 | Rev. John Allen - Astronomy - 1822 - 516 pages
...arch, which a body, by revolving uniformly in a circle with a given centripetal force, describes in any time, is a mean proportional between the diameter of the circle, and the descent of the body performed in the same time by falling with the same given force. Scholium. The... | |
 | Jeremiah Day - Geometry - 1824 - 440 pages
...rf."^~ * ' Rs=l=sin3 45°+cot3 45°=2 sin3 45° Therefore, Sin 4d° = v/^ = 97. The chord of any arc is a mean proportional, between the diameter of the circle, and the versed sine of the arc. Let ADB (Fig. 6.) be an arc, of which AB is the chord. BF the sine, and AF... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...revolves uniformly in a circle, by means of a given centripetal force, the arch, which it describes in any time, is a mean proportional between the diameter of the circle and Ihe space which the body wonld descend through in the game time, and with the same given force. For... | |
 | John Martin Frederick Wright - 1827 - 358 pages
...the tangent, as in the llth lemma : then let a series of curves be drawn in which DBoe AD4, AD5, AD6, &c., the angle of contact in each succeeding case...same force. 7. The velocity at any point of a curve de scribed round a centre of force = the velocity which a body, acted on by the given force at that... | |
 | John Martin F. Wright - 1827 - 632 pages
...5. If the areas described by the radius vector are not proportional to the times, the revolving ,|P body is not acted on solely by a force towards a fixed...same force. 7. The velocity at any point of a curve de scribed round a centre of force = the velocity which a body, acted on by the given force at that... | |
 | Thomas Curtis (of Grove house sch, Islington) - 438 pages
...which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time, is a mean proportional between the diameter of the circle and the space which the same body, falling by the same given force, would descend through in the same given time.... | |
 | Thomas Leybourn - Mathematics - 1830 - 630 pages
...feet and y = PN. Then (prin. sect. 2. p. 4 cor. 9) the arc which a body describes in a circle in any time (/) is a mean proportional between the diameter of the circle and the space fallen thro' by a body in the same time and acted upon by the same force. .-. supposing (t} to be the... | |
 | Jeremiah Day - Logarithms - 1831 - 418 pages
...v/2 R3 = l=sina 45°+cosa 45°=2sin* 45° Therefore, Sin 45° = v/£ = -i-. 97. The chord of any arc is a mean proportional, between the diameter of the circle, and the versed sine. of the arc. , . Let ADB (Fig. 6.) be an arc, of which AB is the chord, BF the sine, and... | |
 | Jeremiah Day - Measurement - 1831 - 394 pages
...R2=l=sin2 45°+cos2 45°=2sin2 45° Therefore, Sin .15° = v/i = -I-. . . \/2 97. The chord of any arc is a mean proportional, between the diameter of the circle, and the versed sine of the arc. Let ADB (Fig. 6.) be an arc, of which AB is the chord, BF the sine, and AF... | |
 | Mathematics - 1836 - 488 pages
...are, in any circle, each equal to the radius, and therefore equal to each other. The chord of any arch is a mean proportional between the diameter of the circle, and the versed sine of the arc. The product of radius into the versed sine of the supplement of twice a given... | |
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From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same... 
