The Mathematical Writings of Duncan Farquharson Gregory |
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Page 10
... positive or negative , or generally if m and ʼn be distributive and permutative functions . The remainder of the proof follows very readily after this step , which is the key - stone of the whole , so that I need not dwell on it longer ...
... positive or negative , or generally if m and ʼn be distributive and permutative functions . The remainder of the proof follows very readily after this step , which is the key - stone of the whole , so that I need not dwell on it longer ...
Page 55
... positive , and P < P ' < P " . This shows that the value of n is impossible , and that of m possible ; therefore there are two directions arising from the doubtful sign in which the ellipsoid may be cut in circular sections , determined ...
... positive , and P < P ' < P " . This shows that the value of n is impossible , and that of m possible ; therefore there are two directions arising from the doubtful sign in which the ellipsoid may be cut in circular sections , determined ...
Page 56
... positive , and according as p ' is greater or less than p , the first or second is to be taken , the other becoming impossible . In either case there are two series of circular sections corresponding to the positive and negative sign ...
... positive , and according as p ' is greater or less than p , the first or second is to be taken , the other becoming impossible . In either case there are two series of circular sections corresponding to the positive and negative sign ...
Page 110
... positive integer powers of n , that is , for cases of ordinary differentiation , is shown by this method to be true when n is fractional or negative , that is , in the cases of integration and general differentiation . If we suppose u ...
... positive integer powers of n , that is , for cases of ordinary differentiation , is shown by this method to be true when n is fractional or negative , that is , in the cases of integration and general differentiation . If we suppose u ...
Page 132
... positive and negative numbers . They argue that since ε or √ ( € ) has two values which we may call + n and -n , we have therefore + n = εt , − n = ε 2 , and , from the ordinary definition of logarithms , 2 132 ON THE IMPOSSIBLE.
... positive and negative numbers . They argue that since ε or √ ( € ) has two values which we may call + n and -n , we have therefore + n = εt , − n = ε 2 , and , from the ordinary definition of logarithms , 2 132 ON THE IMPOSSIBLE.
Other editions - View all
The Mathematical Writings of Duncan Farquharson Gregory (Classic Reprint) Duncan Farquharson Gregory No preview available - 2019 |
The Mathematical Writings of Duncan Farquharson Gregory William Walton,Robert Leslie Ellis,Duncan Farquharson Gregory No preview available - 2015 |
Common terms and phrases
a₁ applied arbitrary constants arithmetical asymptotes axis becomes binomial theorem C₁ Cambridge Mathematical Journal centre coefficients commutative commutative operations conic section consider cosine cosne curve determine Differential Calculus differential equations dt² dx dx dx dy dx² dy² Edition equal expression factor Finite Differences fraction functional equation geometrical given Hence infinite integral intersection inverse operation John Herschel laws of combination linear logarithms maxima and minima method motion multiplying negative original P₁ parabola pendulum perpendicular plane of xy point of suspension principles quantity represent residue result right angles roots sides singular point solution subtraction suppose surface symbols of operation tangent Taylor's theorem term theory tion triangle u₂ values variables whence