary operations that relate to quantity. Hence it is that any quantity may be supposed to enter into algebraic computations, two different ways, which...

Page 75 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.

Page 32 - Rule. Multiply the numerator of the dividend by the denominator of the divifor, their producl Jhall give the numerator of the quotient.

Page 43 - As the exponents of a thus decreafe, and at the fame time thofe of b increafe, " the fum of their exponents is always the fame, and is equal to the exponent of the power required.

Page 70 - Alfo, if all the terms in the equation are multiplied or divided by the fame quantity, it may be taken out of them all.

Page 87 - The numerator oí any of these equations, such as z, consists of all the different products, which can be made of three opposite- coefficients taken from the orders in which z is not found ; and the denominator consists of all the products that can be made of the three opposite coefficients taken from the orders which involve the three unknown quantities.

Page 12 - The negative multiplier, — b, indicates that a is to be taken as many times as there are units in b, but it is to be subtracted, rather than added.