A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xv
... function of two variables SECTION 5. - Successive differentiation of ... homogeneous functions 83. Transformation of partial derived functions .. 137 ... function in terms of the other by means of Maclaurin's Theorem 143 .. 87 ...
... function of two variables SECTION 5. - Successive differentiation of ... homogeneous functions 83. Transformation of partial derived functions .. 137 ... function in terms of the other by means of Maclaurin's Theorem 143 .. 87 ...
Page xxi
... function is ( a ) implicit , ( B ) homogeneous .. 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to the normal . . . . . 334 218. Values of ds , and of sin 7 ...
... function is ( a ) implicit , ( B ) homogeneous .. 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to the normal . . . . . 334 218. Values of ds , and of sin 7 ...
Page xxii
... function 373 245. If the curve is of the nth degree the number of points of ... function is explained which well exhibits some of the peculiarities of cusps 384 251 ... homogeneous and of three variables .. 390 255. Triple points ; and an ...
... function 373 245. If the curve is of the nth degree the number of points of ... function is explained which well exhibits some of the peculiarities of cusps 384 251 ... homogeneous and of three variables .. 390 255. Triple points ; and an ...
Page 82
... function of two independent variables x and y ; and suppose that x and y enter under the functional symbol in a certain combination , such as x divided by y : then = ƒ ( 3 ) ; u = ( 54 ) that is , u is a homogeneous function of x and y ...
... function of two independent variables x and y ; and suppose that x and y enter under the functional symbol in a certain combination , such as x divided by y : then = ƒ ( 3 ) ; u = ( 54 ) that is , u is a homogeneous function of x and y ...
Page 137
... homogeneous functions , which are due to Euler , and are generally known by the name of Euler's Theorems of Homo- geneous Functions . DEF . A homogeneous function ... homogeneous of n dimensions . Thus ax3 + bx2y + cz3 + exyz + gx2z = 0 is a ...
... homogeneous functions , which are due to Euler , and are generally known by the name of Euler's Theorems of Homo- geneous Functions . DEF . A homogeneous function ... homogeneous of n dimensions . Thus ax3 + bx2y + cz3 + exyz + gx2z = 0 is a ...
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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