The Mathematical Writings of Duncan Farquharson Gregory |
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Page xvi
... performed on quan- tities , then indeed the analogy would be altogether precarious . But if , as is really the case , these theorems are true , in virtue of certain funda- mental laws of combination , which hold both for algebraical ...
... performed on quan- tities , then indeed the analogy would be altogether precarious . But if , as is really the case , these theorems are true , in virtue of certain funda- mental laws of combination , which hold both for algebraical ...
Page 3
... performed . I. We assume , then , the existence of two classes of operations F and f , connected together by the following laws : ( 1 ) FF ( a ) = F ( a ) . ( 3 ) Ff ( a ) = ƒ ( a ) . ( 2 ) ff ( a ) = F ( a ) . ( 4 ) ƒF ( a ) = ƒ ( a ) ...
... performed . I. We assume , then , the existence of two classes of operations F and f , connected together by the following laws : ( 1 ) FF ( a ) = F ( a ) . ( 3 ) Ff ( a ) = ƒ ( a ) . ( 2 ) ff ( a ) = F ( a ) . ( 4 ) ƒF ( a ) = ƒ ( a ) ...
Page 15
... performed on y , and it may be represented by f d dx y = x . X. Here y is given at once explicitly if we are able to ... perform that operation on both sides , we get -1 " or , d d • dx f dx Y -1 d X , d Y f X. dx It is plain that in its ...
... performed on y , and it may be represented by f d dx y = x . X. Here y is given at once explicitly if we are able to ... perform that operation on both sides , we get -1 " or , d d • dx f dx Y -1 d X , d Y f X. dx It is plain that in its ...
Page 16
... performed on it . This complementary function may be found from that condition , but the follow- ing more direct ... performing the operations indicated , Hence x2 X3 + ... ) . = = Cε- * . = 0 ( 1 - x + 1 2 - 1938 + ) - C & TM . 1.2 1.2 ...
... performed on it . This complementary function may be found from that condition , but the follow- ing more direct ... performing the operations indicated , Hence x2 X3 + ... ) . = = Cε- * . = 0 ( 1 - x + 1 2 - 1938 + ) - C & TM . 1.2 1.2 ...
Page 19
... perform the inverse operation for each of these suc- cessively , and this will be equivalent to performing the whole d inverse operation of f at once . d dx For , treating the operation exactly as if it were a function of x of the dx ...
... perform the inverse operation for each of these suc- cessively , and this will be equivalent to performing the whole d inverse operation of f at once . d dx For , treating the operation exactly as if it were a function of x of the dx ...
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