| Euclid - 1810 - 518 sider
...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... | |
| Robert Gibson - 1811 - 508 sider
...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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| Jeremiah Day - 1815 - 96 sider
...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... | |
| 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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