 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...  New Series of The Mathematical Repository - الصفحة 122بواسطة Thomas Leybourn - 1819عرض كامل - لمحة عن هذا الكتاب
 | Isaac Newton - 1729 - عدد الصفحات: 444
...which a 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 - 1769 - عدد الصفحات: 370
...revolves 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 - 1769 - عدد الصفحات: 104
...revolves 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 - 1793 - عدد الصفحات: 386
...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... | |
 | Samuel Vince - 1812 - عدد الصفحات: 298
...constant central force, will be increased in the same ratio of 1 : a2 ; 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 time, by the constant action of the centripetal force. Now the... | |
 | John Mason Good - 1819 - عدد الصفحات: 788
...wh.ih 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 ti... | |
 | Jeremiah Day - 1815 - عدد الصفحات: 388
...equal to half radius. For the cosine of 60° is the sine of 30°. (Art. 89.) 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... | |
 | Rev. John Allen - 1822 - عدد الصفحات: 516
...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 - 1824 - عدد الصفحات: 440
...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... | |
 | John Martin Frederick Wright - 1825 - عدد الصفحات: 798
...fixed centre. 6. If a body be acted on by a given force and revolve in a circle, the arc described in any given time is a mean proportional between the diameter of the circle and the space through which a body would descend m the same time from rest if acted on by the same force. 7. The... | |
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