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The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 18
por International Correspondence Schools - 1906
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 páginas
...la any plane triangle ABC, the sum of the two. given sides AB and £C, 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 the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY....
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 páginas
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 páginas
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of -;' the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 páginas
...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, and...
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 428 páginas
...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 the...
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A Course of Mathematics: In Three Volumes : Composed for the Use of the ...

Charles Hutton - 1811
...k readily converted into a very nsefnl proportion, viz, The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs ' or angles, is to the tangent of half their difference. 2f . Operating with the third and...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton, Robert Adrain - 1812
...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 of half the sum of those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volumen2

Charles Butler - 1814
...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 angle...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - 1814 - 346 páginas
...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 latter...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1814 - 508 páginas
...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— BC,...
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