A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 1-5 of 52
Page 2
... zero ; so that b1λ1 + b2 ^ 2 + b3λ3 = 0 , whence by elimination , λι = λο b2c3 - c2b3 bac , — cab C11 + C2 ^ 2 + C3λ3 = 0 ; = 13 b1c2 - c1b2 But thus the ratio only of the multipliers has been determined , and therefore any numbers ...
... zero ; so that b1λ1 + b2 ^ 2 + b3λ3 = 0 , whence by elimination , λι = λο b2c3 - c2b3 bac , — cab C11 + C2 ^ 2 + C3λ3 = 0 ; = 13 b1c2 - c1b2 But thus the ratio only of the multipliers has been determined , and therefore any numbers ...
Page 3
... zero , 2 = d1 ( a2bз — b2αз ) + d2 ( a3b1 − b3α1 ) + d3 ( a1b2 — b1ɑ2 ) C1 ( α2b3 — b2α3 ) + C2 ( α3b1 − b3α1 ) + cз ( α1b2 — b1α2 ) * This method of elimination is generally known by the name of Lagrange's Rule of Cross ...
... zero , 2 = d1 ( a2bз — b2αз ) + d2 ( a3b1 − b3α1 ) + d3 ( a1b2 — b1ɑ2 ) C1 ( α2b3 — b2α3 ) + C2 ( α3b1 − b3α1 ) + cз ( α1b2 — b1α2 ) * This method of elimination is generally known by the name of Lagrange's Rule of Cross ...
Page 17
... zero , the limit is called the inferior limit ; and if the value be in- finity , it is called the superior limit . 1 Thus the inferior limit of of a greater than 0 the quantity is less than 1 , yet the nearer x approaches to 0 , the ...
... zero , the limit is called the inferior limit ; and if the value be in- finity , it is called the superior limit . 1 Thus the inferior limit of of a greater than 0 the quantity is less than 1 , yet the nearer x approaches to 0 , the ...
Page 18
... zero is the inferior limit of an infinitesimal , and absolute infinity is the superior limit of a quantity which is greater than any assignable quantity . 8. ] The symbols by which we shall represent an infinity and an infinitesimal are ...
... zero is the inferior limit of an infinitesimal , and absolute infinity is the superior limit of a quantity which is greater than any assignable quantity . 8. ] The symbols by which we shall represent an infinity and an infinitesimal are ...
Page 19
... zero , but they may also differ from each other : and so may infinities differ from each other , and from a quantity which transcends every assignable quantity , that is , from absolute in- finity . Hence the need of classifying such ...
... zero , but they may also differ from each other : and so may infinities differ from each other , and from a quantity which transcends every assignable quantity , that is , from absolute in- finity . Hence the need of classifying such ...
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Common terms and phrases
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