 | 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 - 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... | |
 | 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... | |
 | Charles Taylor - Mathematics - 1881 - 512 pages
...QV + CD* : CD* = (7F* : CP* ; but we shall at present merely remark that such a definition would bo in accordance with the conventions usually adopted...; but it may also be deduced from the relation PN* : C4'~B<*= Cff : CB*, * Uixjn this subject, see Scholium C. where PN and Pn are the ordinates of any... | |
 | Charles Taylor - Mathematics - 1881 - 486 pages
...adopted * TEE SECOND FOCUS AND DIRECTRIX. PROPOSITION III. 35. Every central conic has a second focm and directrix ; and the sum of the focal distances...; but it may also be deduced from the relation PN* : CA* ~ P/i* = Cff : CIT, * UI,on this subject, see Scholium C. where PN and Pn are the ordinatea of... | |
 | 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
...68) that the distance of/ from the second focus is equal to the major axis, and therefore equal to the sum of the focal distances of any point on the curve. The problem therefore is reduced to finding the centre of a chvle to touch externally two given circles... | |
 | Thomas Henry Eagles - 1885 - 404 pages
...08) that the distance of f from the second focus is equal to the major axis, and therefore equal to the sum of the focal distances of any point on the curve. The problem therefore is reduced to finding the centre of a circle to touch externally two given circles... | |
 | 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... | |
| |
SECOND 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.,... 
