| William Enfield - 1811 - 476 pages
...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... | |
| Francis Nichols - 1811 - 162 pages
...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... | |
| Robert Gibson - 1811 - 580 pages
...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,... | |
| Charles Hutton - 1812 - 624 pages
...This equation is 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...angles, is to the tangent of half their difference.** 26. Operating with the third and fourth formula: of the preceding article, as we have already done... | |
| Robert Gibson - 1814 - 558 pages
...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—... | |
| John Gummere - 1814 - 398 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... | |
| Charles Butler - 1814 - 528 pages
...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... | |
| Jeremiah Day - 1815 - 388 pages
...j(a+b) sin a— sin b~tan %(a— b) ' sin it+sinb:sina—sin b::tan %(a+b) :tan ^(a— b.) That is, **the sum of the sines of two arcs or angles, is to** the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent... | |
| Jeremiah Day - 1815 - 172 pages
...(a+b) sin a— sin b~tan %(a— b) ' sin a+sin b : sin a— sin b::tan %(a + b):tan %(a— b.) That is, **the sum of the sines of two arcs or angles, is to** the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent... | |
| Olinthus Gregory - 1816 - 276 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... | |
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