| John Keill - 1739 - 504 pages
...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 pages
...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 pages
...~ 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, (1.101.) CB x |BC—BZ', multiply by the radius CB, then CB 1 x £BG = CB x BZ 1 therefore... | |
| Euclid - 1810 - 554 pages
...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 BAG oppasite to the base. Let the angles BAC, ABC be bisected by the straight... | |
| Francis Nichols - 1811 - 162 pages
...1, DA : AF :: DA 2 : BA 2 * :: CA 1 : AL 2 . 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 AL 2 =CAxAF. But the radius CA is a constant quantity,... | |
| Euclides - 1814 - 560 pages
...straight lines by which the half of the perimeter exceeds the other two sides, that is, the rectangle BFC, **as the square of the radius is to the square of the** tangent of half the angle BAC opposite to the base. QED PROP. VII. Fie. 12. I3. IN a plane triangle... | |
| Miles Bland - 1819 - 442 pages
...D^5^tang. BAC. PROP. XV. 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 it* base, AB the greater of the sides and AC... | |
| Miles Bland - 1819 - 444 pages
...DAB^t&ng. BAC. PROP. XV. cesses 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... | |
| Miles Bland - 1821 - 898 pages
...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. In AB take AD = AC, join DC; and draw AE perpendicular to DC, and EG parallel... | |
| Euclid, Robert Simson - 1821 - 514 pages
...straight lines by which the half to the perimtter exceeds the othertwo sides, thatis, the rectangle BFC, **as the square of the radius is to the square of the** tangent of half the angle BAC opposite to the base. Q, ED PROP. VII. FIG. 12. 13. IN a plane triangle,... | |
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