| George Salmon - Conic sections - 1852 - 338 pages
...curve again. 137. Equation (2) also includes the following (3) ACE - k2F = 0, or A(C2 ± E2) = A2F, **an equation containing nine constants, and therefore...let BDF coincide, and the equation becomes (4) ACE** - B2 = 0, an equation also containing nine constants. A, C, E are (Art. 42) tangents at points of inflexion,... | |
| Mathematics - 1886 - 258 pages
...(8), where SE (ЗА - a - b - c) (z* + y') - 2 [k (a + b + c} - ab - be - ca] x from which we see that **the product of the distances of any point of the curve from the three** foci is in a constant ratio to the cube of the tangent from the same point to a director circle 8.... | |
| Charles Briot, Bouguet (M., Jean Claude) - Geometry, Analytic - 1896 - 598 pages
...proportional to the distances of any point (x, y) from the sides of the quadrilateral, it follows that **the product of the distances of any point of the curve from the** two opposite sides ab, cd of the inscribed quadrilateral is to the product oj the distances of the... | |
| James Harkness, Frank Morley - Analytic functions - 1898 - 336 pages
...with centre a. Then, if lP = a, we have yt-fi—x— a, and iy-^l \y+b\ = \x—a\ = a. constant. Thus **the product of the distances of any point of the /-curve from** two fixed points b, — b is constant. Such a curve is called a cassinian. Fig. 62 Fig. 62. shows the... | |
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