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Bøker Bok 110 av 70Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the...
" 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. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 5
av Thomas Simpson - 1810 - 125 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...
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A System of Practical Mathematics ...: With a Plain Account of the Gregorian ...

John Potter - 1753 - 395 sider
...To the Sine of its oppofite Angle. Rule 2. When any two Sides with the Angle between them are given. As the Sum of any two Sides Is to their Difference, So is the Tangent of the Half-Sum of the two oppofite Angles " To the Tangent of Half the Difference of thofe two Angles....
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801
...JROSLEM It. Given tiua sides 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
...Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference...of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles and you will have...
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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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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
...Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference...of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles and you will have...
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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 right-lined...
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Mathematics, Volum 1

Samuel Webber - 1808
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : Is to their difference " : : So is the tangent of half the sum of their opposite angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem,...
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