| Nathaniel Bowditch - Nautical astronomy - 1826 - 710 pages
...AE : : DH : AF or HB ; that is, AD, the sum of the legs AC and CB, is to AE their difference, as DH **the tangent of half the sum of the angles at the base** (the radius being AH) is to ИВ the tangent of half the difference of the same angles, (to the same... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 782 pages
...triangle (supposing any aide to be the base, and calling the other two the tide*) the sum of the sida **is to their difference, as the tangent of half the sum of** tht ongfcs at the base is to the tangent of half the difference of the tame angla. Thus, in the triangle... | |
| Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...^r;» ^'otn which tang i (a' -f- 6') sin a' + sin 6' we infer, that the sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** these arcs is to the tangent of half their difference, is obtained immediately by a very elegant geometrical... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...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 of any two sides AB,... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 438 pages
...plane triangle are as the sines of the opposite angles. (73.) The sum of two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine,... | |
| 1829 - 536 pages
...first of these cases is shewn to depend on the theorem, that, " the sum of two sidi\s of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles to the tangent of half their difference." This half difference added to half the sum,... | |
| Charles Davies - Surveying - 1830 - 392 pages
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, **is to their difference, as the tangent of half the sum of the** other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;... | |
| Alexander Ingram - Mathematics - 1830 - 462 pages
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB **is to their difference as the tangent of half the sum of the** opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B... | |
| Jeremiah Day - Measurement - 1831 - 520 pages
...equal to 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 <if half their difference. Therefore, R :tan(ACH-45°)::tan|(ACB +... | |
| Jeremiah Day - Measurement - 1831 - 394 pages
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
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