Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 105
... passing through two angles of the prism ; find the inclination of these planes to the axis of the prism in order that for a given content the total surface may be the least possible . = Let ABC abc ( fig . 6 ) be the base of the prism ...
... passing through two angles of the prism ; find the inclination of these planes to the axis of the prism in order that for a given content the total surface may be the least possible . = Let ABC abc ( fig . 6 ) be the base of the prism ...
Сторінка 123
... passing through the three given points ; and then the actual values of the indeterminate quantities may be found by the condition of the minimum . The two quan- tities which we shall assume are the co - ordinates of the centre of the ...
... passing through the three given points ; and then the actual values of the indeterminate quantities may be found by the condition of the minimum . The two quan- tities which we shall assume are the co - ordinates of the centre of the ...
Сторінка 138
... passing through the centre of the gene- rating circle . The space COD is equal to the square of the radius ; the whole arca ACa is equal to twice that of the generating circle , and if the line AC be drawn , the area AMD is equal to the ...
... passing through the centre of the gene- rating circle . The space COD is equal to the square of the radius ; the whole arca ACa is equal to twice that of the generating circle , and if the line AC be drawn , the area AMD is equal to the ...
Сторінка 151
... passing through the point . But the degree of the equation can always be reduced ; for we may combine ( 2 ) with any multiple of ( 1 ) , and the result of the elimination between the new equation and either of the others will still give ...
... passing through the point . But the degree of the equation can always be reduced ; for we may combine ( 2 ) with any multiple of ( 1 ) , and the result of the elimination between the new equation and either of the others will still give ...
Сторінка 160
... passing through the pole are of constant length . tan p = tan 0 ; 3 therefore p = 0 . ( 7 ) Let the equation to the spiral be Then " = a " sin no . tan p = tann 0 ; and p = 0 . If p , be the value of p corresponding to an angle 0 + ...
... passing through the pole are of constant length . tan p = tan 0 ; 3 therefore p = 0 . ( 7 ) Let the equation to the spiral be Then " = a " sin no . tan p = tann 0 ; and p = 0 . If p , be the value of p corresponding to an angle 0 + ...
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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