A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 6-10 of 60
Page 79
... equivalent form of ( 50 ) , when ( 51 ) is put into the form F ( x , y , z ) = 0 ? From ( 52 ) we have ( d ) dr dr dr dx + dy + dz = 0 ; dr ཝུ ། ཙེ་ dr dy dr dy dr dz dz and substituting these in ( 50 ) , we have dr ( ) P + Q + R dx dy ...
... equivalent form of ( 50 ) , when ( 51 ) is put into the form F ( x , y , z ) = 0 ? From ( 52 ) we have ( d ) dr dr dr dx + dy + dz = 0 ; dr ཝུ ། ཙེ་ dr dy dr dy dr dz dz and substituting these in ( 50 ) , we have dr ( ) P + Q + R dx dy ...
Page 86
... equivalents given in Art . 50 , the result is ( 76 ) , as it ought to be . And if ( 66 ) is cast into the more symmetrical form y - b 2 - c x u = F " 2 - c x - a ' y- ( 77 ) we shall get the same result , viz . ( 76 ) , by the following ...
... equivalents given in Art . 50 , the result is ( 76 ) , as it ought to be . And if ( 66 ) is cast into the more symmetrical form y - b 2 - c x u = F " 2 - c x - a ' y- ( 77 ) we shall get the same result , viz . ( 76 ) , by the following ...
Page 105
... Equivalent expression of ( cos x ) " , in terms of the cosines of the multiple arcs . To abbreviate the notation , let us substitute as follows : ex√ = 1 = 2 , e - x√ - 1 emx √ I = zm 1 = ... e - mx √ - I 1 = ( 41 ) PRICE , VOL . I ...
... Equivalent expression of ( cos x ) " , in terms of the cosines of the multiple arcs . To abbreviate the notation , let us substitute as follows : ex√ = 1 = 2 , e - x√ - 1 emx √ I = zm 1 = ... e - mx √ - I 1 = ( 41 ) PRICE , VOL . I ...
Page 107
... Equivalent expression of ( sin x ) " in terms of the sines and cosines of the multiple arcs . By ( 43 ) , Art . 62 , we have 2√1 sin x = : . 2 " ( − 1 ) % ( sin ) " = ( -- ) ... = z " — nzn − 2 + n ( n - 1 ) zn- 1.2 ( - ) " - 2 n ( n ...
... Equivalent expression of ( sin x ) " in terms of the sines and cosines of the multiple arcs . By ( 43 ) , Art . 62 , we have 2√1 sin x = : . 2 " ( − 1 ) % ( sin ) " = ( -- ) ... = z " — nzn − 2 + n ( n - 1 ) zn- 1.2 ( - ) " - 2 n ( n ...
Page 118
... equivalent is derived from f ' ( x ) , on the dx2 ' supposition that a is the equicrescent variable ; d3y dx3 f ( x ) , or its equivalent is derived from ƒ " ( x ) , on the same supposition ; dry dxn and f " ( x ) = is derived from fa ...
... equivalent is derived from f ' ( x ) , on the dx2 ' supposition that a is the equicrescent variable ; d3y dx3 f ( x ) , or its equivalent is derived from ƒ " ( x ) , on the same supposition ; dry dxn and f " ( x ) = is derived from fa ...
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a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero