Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 34
Page 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 . the geometry of the figure we have the equations v2 + vw + w2 u2 + uw + w2 . u2 + u v + v2 = = and u v + ...
... 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 . the geometry of the figure we have the equations v2 + vw + w2 u2 + uw + w2 . u2 + u v + v2 = = and u v + ...
Page 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 ...
Page 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 ...
Page 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 ACQ ACB = AM AC ; π X whence ACQ 2 a 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 ACQ ACB = AM AC ; π X whence ACQ 2 a But PM CM tan ACQ ...
Page 135
... intersection being ( 2n − 1 ) - dx 2 - 2na being the abscissa of the point where the curve cuts the axis of x . ( 8 ) The Cycloid . Rolling Curves . This curve is generated by a point P in the circumference of a circle b Pc ( fig . 19 ) ...
... intersection being ( 2n − 1 ) - dx 2 - 2na being the abscissa of the point where the curve cuts the axis of x . ( 8 ) The Cycloid . Rolling Curves . This curve is generated by a point P in the circumference of a circle b Pc ( fig . 19 ) ...
Contents
1 | |
12 | |
28 | |
43 | |
62 | |
77 | |
79 | |
84 | |
224 | |
237 | |
249 | |
271 | |
282 | |
291 | |
340 | |
351 | |
94 | |
129 | |
144 | |
162 | |
175 | |
188 | |
200 | |
386 | |
400 | |
412 | |
440 | |
464 | |
506 | |
Other editions - View all
Common terms and phrases
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