 | George Salmon, Arthur Cayley - Curves, Algebraic - 1873 - 379 pages
...tangents drawn at the points where any ordinate meets a circle and the corresponding cycloid. 320. AVe shall conclude this Chapter with some account of spirals....an infinity of different values when we substitute to = 6, *o = 27T + 0, co = 4vr + 0, &c. The same right line then meets the curve in an infinity of... | |
 | George Salmon - Curves, Algebraic - 1879 - 426 pages
...and it also = a$ by hypothesis; but A = (9-1- cos~i—. P Hence the polar equation of the locus is ap The involute of the circle is the locus of the intersection...of tangents drawn at the points where any ordinate to CA meets the circle and the corresponding cycloid having its vertex at A. 320. We shall conclude... | |
 | Thomas Henry Eagles - Conic sections - 1885 - 404 pages
...curvature at any point is the point of contact of the tangent drawn from that point to the circle. The involute of the circle is the locus of the intersection...ordinate meets a circle and the corresponding cycloid. EXAMPLES ON CHAPTER XI. 1. Draw a spiral of Archimedes to touch a given line, the pole 0 and the constant... | |
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... 0, &c. The same right line then meets the curve in an infinity of points, and the curve is transcendental. Let us first take the spiral of Archimedes, which is the path described by a point receding uniformly from the origin, while the radius vector... 