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Bøker Bok 1120 av 183C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides...
" 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 Young Mathematician's Guide: Being a Plain and Easy Introduction to the ... - Side 479
av John Ward - 1771 - 480 sider
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 428 sider
...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 difference,...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 sider
...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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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 128 sider
...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 ..., Volum 2

Charles Hutton - 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 ..., Volum 2

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

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

Robert Gibson - 1814 - 508 sider
...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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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 96 sider
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the...
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - 1815 - 126 sider
...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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