In every plane 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 their difference. Elements of Geometry and Trigonometry - Side 241av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
| Jeremiah Day - 1824 - 440 sider
...equal to the sum, and FH to the di/erencc 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 of half their difference. Therefore, R : Tan(ACH-45°)::Tan^(ACB-fB)... | |
| Edward Riddle - 1824 - 572 sider
...= cot B, and tan DAC = cot C. PROPOSITION VI. The slim of any two sides of a triangle is to tlieir difference, as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. Let А В С be any plane triangle. Then... | |
| Peter Nicholson - 1825 - 1046 sider
...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... | |
| Nathaniel Bowditch - 1826 - 732 sider
...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 ABC,... | |
| Thomas Keith - 1826 - 504 sider
...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... | |
| Silvestre François Lacroix - 1826 - 190 sider
...^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 - 1826 - 764 sider
...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 - 1827 - 546 sider
...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... | |
| Dionysius Lardner - 1828 - 434 sider
...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 sider
...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,... | |
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