 The problem therefore is reduced to finding the centre of a circle to touch externally two given circles (DG, EG) and pass through a given point (Q), which is always possible since the circles must cut each other and Q lie outside both, ie the problem...  Constructive geometry of plane curves - Page 125by Thomas Henry Eagles - 1885Full view - About this book
 | Dublin city, univ - 1871 - 366 pages
...unity, the curve consists of one closed oval whose points correspond symmetrically in pairs, and that the sum of the focal distances of any point on the curve is equal to the axis major. i1. ACB is a spherical triangle, having the angle at fright, the vertex... | |
 | Henry Angel - Geometry, Plane - 1880 - 372 pages
...are mutually perpendicular. The extremities of the major axis (A and A') are called the vertices. 2. The sum of the focal distances of any point on the curve is always equal to the conjugate or major axis. ThusTS + TS1 = AA1. Hence, (Plate Va, fig. 3a) PF1... | |
 | Henry Angel - 1880 - 360 pages
...are mutually perpendicular. The extremities of the major axis (A and A') are called the vertices. 2. The sum of the focal distances of any point on the curve is always equal to the conjugate or major axis. Thus TS + TS1 = AA1. Hence, (Plate Va, fig. 3a) PF1... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...FOCUS AND DIRECTRIX. PROPOSITION III. 35. Every central conic has a second focus and directrix ; and the sum of the focal distances of any point on the curve in the case of the ellipse^ or the difference of the same in the case of the hyperbola., is constant... | |
 | Charles Taylor - Mathematics - 1881 - 488 pages
...FOCUS AND DIRECTRIX. PROPOSITION III. 35. Every central conic has a second focm and directrix ; and the sum of the focal distances of any point on the curve in the case of the ellipse, or the difference of the same in the case of the hyperbola, is constant... | |
 | National cyclopaedia - 1884 - 626 pages
...thread always stretched, it will describe an ellipse: since one of the properties of an ellipse is that the sum of the focal distances of any point on the curve, that i*. its distance from one foc;is added to its distance from the other, is always equal to the... | |
 | Thomas Henry Eagles - Conic sections - 1885 - 401 pages
...equidistant from this circle and from the point $, for it has been shewn (Prob. 68) that the distance of/ from the second focus is equal to the major axis,...problem therefore is reduced to finding the centre of a chvle to touch externally two given circles (DG, EG) and pass through a given point (Q\ which is always... | |
 | Encyclopedias and dictionaries - 1888 - 900 pages
...FK-2KL-2CX. .-. SP + SF-2c.CX. Now, it u easily seen that SP'-S'P: therefore SP + S'P - 2« . CX ; or the sum of the focal distances of -any point on the curve is constant. Again SA:AX-SA':A'Xi:l therefore SA + SA': АХ + А'Х-«:!. But AX + A'X-2CX. .'. SA... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...same curve, if we had started with $' as focus, Z'K' as directrix, and the same eccentricity. 251. The sum of the focal distances of any point on the curve is equal to the major axis. For (Fig. Art. 247) we have SP = e.PM, and S'P = e.PM'. Hence SP + S'P... | |
 | 1904 - 386 pages
...that there are two foci and two corresponding directrices ; and deduce that in the case of an ellipse the sum of the focal distances of any point on the curve is constant. AB is a given line, and C, D given points on the same side of the line. Describe the ellipse... | |
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