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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 ... - Page 108
by Robert Gibson - 1811 - 508 pages
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A Course of Mathematics: In Three Volumes : Composed for the Use of the ...

Charles Hutton - Mathematics - 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 ..., Volume 2

Charles Hutton, Robert Adrain - Mathematics - 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 - Electronic books - 1814 - 508 pages
...AB .- .- S. A ,• 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...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 ..., Volume 2

Charles Butler - Mathematics - 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 - Surveying - 1814 - 346 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 latter...
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - Logarithms - 1815 - 126 pages
...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 - Measurement - 1815 - 96 pages
...the opposite angles, !Ło 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...being given, the fourth is also given. PROP. III. FIG. 8. IN a plane triangle, the sum of any two 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. . Let ABC be a plane triangle, the sum...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - Plane trigonometry - 1816 - 244 pages
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, is to their difference, as the tangent of half the sum of the complements, is to the tangent of halt' their difference. But half the sum of the complements of two...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 432 pages
...cos la + 7 cos5a + 21 cos3a + 35c. ' &e. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half the difference. If A and B denote two arcs ; smA+«'wB : sin A—...
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