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C' (89) (90) (91) (92) (93) 112. In any plane 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.
The Theory and Practice of Surveying: Containing All the Instructions ... - Σελίδα 110
των Robert Gibson - 1814 - 508 σελίδες
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## ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. .Dividing formula (3) "by (4), and considering...

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 σελίδες
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin....

## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and...

## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 σελίδες
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 σελίδες
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 490 σελίδες
...sin ^1 sin £ siu C7° (89) (90) (91) (92) (93) 112. In any plane 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. For, by (90), a : b : : sin A : sin B ;...

## Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1862 - 393 σελίδες
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 σελίδες
...a sin A sin B sin C' (89) (90) (91) (92) (93) 112. In any plane 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. For, by (90), a : b : : sin A : sin B;...

## A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1863 - 256 σελίδες
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»...

## Elements of Plane Trigonometry: And Their Application to the Measurement of ...

...the first proportion in Theorem I. THEOREM III. 41. In any plane 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 a triangle ; then AB + BC:BC—...