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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.
A complete system of mensuration, with additions by J. Trotter - Página 33
por Alexander Ingram - 1851
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## Trigonometry Improv'd, and Projection of the Sphere, Made Easy: Teaching the ...

Henry Wilson - 1720 - 192 páginas
...HI. , • , j In all Triangles, as the Sum of the Legs including any Angle is to their Difference, fo is the Tangent of half the Sum of the unknown Angles, to the Tangent of half th«ir Difference. •' . .; v ,. : "'. • -I AXIOM IV. In all right lined Triangles ; as the Bafe...
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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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Henry Wilson - 1761 - 528 páginas
...find the other Angles, the Proportion is, As the Sum of the Sides, to the Difference of the Sides, fo is the Tangent of half the Sum of the unknown Angles, to the Tangent of half their Difference ; which half Difference added to the half Sum, is the greater Angle, and fubtradted leaves the letter....
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## Mathematics: Compiled from the Best Authors and Intended to be the ..., Volumen2

1801 - 426 páginas
...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 páginas
...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 páginas
...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 páginas
...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 ..., Volumen1

Isaac Dalby - 1807
...are parallel, the 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 = 4100...
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## A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1808 - 168 páginas
...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 páginas
...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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