Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 54
Сторінка 136
... origin , and put CN = a , PN = y , and co'p , we should find x = a ( 1 - cos 4 ) , -1 whence y = a vers = y = a ( p + sin † ) ; - a + ( 2a x − x2 ) 3 . It is easy to see both from geometrical and analytical considerations that the ...
... origin , and put CN = a , PN = y , and co'p , we should find x = a ( 1 - cos 4 ) , -1 whence y = a vers = y = a ( p + sin † ) ; - a + ( 2a x − x2 ) 3 . It is easy to see both from geometrical and analytical considerations that the ...
Сторінка 142
... origin is proportional to the radius of its extremity . Since r = 0 when 0 : ∞ , it appears that the curve makes an infinite number of revolutions before it reaches the pole ; a property which was at first disputed by Descartes . From ...
... origin is proportional to the radius of its extremity . Since r = 0 when 0 : ∞ , it appears that the curve makes an infinite number of revolutions before it reaches the pole ; a property which was at first disputed by Descartes . From ...
Сторінка 143
... origin of light ) are also spirals equal to the primary one ; and if another equal spiral be made to roll on the first , the pole of the rolling spiral will trace out another spiral equal to the original . This property of the ...
... origin of light ) are also spirals equal to the primary one ; and if another equal spiral be made to roll on the first , the pole of the rolling spiral will trace out another spiral equal to the original . This property of the ...
Сторінка 145
... origin is 00 du - du Y adx + ydy dy dx t = ( dx2 + dy3 ) } { ( du ) * 2 du 2 + dy dx The portions of the axes cut off between the origin and the tangent , or the intercepts of the tangent , are dy y ----- x along the axis of y . da dx ...
... origin is 00 du - du Y adx + ydy dy dx t = ( dx2 + dy3 ) } { ( du ) * 2 du 2 + dy dx The portions of the axes cut off between the origin and the tangent , or the intercepts of the tangent , are dy y ----- x along the axis of y . da dx ...
Сторінка 147
... origin on the tangent we find p = ( axy ) 3 . ( 4 ) In the cissoid of Diocles , y2 = 2 a X3 - whence the subtangent and the subnormal ( 5 ) In the logarithmic curve y = ce . x ( 2 a - x ) . = ; 3 a - = x x2 ( 3a - x ) ( 2a - x ) 2 The ...
... origin on the tangent we find p = ( axy ) 3 . ( 4 ) In the cissoid of Diocles , y2 = 2 a X3 - whence the subtangent and the subnormal ( 5 ) In the logarithmic curve y = ce . x ( 2 a - x ) . = ; 3 a - = x x2 ( 3a - x ) ( 2a - x ) 2 The ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³