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 38
... follows . X a + b Root . xa + b a2 + ab ++ + ab + b2 a2 + 2ab + b2 = the Square or 2d Power . + ox b a3 + 2a2b + 290 + a2b + 2ab2 + b3 a2 + 3a2b + xa + b zab2 + b = Cube or 3d Power . a + + 3a3b + + ab + zab2 + abs 3a2b2 + 3ab3 + b + a ...
... follows . X a + b Root . xa + b a2 + ab ++ + ab + b2 a2 + 2ab + b2 = the Square or 2d Power . + ox b a3 + 2a2b + 290 + a2b + 2ab2 + b3 a2 + 3a2b + xa + b zab2 + b = Cube or 3d Power . a + + 3a3b + + ab + zab2 + abs 3a2b2 + 3ab3 + b + a ...
Página 41
... follows therefore by these last rules , that m a + b a " + ma " -1 b + m x = m - I 2 xam - 262 M - I + m x X m - 2 3 MI × a " -3 b3 + m x 3 2 m - 2 m - 3 X X 3 4 × at −4 b4 + & c . which is the general Theorem for railing a quantity ...
... follows therefore by these last rules , that m a + b a " + ma " -1 b + m x = m - I 2 xam - 262 M - I + m x X m - 2 3 MI × a " -3 b3 + m x 3 2 m - 2 m - 3 X X 3 4 × at −4 b4 + & c . which is the general Theorem for railing a quantity ...
Página 78
... 3y 2 - 32 3d 12 — y − z = 20 - value . 23-32 ЗУ 1 2 — y — z = 18 - 32 These two laft equations involve only y and z , and are to be refolved , by Direction 3 , as follows . - 2y — y + 32 — Z = 20 2y 78 PART J. A TREATISE of.
... 3y 2 - 32 3d 12 — y − z = 20 - value . 23-32 ЗУ 1 2 — y — z = 18 - 32 These two laft equations involve only y and z , and are to be refolved , by Direction 3 , as follows . - 2y — y + 32 — Z = 20 2y 78 PART J. A TREATISE of.
Página 100
... follows that d is also prime to b : that is , dis prime to a number which it mea- fures , which is abfurd . 102. It follows from the laft article , that if a and c are prime to each other , then a ' will be prime to c : For by fuppofing ...
... follows that d is also prime to b : that is , dis prime to a number which it mea- fures , which is abfurd . 102. It follows from the laft article , that if a and c are prime to each other , then a ' will be prime to c : For by fuppofing ...
Página 101
... follows , that if a and c are prime to each other , then shall a2 be prime to c ' , by fuppofing , in the laft , that ab , and cd . It is alfo evident that a3 will be prime to c , and in general any power of a to any power of whatsoever ...
... follows , that if a and c are prime to each other , then shall a2 be prime to c ' , by fuppofing , in the laft , that ab , and cd . It is alfo evident that a3 will be prime to c , and in general any power of a to any power of whatsoever ...
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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.