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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.
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811

## Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 476 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half...

## A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 162 pages
...angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any 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 the proposed triangle, whose...

## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 580 pages
...In any Jilane triangle ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to Che tangent of half their difference. Produce AB and make HB=BC,...

## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1812 - 624 pages
...This equation is readily converted into a very useful proportion, viz, The sum of the sines of tiuo arcs or angles, is to their difference, as the tangent...angles, is to the tangent of half their difference. 26. Operating with the third and fourth formula: of the preceding article, as we have already done...

## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1814 - 558 pages
...aIn any jilane triangle AUC, the sum of the two gruen sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and Cix tg the tangent of half their difference. Produce AB, and make HB—...

## A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - 1814 - 398 pages
...therefore since BC, FG are parallel EB : BF : : EC : CG (2. 6.) ; that is, the * sum of the sides AC, AB, is to their difference, as the tangent of half the sum of the angles ABC, ACB, is to the tangent of half their difference. • *• •• To demonstrate the...

## An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - 1814 - 528 pages
...1.), V AF : FB : : AE : ED (4. 6.) and AF : AE : : FB : ED (16. 5.) ; that is, the sum of the sides : is to their difference : : as the tangent of half the sum of the angles at the base : to the tangent of half their difference. QED When two sides and the included...

## A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 388 pages
...j(a+b) sin a— sin b~tan %(a— b) ' sin it+sinb:sina—sin b::tan %(a+b) :tan ^(a— b.) That is, the sum of the sines of two arcs or angles, is to the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent...