| Industrial arts - 1824 - 492 pages
...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... | |
| Jeremiah Day - Geometry - 1824 - 440 pages
...THE OPPOSITE ANGLES ; To 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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...obtuse R 42. From the proportion AC + CB : 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 - 504 pages
...are to each other as the chords of double their opposite angles. PROPOSITION IV. (E) 1. In any plane **triangle, the sum of any two sides is to their difference, as the tangent of half the sum of** their ^opposite angles, is to the tangent of half their difference. Let ABC be any triangle; make BE... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...any triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the **sides is to their difference, as the tangent of half the sum of the** angles at the base is to the tangent of half the difference of the tame angles. Thus, in the triangle... | |
| 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 - 546 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 of... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 434 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, tangent, and cotangent... | |
| 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, gives the greater,... | |
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