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Bøker Bok 110 av 94AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles...
" AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. "
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Side 18
av Olinthus Gregory - 1816 - 244 sider
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Spherical trigonometry

Benjamin Martin - 1736
...Sides, Is to the Sine of their Difference, ( So is the Sine of the Sum of the Angles, to the Sine of their Difference ; ) So is the Tangent of half the Sum of the Angles, To the Tangent of halt their Différence. 14. That is, IK : IH: : AP :AO. Therefore IK+IH m IK-IH ....
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801 - 426 sider
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1804 - 168 sider
...this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 452 sider
...wholes are as their halves, ie AH : IH : : CE : ED, that is .as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 sider
...included angle are given, to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, is to their difference, so is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 sider
...Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce 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 greater side for...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volum 1

Isaac Dalby - 1807
...triangles DRA, DGB will be similar; whence we have, DG : DR :: GB : RA; That is, as the sum of the sides, is to their difference, so is the tangent of half the sum of the unknown or opposite angles, to the tangent of half the difference of those angles. Examp. 1. Let CD...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1808 - 168 sider
...this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 sider
...wholes areas their halves, ie AH : IH : : CE : ED, that is, as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED Plate V. THEO. III. In any...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 sider
...consequently AB: BC:: S,C: S,A. PROP.X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB + AC : AB— AC : : T, : f ., ( ,— [ t 2 -For, by the last proposition, AB...
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