A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xviii
... determining such singular values of f ( x ) 236 146. Easy detection of the singular values when f ' ( x ) is alge ... determining such values , and examples 250 ...... SECTION 3. - Maxima and minima of an explicit function of two ...
... determining such singular values of f ( x ) 236 146. Easy detection of the singular values when f ' ( x ) is alge ... determining such values , and examples 250 ...... SECTION 3. - Maxima and minima of an explicit function of two ...
Page 2
... determining cach of the unknown quantities in terms of the constants . Multiply ( 1 ) by A1 , ( 2 ) by A2 , ( 3 ) by ... determined hereafter , let two be , that the coefficients of y and z be equal to zero ; so that b1 λ 1 + b 2 λ 2 + b ...
... determining cach of the unknown quantities in terms of the constants . Multiply ( 1 ) by A1 , ( 2 ) by A2 , ( 3 ) by ... determined hereafter , let two be , that the coefficients of y and z be equal to zero ; so that b1 λ 1 + b 2 λ 2 + b ...
Page 14
... determine the relative sizes of their orbits ; but when we extend our observations to other bodies in the celestial space , we find stars situated at such a distance from the sun , that , taking the star to be the vertex of an isosceles ...
... determine the relative sizes of their orbits ; but when we extend our observations to other bodies in the celestial space , we find stars situated at such a distance from the sun , that , taking the star to be the vertex of an isosceles ...
Page 20
... determining the orders of the more complex forms and it will then appear that we can always determine the order of an infinity or of an infinitesimal relatively to a * See Poisson , Traité de Mécanique , Tome I , pp . 14 , 16 , 2de ed ...
... determining the orders of the more complex forms and it will then appear that we can always determine the order of an infinity or of an infinitesimal relatively to a * See Poisson , Traité de Mécanique , Tome I , pp . 14 , 16 , 2de ed ...
Page 27
... are implicit , there are no general marks whereby to determine the variable , which may first most conveniently change value . 14. ] Functions have again been divided into two classes E 2 13. ] 27 ON EXPLICIT AND IMPLICIT FUNCTIONS .
... are implicit , there are no general marks whereby to determine the variable , which may first most conveniently change value . 14. ] Functions have again been divided into two classes E 2 13. ] 27 ON EXPLICIT AND IMPLICIT FUNCTIONS .
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Common terms and phrases
a₁ algebraical angles asymptote axis b₁ becomes Calculus change of sign changes sign circle coefficients constants critical values curve cycloid d2F d2F d²x d²y d2y dx2 d³u d³y determine differential equation dimensions dr dr dr dy drawn dx dx dx dy dx² dy dx dy dy dy dz dy² elimination epitrochoid equa equal equicrescent expression F(xo F(xo+h factors finite quantity function geometrical Hence homogeneous function hyperbola increases infinite infinitesimal Infinitesimal Calculus infinity maxima and minima maximum or minimum minimum value negative nth degree origin partial derived-functions pass plane of reference positive radius real roots right-hand member roots of f(x shewn Similarly singular value straight line Sturm's Theorem substituting symbols tangent Theorem tion u₁ vanish variables variations whence zero