A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules and Operations. II. The Composition and Resolution of Equations of All Degrees; and the Different Affections of Their Roots. III. The Application of Algebra and Geometry to Each Other. To which is Added, an Appendix, Concerning the General Properties of Geometrical LinesF. Wingrave; T. Longman; W. Richardson; G. G. and J. Robinson; F. and C. Rivington; W. Lowndes; and Cadell and Davies., 1796 - 504 páginas |
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Página 24
... also called 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 . 2 Thus expresses the quotient of 2 ...
... also called 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 . 2 Thus expresses the quotient of 2 ...
Página 31
... also measure the dividend ; because the dividend is equal to the fum of the divifor multiplied into the quotient , and of the remainder added together * . Thus in the last example , ab measures the divifor a2 b2 , and the remainder ...
... also measure the dividend ; because the dividend is equal to the fum of the divifor multiplied into the quotient , and of the remainder added together * . Thus in the last example , ab measures the divifor a2 b2 , and the remainder ...
Página 34
... quotient must , by this Rule , be negative . Thus = a + - " = a - 2 . But 2 a ; Q4 and hence is expressed also by 6- with a negative exponent . It is alfo obvious that a but a a = It 34 PART I. A TREATISE of Of the Involution of quantities.
... quotient must , by this Rule , be negative . Thus = a + - " = a - 2 . But 2 a ; Q4 and hence is expressed also by 6- with a negative exponent . It is alfo obvious that a but a a = It 34 PART I. A TREATISE of Of the Involution of quantities.
Página 35
... also a — ˆ × a * = a − 6 ++ = a − 2 ( or —— ) ; and a ~ 3 × a1 = a ° = 1. And , in gene- = ral , any pofitive power of a multiplied by a nega- tive power of a of an equal exponent gives UNIT for the product ; for the pofitive and ...
... also a — ˆ × a * = a − 6 ++ = a − 2 ( or —— ) ; and a ~ 3 × a1 = a ° = 1. And , in gene- = ral , any pofitive power of a multiplied by a nega- tive power of a of an equal exponent gives UNIT for the product ; for the pofitive and ...
Página 36
... also , = ་ 3 ral , " I and ; therefore a ' : And , in gene- -3 = any quantity placed in the denominator of a fraction may be tranfpofed to the nume- rator , if the fign of its exponent be changed . " I Thus = 43 , and I 3 = a3 . $ 39 ...
... also , = ་ 3 ral , " I and ; therefore a ' : And , in gene- -3 = any quantity placed in the denominator of a fraction may be tranfpofed to the nume- rator , if the fign of its exponent be changed . " I Thus = 43 , and I 3 = a3 . $ 39 ...
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Página 88 - 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.
Página 431 - APM, cut a geometrical line of any order in as many points as it has dimensions, the product of the segments of the first terminated by P and the curve, will always be to the product of the segments of the latter, terminated by the same point and the curve, in an invariable ratio.
Página 426 - And by iimilar 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...
Página 43 - The general Theorem vhich 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...
Página 61 - 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.