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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... ad Specimen Comment . in Arith . Uni- + Viz . The finding of Divisors , and the evolution of Binomial Surds . See $ 59-72 . Part II . § 127. Part I. A 4 What What this learned Profeffor fo earnestly wished for , we 1 TO THE READER .
... ad Specimen Comment . in Arith . Uni- + Viz . The finding of Divisors , and the evolution of Binomial Surds . See $ 59-72 . Part II . § 127. Part I. A 4 What What this learned Profeffor fo earnestly wished for , we 1 TO THE READER .
Página 18
... a ; then mul tiply this quotient by the whole divisor , and sub- tract the product from the dividend , and the re- mainder fhall give a new dividend , which in this example is ab + b2 . a + b a + b ) a2 + 2ab + b2 ( 18 A TREATISE of PART I.
... a ; then mul tiply this quotient by the whole divisor , and sub- tract the product from the dividend , and the re- mainder fhall give a new dividend , which in this example is ab + b2 . a + b a + b ) a2 + 2ab + b2 ( 18 A TREATISE of PART I.
Página 118
... divisor , C r + and let the quotient be s , and let — in the 25 nearest integer number be t , fo fhall the root required be -n if the c root of Vē A + B can be extracted . EXAMPLE - I. Thus to find the cube root of 968 + 25 ,, we have A ...
... divisor , C r + and let the quotient be s , and let — in the 25 nearest integer number be t , fo fhall the root required be -n if the c root of Vē A + B can be extracted . EXAMPLE - I. Thus to find the cube root of 968 + 25 ,, we have A ...
Página 197
... DIVISORS . § 62. Ta $ 62.0 find the roots of an equation is the same thing as to find the simple equal tions , by the multiplication of which into one another it is produced , or to find the fimple equations that divide it without a ...
... DIVISORS . § 62. Ta $ 62.0 find the roots of an equation is the same thing as to find the simple equal tions , by the multiplication of which into one another it is produced , or to find the fimple equations that divide it without a ...
Página 210
... divisors of the laft terms , we may confider one of them ( viz . 1 ) as known ; and in order to find m or k , we need only compare the terms of this equation with the terms of the propofed equation refpec- tively , which gives , 1o . k ...
... divisors of the laft terms , we may confider one of them ( viz . 1 ) as known ; and in order to find m or k , we need only compare the terms of this equation with the terms of the propofed equation refpec- tively , which gives , 1o . k ...
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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...
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