A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page x
... pass from the infinitesimal element to the finite func- tion , then the finite function becomes the exact and adequate representative of the geometrical quantity , and a compensation has taken place in the act of passing from the ...
... pass from the infinitesimal element to the finite func- tion , then the finite function becomes the exact and adequate representative of the geometrical quantity , and a compensation has taken place in the act of passing from the ...
Page xxi
... pass 327 212. The number of these points which may be on a curve of the mth degree .... 330 CHAPTER X. PLANE CURVES REFERRED TO RECTANGULAR COORDINATES . SECTION 1. - Tangents and normals . 213. The principle of application of ...
... pass 327 212. The number of these points which may be on a curve of the mth degree .... 330 CHAPTER X. PLANE CURVES REFERRED TO RECTANGULAR COORDINATES . SECTION 1. - Tangents and normals . 213. The principle of application of ...
Page 15
... pass from 2 to 4x , and from 4x to 8x , by the successive addition of 2x and 4x ; and the changes are made " per saltus . " But continuous increase is when number grows , that is , passes from one value to another only by going through ...
... pass from 2 to 4x , and from 4x to 8x , by the successive addition of 2x and 4x ; and the changes are made " per saltus . " But continuous increase is when number grows , that is , passes from one value to another only by going through ...
Page 16
... pass from 3 to 3.1 not only by going through 3.01 , 3.02 , 3.03 , ... and if we pass from 3 to 3.01 not only by going through 3.001 , 3.002 , ... and so on to any finite number of divisions , the increase is discontinuous ; but if the ...
... pass from 3 to 3.1 not only by going through 3.01 , 3.02 , 3.03 , ... and if we pass from 3 to 3.01 not only by going through 3.001 , 3.002 , ... and so on to any finite number of divisions , the increase is discontinuous ; but if the ...
Page 117
... pass- ing over the distance x - xo to be t ; resolve this time into equal elements dt , and the space o into corresponding If the body moves elements , of each of which the type is da . through the whole space at the same rate , viz ...
... pass- ing over the distance x - xo to be t ; resolve this time into equal elements dt , and the space o into corresponding If the body moves elements , of each of which the type is da . through the whole space at the same rate , viz ...
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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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