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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. "
A Treatise of Practical Surveying, ... - Página 94
por Robert Gibson - 1808 - 440 páginas
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 páginas
...AH: Iff : : CE : ED, that ia as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. 2. E. DK THEO. III. fig. 12. In any right lined filane triangle...
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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 Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 128 páginas
...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...
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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 ..., Volumen2

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

Robert Gibson - 1814 - 508 páginas
...BC, 6fc. QED THEO. II. fig. aIn any jilane triangle AUC, the sum of the two gruen sides AB and BC, including a given angle ABC, is to their difference,...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, and join HC: Jet fall the...
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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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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - 1815 - 126 páginas
...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 tfACB+B)...
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 96 páginas
...the opposite angles, !£o the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making...
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