Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 9
Сторінка 190
... 3a2 ( 2ay - y2 ) 1 y ; ' dy 2 2 a 1 + = = dx ) y = da -- p - 8ay . ( 8 ) In the catenary 9 = ( + € ̈13 ) , y d2y y y2 p = 4-16-3 2-3 -1 . dy = dx 2 dx2 ( 9 ) In the tractory y + ( a2 190 ON THE CURVATURE OF CURVED LINES .
... 3a2 ( 2ay - y2 ) 1 y ; ' dy 2 2 a 1 + = = dx ) y = da -- p - 8ay . ( 8 ) In the catenary 9 = ( + € ̈13 ) , y d2y y y2 p = 4-16-3 2-3 -1 . dy = dx 2 dx2 ( 9 ) In the tractory y + ( a2 190 ON THE CURVATURE OF CURVED LINES .
Сторінка 191
Duncan Farquharson Gregory. ( 9 ) In the tractory y + ( a2 — y2 ) } - dy dx = 0 . Taking the expression for p in which y is the independent variable we find , ( a2 - p ' = = = ( « ' − y ) . y ( 10 ) In the hypocycloid a3 + y = a3 , p2 ...
Duncan Farquharson Gregory. ( 9 ) In the tractory y + ( a2 — y2 ) } - dy dx = 0 . Taking the expression for p in which y is the independent variable we find , ( a2 - p ' = = = ( « ' − y ) . y ( 10 ) In the hypocycloid a3 + y = a3 , p2 ...
Сторінка 196
... tractory is dy y dx ( a2 - y2 ) 11 whence B = Substituting this value in da = a y 9 αβ da a = y dB ( B2 — ao ) } ' - ? β dx we find dy which is the differential equation to the catenary . ( 8 ) The equation to the catenary is dy = с dx ...
... tractory is dy y dx ( a2 - y2 ) 11 whence B = Substituting this value in da = a y 9 αβ da a = y dB ( B2 — ao ) } ' - ? β dx we find dy which is the differential equation to the catenary . ( 8 ) The equation to the catenary is dy = с dx ...
Сторінка 421
... a constant . ( 7 ) The equation to the tractory is dy dx + y ( a2 — y3 ) = 0 . Then = a log2 2 8 = supposing the arc to be measured from the point where y = a . When a curve is the evolute of another curve , RECTIFICATION OF CURVES . 421.
... a constant . ( 7 ) The equation to the tractory is dy dx + y ( a2 — y3 ) = 0 . Then = a log2 2 8 = supposing the arc to be measured from the point where y = a . When a curve is the evolute of another curve , RECTIFICATION OF CURVES . 421.
Сторінка 433
... tractory is ( a * — y3 ) } dy - + y = 0 ; dx and the volume of the solid generated by its revolution round the axis of x , and taken from x = = 0 to x = 8 is πα . ( 19 ) The equation to the Witch of Agnesi is xy = 2a ( 2ay- y2 ) 3 . If ...
... tractory is ( a * — y3 ) } dy - + y = 0 ; dx and the volume of the solid generated by its revolution round the axis of x , and taken from x = = 0 to x = 8 is πα . ( 19 ) The equation to the Witch of Agnesi is xy = 2a ( 2ay- y2 ) 3 . If ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³