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" of half the perimeter above those sides, as the square of the radius is to the square of the sine of half the angle included by "
Course of Civil Engineering: Comprising Plane Trigonometry, Surveying, and ... - Page 38
by John Gregory - 1842
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An Introduction to the True Astronomy: Or, Astronomical Lectures,: Read in ...

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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...
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An Introduction to the Theory and Practice of Plane and Spherical ...

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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

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,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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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