| 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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