Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 1-5 із 33
Сторінка 121
... axes , a212 7.2 a2 - b2 m2 2 + b2 + 2 - c2 n2 go2 - a2 = 0 . The last term of this when arranged according to powers of 2 is a2 b2 c2 a2 l2 + b2 m2 + c2 n2 and this being equal to the product of the roots , the area of the section is ...
... axes , a212 7.2 a2 - b2 m2 2 + b2 + 2 - c2 n2 go2 - a2 = 0 . The last term of this when arranged according to powers of 2 is a2 b2 c2 a2 l2 + b2 m2 + c2 n2 and this being equal to the product of the roots , the area of the section is ...
Сторінка 122
... axes , or rather of their product ; and if this be aẞy , then the 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 ; x , y ...
... axes , or rather of their product ; and if this be aẞy , then the 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 ; x , y ...
Сторінка 123
... axes ; and its square root is the quantity which we seek . Multiplying it therefore by we find that the volume of the ellipsoid is equal to ( 18 ) 4.π 3 ( aa'a " - ab a′b " - a " b " " + 2bb'b ' ' ) - 4.π 3 To find the least ellipse ...
... axes ; and its square root is the quantity which we seek . Multiplying it therefore by we find that the volume of the ellipsoid is equal to ( 18 ) 4.π 3 ( aa'a " - ab a′b " - a " b " " + 2bb'b ' ' ) - 4.π 3 To find the least ellipse ...
Сторінка 124
... − ẞ ) 2 − 2 ( x − a ) ( y - ẞ ) cos 0 , the axes of the ellipse are determined by the equation ( AC - B3 ) 1 — ( A + C - 2 B cos 0 ) r2 + sin2 0 = 0 . - The area of the ellipse will therefore be π sin 124 MAXIMA AND MINIMA .
... − ẞ ) 2 − 2 ( x − a ) ( y - ẞ ) cos 0 , the axes of the ellipse are determined by the equation ( AC - B3 ) 1 — ( A + C - 2 B cos 0 ) r2 + sin2 0 = 0 . - The area of the ellipse will therefore be π sin 124 MAXIMA AND MINIMA .
Сторінка 140
... axes of which are a a + h and - h . 2 If h = · a 2 the hypocycloid becomes a straight line , which is one of the diameters of the fixed circle . Professor Wallace * has made a very elegant application of the preceding property of the ...
... axes of which are a a + h and - h . 2 If h = · a 2 the hypocycloid becomes a straight line , which is one of the diameters of the fixed circle . Professor Wallace * has made a very elegant application of the preceding property of the ...
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Загальні терміни та фрази
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