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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...
The Mathematical Principles of Natural Philosophy - الصفحة 46
بواسطة Sir Isaac Newton - 1803
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## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - عدد الصفحات: 370
...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...
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## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - عدد الصفحات: 472
...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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## A Course of Mathematics: Containing the Principles of Plane ..., المجلدات 1-3

Jeremiah Day - 1838
...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...
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## A Course of Mathematics: Containing the Principles of Plane ..., الأجزاء 2-4

Jeremiah Day - 1839 - عدد الصفحات: 370
...^. 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...
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## A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - 1848 - عدد الصفحات: 153
...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...
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## An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1849 - عدد الصفحات: 528
...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,...
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## The Three First Sections and Part of the Seventh Section of Newton's ...

Sir Isaac Newton - 1850 - عدد الصفحات: 163
...9. The arc, which a body, uniformly revolving in a circle with 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, descending by the same given force, would describe in the same given time....
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## New Elements of Geometry

Seba Smith - 1850 - عدد الصفحات: 200
...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...
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## A Treatise on the Steam Engine in Its Application to Mines, Mills, Steam ...

John Bourne, John Bourne (C.E.) - 1851 - عدد الصفحات: 258
...a 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...
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## The Practical Model Calculator: For the Engineer, Mechanic, Machinist ...

Oliver Byrne - 1851 - عدد الصفحات: 588
...a 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...
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