A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page vi
... increase . Number under this aspect is what Infinitesimal Calculus con- templates and investigates the new properties of it , the new symbols required to express them , and the new laws to which they are subject ; it has thus to create ...
... increase . Number under this aspect is what Infinitesimal Calculus con- templates and investigates the new properties of it , the new symbols required to express them , and the new laws to which they are subject ; it has thus to create ...
Page xvi
... increases , f ( x ) de- creases , and vice versá 187 188 111. The proof that — F ( x ) F ( x ) = ( x , xo ) F ' { xo + 0 ( x , - — ( xn− x ) } , F ( x ) being finite and continuous for all values of x be- tween x and xo 112. The proof ...
... increases , f ( x ) de- creases , and vice versá 187 188 111. The proof that — F ( x ) F ( x ) = ( x , xo ) F ' { xo + 0 ( x , - — ( xn− x ) } , F ( x ) being finite and continuous for all values of x be- tween x and xo 112. The proof ...
Page 15
... increase is when number grows , that is , passes from one value to another only by going through all the inter- mediate numbers , whereby the successive increments or aug- ments which the numbers receive are infinitesimal ; thus , if we ...
... increase is when number grows , that is , passes from one value to another only by going through all the inter- mediate numbers , whereby the successive increments or aug- ments which the numbers receive are infinitesimal ; thus , if we ...
Page 16
... increase is discontinuous ; but if the number of divisions be infinite , and if the lesser number pass into the greater number by receiving at each successive step an infinitesimal increase , the mode of increase is continuous . For the ...
... increase is discontinuous ; but if the number of divisions be infinite , and if the lesser number pass into the greater number by receiving at each successive step an infinitesimal increase , the mode of increase is continuous . For the ...
Page 17
... increases , the quan- tity becomes less and less , and ultimately , when x is greater than any assignable quantity , the difference between and O is less than any quantity , and thus the limit is zero . again , as the difference between ...
... increases , the quan- tity becomes less and less , and ultimately , when x is greater than any assignable quantity , the difference between and O is less than any quantity , and thus the limit is zero . again , as the difference between ...
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Common terms and phrases
a₁ algebraical ascending powers b₁ becomes calculated change of sign changes sign coefficients constant curve d²u d²x d²y d2y dx2 d³u d³y denominator determine differential equation dr dr dr dx dx dr dx dx dx dy dx dz dx² dx2 dy2 dy d2u dy dx dy dy dy dz dy² dy³ dz dx dz dz equal equicrescent Evaluate explicit function expression F(xo F(xo+h factor finite quantity fraction given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity logarithm loge maxima and minima minimum value negative partial derived-functions particular values positive primitive equation proper fraction replaced result roots Similarly sin x singular value substituting suppose symbols Taylor's Series tion total differentials vanish variation whence x+▲x zero
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