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 156
... 39. So that the propofed cubic 3 will be transformed into an equation wanting the third term by fuppofing y = x- 3 J - 37 or y = x - p + √ p2 3 39 If the propofed equation is of n dimenfions , the If 156 A TREATISE of PART II .
... 39. So that the propofed cubic 3 will be transformed into an equation wanting the third term by fuppofing y = x- 3 J - 37 or y = x - p + √ p2 3 39 If the propofed equation is of n dimenfions , the If 156 A TREATISE of PART II .
Página 157
... transformed , as in the fecond article of this chapter . The fifth term may be taken away by folving a biquadratic ; and after the fame manner the other terms can be exterminat- ed if there are any . 29. There are other tranfmutations ...
... transformed , as in the fecond article of this chapter . The fifth term may be taken away by folving a biquadratic ; and after the fame manner the other terms can be exterminat- ed if there are any . 29. There are other tranfmutations ...
Página 158
... transformed equation ; and the following coefficients are produced by the following coefficients of the proposed equa- tion ( as q , r , & c . ) multiplied into the powers of ƒ ( ƒ3 , ƒ3 , & c . ) Therefore , " to transform any equation ...
... transformed equation ; and the following coefficients are produced by the following coefficients of the proposed equa- tion ( as q , r , & c . ) multiplied into the powers of ƒ ( ƒ3 , ƒ3 , & c . ) Therefore , " to transform any equation ...
Página 159
... transformed into the equation y3 3 y3 - - 13y2 + 14 × 3 × y + 16 × 9 = 0 , or 13y2 + 42y + 144 ≈ 0 . Then finding ... transforming the equation . into one that fhall have unit for the coefficient of the highest term , you find y3 - nep ...
... transformed into the equation y3 3 y3 - - 13y2 + 14 × 3 × y + 16 × 9 = 0 , or 13y2 + 42y + 144 ≈ 0 . Then finding ... transforming the equation . into one that fhall have unit for the coefficient of the highest term , you find y3 - nep ...
Página 161
... transformed into the leaft root in the other . " For fince x = I and y = — , it is plain that when the value of x x is greateft , the value of y is least , and con- verfely . How an equation is transformed fo as to have all its roots ...
... transformed into the leaft root in the other . " For fince x = I and y = — , it is plain that when the value of x x is greateft , the value of y is least , and con- verfely . How an equation is transformed fo as to have all its roots ...
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adeoque affumed afymptote alfo alſo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently conic fection contactus Corol cube cubic equation curvæ curvam curvature demonftrated dimenfions divided divifor drawn ducantur ducta enim equa equal erit expreffed fame manner fame right line fecond term feries fhall fide figns fimple equations fince firft firſt flexus fome fquare root fubftitute fubtract fuch fuppofe furd greateſt harmonical mean impoffible interfections laft term laſt leaft lefs lineæ locus meet the curve metical multiplied muſt negative occurrat parallel pofitive PROP propofed equation puncto punctum px² quadratic equation quæ quævis quotient recta rectæ refolved refult Rule ſhall ſuppoſe tangents tertii ordinis thefe theſe third order thofe tion touching the curve unknown quantity vaniſh whence whoſe
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