Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 127
... intersection will determine the point 0. The actual length of the lines u , v , w , and the value of the minimum sum may be found . For from the geometry of the figure we have the equations v2 + vw + w2 = a2 , u2 + uw + w3 = b2 , u2 + ...
... intersection will determine the point 0. The actual length of the lines u , v , w , and the value of the minimum sum may be found . For from the geometry of the figure we have the equations v2 + vw + w2 = a2 , u2 + uw + w3 = b2 , u2 + ...
Сторінка 131
... intersection with BC will determine the point P. Nicomedes appears to have been led to the invention of this curve as a means of solving the celebrated problems mentioned above , by the facility with which it could be con- structed ...
... intersection with BC will determine the point P. Nicomedes appears to have been led to the invention of this curve as a means of solving the celebrated problems mentioned above , by the facility with which it could be con- structed ...
Сторінка 132
... intersections of tangents to a rect- angular hyperbola with perpendiculars drawn to them from the centre , and its form is that of the figure . Of the properties of the arcs of this curve , which have been in- vestigated by Fagnani and ...
... intersections of tangents to a rect- angular hyperbola with perpendiculars drawn to them from the centre , and its form is that of the figure . Of the properties of the arcs of this curve , which have been in- vestigated by Fagnani and ...
Сторінка 134
... intersection will be the quadratrix of Dinos- tratus . To find its equation , let AM = x , PM = y , AC = a . Then from the uniformity of the motion of CQ and MN , we have AM : AC ; ACQ ACB = π I whence ACQ = 3 But PM CM tan ACQ ...
... intersection will be the quadratrix of Dinos- tratus . To find its equation , let AM = x , PM = y , AC = a . Then from the uniformity of the motion of CQ and MN , we have AM : AC ; ACQ ACB = π I whence ACQ = 3 But PM CM tan ACQ ...
Сторінка 135
... intersection being ( 2n − 1 ) dy dx - - " 2na being the 2 abscissa of the point where the curve cuts the axis of x . Rolling Curves . ( 8 ) The Cycloid . This curve is generated by a point P in the circumference of a circle b Pc ( fig ...
... intersection being ( 2n − 1 ) dy dx - - " 2na being the 2 abscissa of the point where the curve cuts the axis of x . Rolling Curves . ( 8 ) The Cycloid . This curve is generated by a point P in the circumference of a circle b Pc ( fig ...
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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