Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка iii
... called for by the increased cultivation of Analysis in this University . Accordingly I have not limited myself to the mere collection of Examples and Problems illustrative of Theorems given in Elementary Treatises on the subject , but I ...
... called for by the increased cultivation of Analysis in this University . Accordingly I have not limited myself to the mere collection of Examples and Problems illustrative of Theorems given in Elementary Treatises on the subject , but I ...
Сторінка 4
... called , the logarithmic differential of the function . ( 31 ) Let u = ( a + x ) " ( b + x ) " , ( 32 ) ( 33 ) ( 34 ) ( 35 ) log u = m log ( a + x ) + n log ( b + x ) , 1 du u dx du dx И du dx m = = a + x + n b + x ( a + x ) " ( b + x ) ...
... called , the logarithmic differential of the function . ( 31 ) Let u = ( a + x ) " ( b + x ) " , ( 32 ) ( 33 ) ( 34 ) ( 35 ) log u = m log ( a + x ) + n log ( b + x ) , 1 du u dx du dx И du dx m = = a + x + n b + x ( a + x ) " ( b + x ) ...
Сторінка 56
... called Maclaurin's , but which ought to bear the name of Stirling , was first given by James Stirling in his Lineæ Tertii Ordinis Newtonianæ , p . 32 . Maclaurin introduced it into his Treatise of Fluxions , p . 610 , and his name has ...
... called Maclaurin's , but which ought to bear the name of Stirling , was first given by James Stirling in his Lineæ Tertii Ordinis Newtonianæ , p . 32 . Maclaurin introduced it into his Treatise of Fluxions , p . 610 , and his name has ...
Сторінка 121
... called the surface of elasticity . See Fresnel , Mémoires de l'Institut , Vol . VII . p . 130 , and Herschel's Light , Sect . 1012 . = ( 16 ) To find the area of a section of the ellipsoid , 2 y ' a2 b2 = 1 , made by the plane la + my + ...
... called the surface of elasticity . See Fresnel , Mémoires de l'Institut , Vol . VII . p . 130 , and Herschel's Light , Sect . 1012 . = ( 16 ) To find the area of a section of the ellipsoid , 2 y ' a2 b2 = 1 , made by the plane la + my + ...
Сторінка 131
... called the inferior conchoid . To determine the equation , let AN , PN = y , PM ( which is of constant length ) = a , OA = b . Then as PM2 = PN2 + MN2 , and OA ― MN AN AM = AN - MN , PN we have x2 y2 = ( a2 − y3 ) ( b + y ) 2 , - which ...
... called the inferior conchoid . To determine the equation , let AN , PN = y , PM ( which is of constant length ) = a , OA = b . Then as PM2 = PN2 + MN2 , and OA ― MN AN AM = AN - MN , PN we have x2 y2 = ( a2 − y3 ) ( b + y ) 2 , - which ...
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a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³