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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 Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 359 σελίδες
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin...

A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Ralph Smyth, Sir Henry Edward Landor Thuillier - 1851 - 718 σελίδες
...AB : : the Sine of A : BC, etc. QED H THEO. II. In any plane triangle ABC, the sum of the tivo given sides AB and BC, including a given angle ABC, is to their difference, as theJangent of half the sum of the two unknown angles A and C is to the tangent of half their difference....

A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1851
...the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan...

A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - 1851 - 372 σελίδες
...: tan £ (A + B) : tan ^ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 76 This proportion is employed when two...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3 + AC...

A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle 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 the preceding article, a : b =...

Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1886 - 324 σελίδες
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...

A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1853 - 5 σελίδες
...therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to...

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

Charles Davies - 1854 - 322 σελίδες
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 σελίδες
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,...




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