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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 ... - Σελίδα 110
των Robert Gibson - 1814 - 508 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...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...

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

Robert Gibson - 1811 - 508 σελίδες
...AB : : S. A : BC, #c. 2. ED THEO. II. Fig. 11. In any Jilane triangle ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to...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 join HC : let fall the...

Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 428 σελίδες
...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...

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

Francis Nichols - 1811 - 128 σελίδες
...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...

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...

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

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...

An Easy Introduction to the Mathematics: In which the Theory and ..., Τόμος 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...

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

John Gummere - 1814 - 346 σελίδες
...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...

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

Jeremiah Day - 1815 - 96 σελίδες
...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...

A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - 1815 - 126 σελίδες
...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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