A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 6-10 of 19
Page 314
... hyperbola at which the tangent is drawn ; the equations to the hyperbola and the tangent are respectively x ' x22 — y'2 = a2 , - xx - yy = a2 ; whence the equation to op is y = - y ; ( 19 ) ( 20 ) X У = ; y ( 21 ) and multiplying each ...
... hyperbola at which the tangent is drawn ; the equations to the hyperbola and the tangent are respectively x ' x22 — y'2 = a2 , - xx - yy = a2 ; whence the equation to op is y = - y ; ( 19 ) ( 20 ) X У = ; y ( 21 ) and multiplying each ...
Page 335
... hyperbola is xy = k2 , the equations to the tangent and to the perpendicular on the tangent from the origin are respectively n હૃ η + = 2 , 20 У and = x y between which and the equation to the curve , if we eliminate a and y , we have ...
... hyperbola is xy = k2 , the equations to the tangent and to the perpendicular on the tangent from the origin are respectively n હૃ η + = 2 , 20 У and = x y between which and the equation to the curve , if we eliminate a and y , we have ...
Page 361
... hyperbola being is required to find its rectilinear asymptotes . x2 42 a2 b2 = 1 , it As this equation is of two dimensions and has no term of one dimension , the asymptotes pass through the origin , which is the centre of the curve ...
... hyperbola being is required to find its rectilinear asymptotes . x2 42 a2 b2 = 1 , it As this equation is of two dimensions and has no term of one dimension , the asymptotes pass through the origin , which is the centre of the curve ...
Page 364
... hyperbola , viz . xy = α1x2 + αox + b1 ; and this curve is asymptotic to the given curve , because the difference between the lengths of their ordinates is a quantity which diminishes without limit as a increases without limit . And so ...
... hyperbola , viz . xy = α1x2 + αox + b1 ; and this curve is asymptotic to the given curve , because the difference between the lengths of their ordinates is a quantity which diminishes without limit as a increases without limit . And so ...
Page 366
... hyperbola . Similarly , in Ex . 4 , the equation may be expressed in the form ( x + y ) ( x2 — xy + y2 ) + 3a2x + 3b2y + c3 = 0 , and x + y = 0 is the equation to a rectilinear asymptote . Suppose also a1 and a2 to be linear functions ...
... hyperbola . Similarly , in Ex . 4 , the equation may be expressed in the form ( x + y ) ( x2 — xy + y2 ) + 3a2x + 3b2y + c3 = 0 , and x + y = 0 is the equation to a rectilinear asymptote . Suppose also a1 and a2 to be linear functions ...
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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