 | David Gregory - 1715 - 566 σελίδες
...of a Body moving in a Parabola at the leaft diftance from the Focus (that is, in the Vertex of the Parabola; is to the velocity of a Body moving in a Circle at the fame diftance about the fame center of Forces, in a fubduplicate ratio of the principal Latus re&um of the... | |
 | William Emerson - 1757 - 466 σελίδες
...Hyperbola, the Square of the Velocity of a Projedtile moving round the Focus : is to the Square of the Velocity of a Body moving in a Circle at the fame Diftance : : as the Projectiles Diftance from the other Focus : is to the Semi-traafverfe. For let... | |
 | William Emerson - 1769 - 104 σελίδες
...cube of the diftance. PROP. XIV. jf The velocity of a body moving in any curve QAO, in any point A ; is to the velocity of a body moving in a circle at the fame diftance ; as vC^ to Putting d — diftance SA, andp = SP the perpendicular on the tangent at A. Let... | |
 | William Emerson - 1769 - 370 σελίδες
...of the diftance. PROP. XIV. ; - T^e velocity of a body moving in any curve QAO, /» any point A ; M to the velocity of a body moving in a circle at the fame diftance ; as %/r to ~ Putting d = diftance SA, andf = SP the perpendicular on the tangent at A. Let... | |
 | Charles Hutton - 1775 - 406 σελίδες
...elevation, not to return. Or, fince it is demonftrated (by ths writers on phyfics) that the velocity of a body moving in a parabola is to the velocity...at the fame diitance from the center of force, as л/* to i, v 4'сг x i'4i4z ~ 6'9.?? miles, the projectile's velocity per f¿cond, as before. ^- EF... | |
 | William Emerson - 1793 - 386 σελίδες
...cube of the diftance. PROP. XIV. The velocity of a body moving in any curve QAO, 15. in any point A; is to the velocity of a body moving in a circle at the fame diftance; as \ pd to \J dp. Putting d— diftance SA, and ^>=SP the perpendicular on the tangent at... | |
 | Thomas Leybourn - 1817 - 468 σελίδες
...elevation, not to return. Or, since it is demonstrated (by the writers on physics) that the velocity of a body moving in a parabola is to the velocity of a body moving in a circle, at the same distance from the centre of force, as V2 to 1, .•. 4-92 X 1-4142 = 6-958 miles, the projectile's... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...Fig. 12. Fif. 11. 43.— The velocity oj a body moving in any curve QAO, fßg. 13,) in any point A, is, to the velocity of a body moving in a circle at the tame distance, as ^ ¿i to ^7f. Putting d — distance SA, and p — SP, the per¡)tndicnlar on the... | |
| |
SP the perpendicular on the tangent at A. Let AR be the radius of curvature; from the point a in the curve infinitely near A, draw am, an parallel to AS, AR. Let C — velocity in the curve, c •=. velocity in the circle. 