| Adrien Marie Legendre - Geometry - 1822 - 367 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 proportion... | |
| Jeremiah Day - Geometry - 1824 - 440 pages
...opposite angles. It follows, therefore; from the preceding proposition, (Alg. 339.) 'et 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 thesecoud theorem applied to the... | |
| Industrial arts - 1824 - 492 pages
...DCA= BCD, because DA C = AC B, (Euc. 1. 29.) Therefore, DAC+ DCA = 130o, and consequently ADC = of any **triangle is to their difference, as the tangent of half the sum of the angles** opposite them, is to the tangent of half their difference. Therefore, by logarithms, As, CD + DA =... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...: AC— CB:: tangí (B+C) : tang-i (B—C) it follows that in any triangle the sum of any two sides **is to their difference, as the tangent of half the sum of the** two angles opposite these sides, is to the tangent of half the difference of these same angles. Let... | |
| Thomas Keith - Navigation - 1826 - 442 pages
...OF THE DIFFERENCES OF ARCS. PROPOSITION xiii. (Plate L Fig. 2.J (P) The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** those arcs is to the tangent of half their difference. Let BA and во be the two arcs ; draw the diameter... | |
| 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... | |
| 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... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...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
...of a 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 - 530 pages
...given. The solution of the first of these cases is shewn to depend on the theorem, that, " the sum of **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 half difference added to half the sum,... | |
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