A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xvi
... Hence also under certain conditions - F ( xo + h ) — F ( x0 ) - f ( xo + h ) − f ( x0 ) 190 191 F " ( x + 0h ) = f " ( xo + 0h ) 193 and corollaries are deduced therefrom 114. If in the theorem of the last Article ƒ xvi ANALYTICAL TABLE.
... Hence also under certain conditions - F ( xo + h ) — F ( x0 ) - f ( xo + h ) − f ( x0 ) 190 191 F " ( x + 0h ) = f " ( xo + 0h ) 193 and corollaries are deduced therefrom 114. If in the theorem of the last Article ƒ xvi ANALYTICAL TABLE.
Page 16
... Hence it appears , that numerical continuity requires infinite numerical divisibility , and expresses the property of quantity considered under the aspect of generation by growth : thus the difference of the two modes of increase is one ...
... Hence it appears , that numerical continuity requires infinite numerical divisibility , and expresses the property of quantity considered under the aspect of generation by growth : thus the difference of the two modes of increase is one ...
Page 18
... Hence absolute 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 ...
... Hence absolute 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 ...
Page 19
... Hence the need of classifying such quantities . Assuming then the order to depend on the exponent , it is plain that such orders must exist relatively to a certain de- terminate quantity , which is the subject of the exponent , and ...
... Hence the need of classifying such quantities . Assuming then the order to depend on the exponent , it is plain that such orders must exist relatively to a certain de- terminate quantity , which is the subject of the exponent , and ...
Page 20
... Hence then it appears , that there will be a scale of infinities and of infinitesimals in regular sequence : such that an infinity of the nth order must be infinitely subdivided to produce an infinity of the ( n − 1 ) th order , and ...
... Hence then it appears , that there will be a scale of infinities and of infinitesimals in regular sequence : such that an infinity of the nth order must be infinitely subdivided to produce an infinity of the ( n − 1 ) th order , and ...
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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