 In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.  Documents of the City of Boston - Pàgina 139per Boston (Mass.). City Council - 1869Visualització completa - Sobre aquest llibre
 | Peter Nicholson - 1825 - 1046 pàgines
...: 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 then'AC=a,... | |
 | Nathaniel Bowditch - 1826 - 732 pàgines
...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... | |
 | Silvestre François Lacroix - 1826 - 190 pàgines
...^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 pàgines
...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... | |
 | Thomas Keith - 1826 - 504 pàgines
...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... | |
 | Robert Simson - 1827 - 546 pàgines
...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 - 1828 - 434 pàgines
...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 pàgines
...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 - 1830 - 390 pàgines
...AB, AC, in a similar manner, we 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 ;... | |
 | Charles Davies - 1830 - 318 pàgines
...similar manner, we should obtain, AC : AB : : sin. B : sin. C. THEOREM. 44. In any plane triangle, ike sum of the two sides containing either angle, is to their difference, as the tangent of half tfte sum of the other two angles, to the tangent of half their difference. .Let ABC (PI. I. Fig. 3)... | |
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