 | Humphry Ditton - 1705 - 280 pages
...both Z, £1 by x. ) comes to L», and \/2xz,', or \/L, and \/2z. j fo that V : W : :• \/L : \/Tz.. That is, the Velocity in a Conick Seftion, at the greateft or leaft Diftance from the F««#, is to the Velocity in a Circle at the fame Diftance, in the fubduplicate Ratio of the Parameter... | |
 | Isaac Newton - 1729 - 444 pages
...perpendiculars are now the diftances. COR. 3. And therefore the velocity in a conic fedion, at its greateft or leaft diftance from the focus, is to the velocity in a circle at the fame diftance from the centre, in the fubduplicate ratio of the principal ktus reftum to the double of that diftance.... | |
 | William Emerson - 1757 - 466 pages
...DD. And с : e : : Conjugate of D : to D. COR. 3. The Velocity of a Body moving in a Parabola about the Focus, is to the Velocity in a Circle at the fame Diftance : : as v/2 to i. For let r = Latus Rectum, then by the Nature of the Parabola, P— — — , and p... | |
 | William Emerson - 1769 - 104 pages
...+ cc — dd to dd, eras bb to dd. See Ex. 2. Prop. XIII. Cor. 3. 2^1? velocity in a -parabola round the focus, is to the velocity in a circle at the fame diftance •, as <2 to I. For f = * v/W, and = - (See Ex. 5. Prop. XIII.) Whence the fquares of thefe velocird'd... | |
 | William Emerson - 1769 - 370 pages
...+ cc — ddtQ **, or as to to ^. See Ex. 2. Prop. XIII. Cor. 3. 2^* w/0«./jy ?.» a parabola round the focus, is to the velocity in a circle at the fame diftance y as for p — i ^, and^ = (See Ex. 5. Prop. XIII.) Whence the fquares of thefe velocirdd . ties are... | |
 | William Emerson - 1793 - 386 pages
...dd to dd, rr + cc-dd or as bb to dd. See Ex. 2. Prop. XIII. Cor. 3. The velocity in a parabola round the focus, is to the velocity in a circle at the fame diftance; as •J^ to i. For p = -I ./rd, and p = — — - (See Ex. 5. Q^4 Prop Fig. Prop. XIII.) Whence the... | |
 | Isaac Newton - 1803 - 310 pages
...now the diftances. COR. 3. And therefore the velocity in a conic fection, at its greateft or leal! diftance from the focus, is to the velocity in a circle, at the fame diftance from the centre, in the fubduplicate ratio of the priucipal latus rectum to the double of that diftance.... | |
 | Rev. John Allen - 1822 - 508 pages
...inversely. Co. 3. And therefore the velocity in a conick section, in the greatest or least distance from the focus, is to the velocity in a circle at the same distance from the centre, in a subduplicate ratio of the principal parameter of the section to... | |
 | Harvey Goodwin - 1849 - 588 pages
...tangents. COR. 3. And therefore the velocity in a conic section, at the greatest or least distance from the focus, is to the velocity in a circle at the same distance in the subduplicate ratio of the latus rectum to twice that distance. [For let V be the... | |
 | Isaac Newton - 1900 - 320 pages
...distances. COR. 3. And therefore the velocity in a conic section, at the greatest or least distance from the focus, is to the velocity in a circle at the same distance from the centre in the subduplicate ratio of the latus rectum to twice that distance.... | |
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And therefore the velocity in a conic section, at its greatest or least distance from the focus, is to the velocity in a circle, at the same distance from the centre, in the subduplicate ratio of the principal latus rectum to the double of that distance. 