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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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A Course of Mathematics in Two Volumes for the Use of Academies as Well as ...

Charles Hutton - 1807 - 460 pages
...be as BE : BD : : AE : DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. EXAMPLE I. In the plane triangle ABC, C AB 345 yards Given < AC 174-07 yards / / A 17° <?(Y I f- AOI...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 488 pages
...la any plane triangle ABC, the sum of the two. given sides AB and £C, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY....
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 pages
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 pages
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of -;' the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 444 pages
...as BE : BD : : AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. EXAMPLE I. In the plane triangle ABC, f AB 345 yards Given j AC 174-07 yards I / A 37° 20' Required...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 162 pages
...angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be the proposed triangle, whose sides are AC, BC,...
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A Course of Mathematics: In Three Volumes : Composed for the Use of the ...

Charles Hutton - 1811 - 496 pages
...as BE : BD : : AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half th«ir difference. EXAMPLE I. In the plane triangle ABC, f AB 345 yards Given } AC 174-07 yards C /A...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 592 pages
...In any Jilane triangle ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to Che tangent of half their difference. Produce AB and make HB=BC, and...
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 476 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the...
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A Course of Mathematics: In Three Volumes : Composed for the Use of the ...

Charles Hutton - 1811 - 424 pages
...k readily converted into a very nsefnl proportion, viz, The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs ' or angles, is to the tangent of half their difference. 2f . Operating with the third and...
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