| Jeremiah Day - Measurement - 1815 - 388 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... | |
| Euclides - 1816 - 588 pages
...in a plane triangle, any three 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... | |
| Olinthus Gregory - Plane trigonometry - 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 two... | |
| Sir John Leslie - Geometry - 1817 - 456 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—... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...found*. * The preceding expressions not being easy for calculation, values i . may PROP. XIII. (88.) **In any triangle, the sum of any two sides is to their difference as the tangent of** the semi-sum of the angles at the base is to the tangent of their semi-difference. Let ABC be any triangle,... | |
| Thomas Leybourn - Mathematics - 1819 - 430 pages
...: BC* : AC*. Required a proof. 8. Prove, geometrically, that in any plane triangle, 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. 9. Shew that tan.3 60 = 3 tan. 60 to rad.... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...the difference between either of them and 45o. * PROP. IV. The sum of any troo sides of a triangle **is to their difference, as the tangent of half the sum of the** angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle... | |
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal triangle, the sum of **two sides is to their difference, as the tangent of half the sum of the** angles opposite those sides is to the tangent of half the difference of those same angles. From the... | |
| Rev. John Allen - Astronomy - 1822 - 516 pages
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC **is to their difference, as the tangent of half the sum of the** angles CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If to... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of the** angles at the base is to the tangent of half their difference. Let ABC be a triangle ; then, of the... | |
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