Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 6-10 із 29
Сторінка 122
... volume of the ellipsoid will be 4. π 3 αβγ . Now the principal axes are maxima or minima values of the radius ; we therefore have r2 = x2 + y2 + x2 a maximum ; , y , being subject to the equation of condition a x ' + a'y2 + a ′′ z2 + ...
... volume of the ellipsoid will be 4. π 3 αβγ . Now the principal axes are maxima or minima values of the radius ; we therefore have r2 = x2 + y2 + x2 a maximum ; , y , being subject to the equation of condition a x ' + a'y2 + a ′′ z2 + ...
Сторінка 123
... volume of the ellipsoid is equal to ( 18 ) 4. π 3 ( aa'a " - ab - j a′b'2 – a ′′ b " 2 + 2bb′b ′′ ) § ' 4π 3 To find the least ellipse which will circumscribe a given triangle . Let ABC ( fig . 10 ) be the triangle . Take C as the ...
... volume of the ellipsoid is equal to ( 18 ) 4. π 3 ( aa'a " - ab - j a′b'2 – a ′′ b " 2 + 2bb′b ′′ ) § ' 4π 3 To find the least ellipse which will circumscribe a given triangle . Let ABC ( fig . 10 ) be the triangle . Take C as the ...
Сторінка 125
... volume he has also discussed the more general problem- To describe the least ellipse which passes through four given points . The preceding solution is due to Bérard . Annales de Gergonne , Vol . IV . p . 288 . ( 19 ) To inscribe the ...
... volume he has also discussed the more general problem- To describe the least ellipse which passes through four given points . The preceding solution is due to Bérard . Annales de Gergonne , Vol . IV . p . 288 . ( 19 ) To inscribe the ...
Сторінка 202
... volume of the pyramid included between the tangent plane and the co - ordinate planes is 9xyz 9a3 2 = 2 The volume of this pyramid is smaller than that of any other pyramid formed with the co - ordinate planes by a plane passing through ...
... volume of the pyramid included between the tangent plane and the co - ordinate planes is 9xyz 9a3 2 = 2 The volume of this pyramid is smaller than that of any other pyramid formed with the co - ordinate planes by a plane passing through ...
Сторінка 231
... volume . Taking the vertex of the cone as origin , and its axis as the axis of x , the equation to the cone is x2 + y2 = c2x2 where c is the tangent of the half angle of the cone . ( 1 ) The equation to the cutting plane is lx + my + nx ...
... volume . Taking the vertex of the cone as origin , and its axis as the axis of x , the equation to the cone is x2 + y2 = c2x2 where c is the tangent of the half angle of the cone . ( 1 ) The equation to the cutting plane is lx + my + nx ...
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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