A Treatise on Infinitesimal Calculus ... |
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Page 3
... increases by infinitesimal increments from a to r ; and it takes the following form ; Let - be divided into n ... increase of 2 due to the infinitesimal increase of x is 2x dx : suppose a similar process of augmentation to be performed ...
... increases by infinitesimal increments from a to r ; and it takes the following form ; Let - be divided into n ... increase of 2 due to the infinitesimal increase of x is 2x dx : suppose a similar process of augmentation to be performed ...
Page 4
... increase , on which principle equations ( 2 ) are constructed , is equivalent to the reso- lution of F ( x ) — F ( x ) ... increases from x 。 to xn ; for the sake of simplicity , let x - xo be divided into n equal infinitesimal parts ...
... increase , on which principle equations ( 2 ) are constructed , is equivalent to the reso- lution of F ( x ) — F ( x ) ... increases from x 。 to xn ; for the sake of simplicity , let x - xo be divided into n equal infinitesimal parts ...
Page 95
... increase by units , the preceding process will probably be considered to be wanting in rigorousness ; but if infinity admits of only continuous increase , so that 2 may be considered an in- finitesimal increment of an infinite arc ...
... increase by units , the preceding process will probably be considered to be wanting in rigorousness ; but if infinity admits of only continuous increase , so that 2 may be considered an in- finitesimal increment of an infinite arc ...
Page 142
... increases , the sum of the areas corresponding to the finite partition of the range of the x - inte- gration will be greater than the true result by the sum of similar triangles . The differences however between the true results and the ...
... increases , the sum of the areas corresponding to the finite partition of the range of the x - inte- gration will be greater than the true result by the sum of similar triangles . The differences however between the true results and the ...
Page 158
... increases as n increases ; and г ( n ) : = ∞ , when n = ∞ . 125. ] In ( 250 ) let n be replaced by m + n , and let a be re- placed by 1 + z , where z is a new variable independent of x ; then e ̄ ( 1 + 2 ) x xm + n − 1 dx = г ( m + n ) ...
... increases as n increases ; and г ( n ) : = ∞ , when n = ∞ . 125. ] In ( 250 ) let n be replaced by m + n , and let a be re- placed by 1 + z , where z is a new variable independent of x ; then e ̄ ( 1 + 2 ) x xm + n − 1 dx = г ( m + n ) ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα