 | Jeremiah Day - Geometry - 1838 - 416 pages
...For V2 R»=l=sin2 45°+cosa 45=2sina 45° Therefore, Sin 45°= Vf — JL 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... | |
 | Jeremiah Day - Geometry - 1839 - 434 pages
...^. For V2 R2=l=sin2 45°+cos2 45=2sin2 45° Therefore, Sin 45°=Vi=— ,. 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... | |
 | Jeremiah Day - Logarithms - 1848 - 354 pages
...For V2 R*=1=sin" 45°+cos' 45=2 sin' 45° 1 Therefore, Sin 45°=Vi= — . V2 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, be an arc, of which AB is the chord, BF the sine, and AF the versed... | |
 | Harvey Goodwin - Mathematics - 1849 - 588 pages
...which a body moving uniformly in a circle under the action of a given central force describes in a given time, is a mean proportional between the diameter of the circle and the space through which the body would fall under the action of the same force and in the same time. [For, let T be the time,... | |
 | Isaac Newton - Curves, Plane - 1850 - 184 pages
...Corollorary of Newton's text can e better illustrated under Prop. VI. as is done by Svans. describes in any time, is a mean proportional between the diameter of the circle and the space, which the same body, descending by the same given force, would describe in the same given time. Let... | |
 | Seba Smith - Geometry - 1850 - 214 pages
...square root of the diameter of the circle multiplied by the diameter of the segment ; or the chord is a mean proportional between the diameter of the circle and the diameter of the segment. AC, the diameter of the second circle, is 2. Therefore the chord IK cuts segments... | |
 | John Bourne - Steam engineering - 1851 - 346 pages
...circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued... | |
 | Oliver Byrne - Engineering - 1851 - 310 pages
...circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...45°=-=. For V2 R2=l-=sm2 45°+cos2 45=-2sin2 45° Therefore, Sin 45°= V£ =~-^. 97. The chord of an^ 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... | |
 | Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...moving with uniform velocity in a circle under the action of a given centripetal force, describes in any time, is a mean proportional between the diameter of the circle, and the space through which the body would fall from rest under the action of the same force and in the same time. For, let AL... | |
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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... 
