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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Pągina 30
per Olinthus Gregory - 1816 - 244 pągines
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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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## Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801
...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 pągines
...solution of 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 pągines
...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 pągines
...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
...their included angle arc given. The tv.-o remaining angles will be found from the following Theorem : As the sum of the given sides, Is to their difference, So is the tungcnlof half the sum of the two unknown angles, To the tangent of half their difference. Demonstration....
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## A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1808 - 168 pągines
...solution of 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 pągines
...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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## 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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## The British encyclopedia, or, Dictionary of arts and sciences

William Nicholson - 1809
....56.88 ................ l .75486 Axiom III. In every plane triangle it will bn as the sum of any two sides is to their difference; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which lialf difference, being added...
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