A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page ix
... infinity . And it is supposed that an error is hereby introduced , which vitiates and destroys the accuracy of the whole work , and that the results are at last true only because a compensation is made . Now let the nature of our ...
... infinity . And it is supposed that an error is hereby introduced , which vitiates and destroys the accuracy of the whole work , and that the results are at last true only because a compensation is made . Now let the nature of our ...
Page 13
... infinity of them . Hence also we have a new aspect of such quantities . In refe- rence to a finite quantity , infinity and infinitesimal are reci- procal terms , each implying the other ; the finite quantity may be the infinitesimal ...
... infinity of them . Hence also we have a new aspect of such quantities . In refe- rence to a finite quantity , infinity and infinitesimal are reci- procal terms , each implying the other ; the finite quantity may be the infinitesimal ...
Page 15
... infinity and infinitesimal of the same order is equal to the original finite quantity . Here perhaps it may be asked , when does a quantity pass from the finite to the infinite and to the infinitesimal ? How many finite quantities must ...
... infinity and infinitesimal of the same order is equal to the original finite quantity . Here perhaps it may be asked , when does a quantity pass from the finite to the infinite and to the infinitesimal ? How many finite quantities must ...
Page 17
... infinity ; similarly 1 + x π the inferior limit of tan x is 0 , and , as a becomes the differ- π 2 ' ence between tan and infinity vanishes , and infinity is the limit of tan π 2 PRICE , VOL . I. D Again : suppose that we have a series ...
... infinity ; similarly 1 + x π the inferior limit of tan x is 0 , and , as a becomes the differ- π 2 ' ence between tan and infinity vanishes , and infinity is the limit of tan π 2 PRICE , VOL . I. D Again : suppose that we have a series ...
Page 18
... infinity can do it ; and from the illustrations of Article 5 it ap- pears that it must be an infinity of a particular kind . It will be observed , that O does not represent absolute zero , and that ∞ does not express absolute infinity ...
... infinity can do it ; and from the illustrations of Article 5 it ap- pears that it must be an infinity of a particular kind . It will be observed , that O does not represent absolute zero , and that ∞ does not express absolute infinity ...
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Common terms and phrases
a₁ algebraical angles b₁ Calculus change of sign changes sign circle coefficients constant curve d2F d2F d²u d²x d²y d2y dx2 d³u d³y derived determine differential equation dr dr dx dx dx dy dx² dy dx dy dy dy dz dy² equal equicrescent explicit function expression F(xo F(xo+h factors finite quantity func geometrical given Hence homogeneous function increases increments indeterminate form infinitesimal Infinitesimal Calculus infinity involved Let f(x logarithm Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions particular values plane positive primitive equation proper fraction real roots replaced result right-hand member Similarly singular value straight line Sturm's Theorem substituting suppose symbols Taylor's Series Theorem tion vanish variables variation versin whence zero
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