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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 ... - Page 106
by Robert Gibson - 1811 - 508 pages

## Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 pages
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin. B....

## Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - Boston (Mass.) - 1868 - 508 pages
...and cosecant. 2. Demonstrate that, 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. 3. Given two sides and an opposite angle, in...

## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Electronic book - 1868 - 530 pages
...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III.— In every plane...

## Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 346 pages
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180° —...

## Documents of the City of Boston, Volume 3

Boston (Mass.). City Council - Boston (Mass.) - 1869 - 1192 pages
...and cosecant. 2. Demonstrate that, 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. 8. Given two sides and an opposite angle, in...

## Annual Report and Documents of the New York ..., Volume 50, Parts 1868-1873

New-York Institution for the Instruction of the Deaf and Dumb - Deaf - 1869 - 698 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem...

## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1869 - 550 pages
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane...

## Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 398 pages
...0 : sin B. Theorems. THEOREM 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. Let ACB be a triangle: then will AB + AC: AB—...