 | 1723 - 1336 sider
...or «« of OC to DO j that i?, the Decreafe of Gravity at ** the /Equator is to its encreafe at C, as the Square of the " Radius is to the Square of the Sine of the Lati« tude. «« By this alfo it will appear, that the Diredion of « heavy Bodies is not to the... | |
 | John Keill - 1739 - 504 sider
...KS on each Hand, fo that KG and SH, , and may be to KS (which is the Projection of the Eccentricity) as the Square of the Radius is to the . Square of the Sine of the Ohliq ,ity of the Ecliptick : f't- 7- Thro' K draw Y * parallel to the common Section of the ^Equator... | |
 | Robert Simson - 1806 - 546 sider
...contained by the straight lines by which the half of the perimeter exceeds the other two sides AB, AC, as the square of the radius is to the square of the tangent of half the angle BAC opposite to the base. Let the angles BAC, ABC be bisected by the straight... | |
 | Thomas Keith - 1810 - 478 sider
...=: cosine of the arc BZ. (L) CoROL IV. The diameter of the circle is to the versed sine of any arc, as the square of the radius is to the square of the sine of half that arc. For, (I. 101.) CBX^BG=BZ% multiply by the radius CB, then CB2 x ^-BG = CB X BZ~ therefore... | |
 | Francis Nichols - 1811 - 162 sider
...Frorrrno. 1, DA : AF :: DA2 : BA2* :: CA' : AL2. That is, the diameter is to the versed sine of any arc, as the square of the radius is to the square of the right sine of half that arc. Cor. 3. From no. 3, 2 AL2=CAxAF. But the radius CA is a constant quantity,... | |
 | Euclides - 1816 - 588 sider
...rectangle contained by HK, DG, or the rectangle BFC, (as the square of AD is to the square of DG, that is) as the square of the radius is to the square of the tangent of the angle DAG, that is, the half of BAC : But HA is half the perimeter of the triangle ABC,... | |
 | Miles Bland - 1819 - 444 sider
...rectangle contained by the excesses of half the perimeter above each of them respectively as the square of radius is to the square of the sine of half the angle contained by those sides. Let AEC be any triangle, BC its base, AB the greater of the sides and AC... | |
 | Miles Bland - 1819 - 442 sider
...rectangle contained by the excesses of half the perimeter above each of them respectively as the square of radius is to the square of the sine of half the angle contained by those sides. Let ABC be any triangle, BC its- base, AB the greater of the sides and AC... | |
 | Rev. John Allen - 1822 - 508 sider
...excesses of the half sum of AB, BC and AC above AC, and of the same half sum above BC, as the square of radius, is to the square of the sine of half the angle ACB (16. 5 Eih); or, which is equal (20. 6 Eu.), in a duplicate ratio of radius to the sine of half... | |
 | Thomas Keith - 1826 - 504 sider
...BF=cosine of the arc BI. (L) COROL. IV. The diameter of the circle is to the versed sine of any arc, as the square of the radius is to the square of the sine of half that arc. For, (I. 107.) ев x ^BG=Bz2, multiply by the radius ев, then ев2 x JBG=CB x BZ* therefore... | |
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BFC, as the square of the radius is to the square of the tangent of half the angle BAC opposite to the base. 
