 | Isaac Newton - Celestial mechanics - 1729 - 444 pages
...body, uniformly revolving in a circle by means of a given centripetal force, defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the fame body falling by the fame given force would defcend thro' in the .fame given time.... | |
 | William Emerson - Centrifugal force - 1769 - 104 pages
...uniformly in a circle, by means of a given centripetal force ; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the bod}' would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)... | |
 | William Emerson - Mathematics - 1769 - 370 pages
...uniformly in a circle, by means of a given centripetal force; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpacf which the body would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)... | |
 | William Emerson - Centrifugal force - 1793 - 386 pages
...uniformly in a circle, by means of a given centripetal force ; the arch -which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace -which the body would defcend through in the fame time, and -with the fame given force. For 2R... | |
 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...propositions are derived 1. The triangles DAB, BAF give the following analogy. DA : BA :: BA : AF. That is, the chord of any arc is a mean proportional between the diameter and the versed sine of that arc. . 2. Again, the triangles AFB, DFB give the following analogy. AF:... | |
 | Samuel Vince - Calculus - 1812 - 274 pages
...central force, will be increased in the same ratio of 1 : a8 ; therefore the arc described in any time is a mean proportional between the diameter of the circle and the distance fallen through in the same timc5 by the constant action of the centripetal force. Now the... | |
 | John Mason Good - 1819 - 788 pages
...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, lulling by the same gi .'en fo ce, would desceud thiou^h in the same given... | |
 | Jeremiah Day - Logarithms - 1815 - 172 pages
...of 60° k the sine of- 30°. (Art. 89.), 97. The chord of any arc is a mean proportional, betweenthe diameter of the circle, and the versed sine of the...sine, and AF the versed sine. The angle ABH is a right angJa, (Euc. 31. 3.) and the triangles ABH and ABF are similar. (Euc. 8. 6.) Therefore, AH : AB : :... | |
 | Thomas Leybourn - Mathematics - 1819 - 430 pages
...of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference... | |
 | University of Cambridge - Mathematics - 1821 - 254 pages
...of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference... | |
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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... 
