A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xxii
... negative .... SECTION 3. - Direction of curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards d2y dx2 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in ...
... negative .... SECTION 3. - Direction of curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards d2y dx2 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in ...
Page xxiii
... negative signs 411 262-265 . Equations to the Spiral of Archimedes , the Reciprocal Spiral , the Lituus , and the Logarithmic Spiral 412 266-268 . Equations in terms of r and p of the involute of the circle , the circle , and the ...
... negative signs 411 262-265 . Equations to the Spiral of Archimedes , the Reciprocal Spiral , the Lituus , and the Logarithmic Spiral 412 266-268 . Equations in terms of r and p of the involute of the circle , the circle , and the ...
Page 4
... negative number , the sign of the inequality is reversed : that is , a > is changed into a < , and a < into a > . This is easily shewn by an example ; as , for instance , 5 is greater than 2 ; let each side be multiplied by + 4 , then ...
... negative number , the sign of the inequality is reversed : that is , a > is changed into a < , and a < into a > . This is easily shewn by an example ; as , for instance , 5 is greater than 2 ; let each side be multiplied by + 4 , then ...
Page 5
... negative , the signs of the ine- qualities would have been changed in the first multiplication , and would have been again changed in the final result , because a1 + a2 + ...... + a , would be a negative quantity , and thus the same ...
... negative , the signs of the ine- qualities would have been changed in the first multiplication , and would have been again changed in the final result , because a1 + a2 + ...... + a , would be a negative quantity , and thus the same ...
Page 6
... negative ; then , as before , a1 | bi is > L , < G 12 is > L , < G b2 an is > L , < G ; b ,, let these inequalities be severally multiplied by the negative quantities b1 , b2 , bз , ...... bn , so that the signs of them are changed ...
... negative ; then , as before , a1 | bi is > L , < G 12 is > L , < G b2 an is > L , < G ; b ,, let these inequalities be severally multiplied by the negative quantities b1 , b2 , bз , ...... bn , so that the signs of them are changed ...
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according algebraical applicable assume becomes calculated called Chapter circle coefficients consider constant contains continuous convenient corresponding curve d³u denominator derived derived-functions determine differential divided dx dy dx² dy dx dy dy dy dz elimination equal equation equicrescent equivalent Evaluate examples expand expression F(xo+h factor finite fraction function given gives greater Hence homogeneous function increases increments independent infinite infinitesimal infinity involved less limit maximum means method negative observed original partial particular pass positive powers preceding quantity reason relation replaced represent respectively result roots sides similar Similarly substituting successive suppose symbols Theorem tion true values vanish variables variation vary whence zero
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