| Jeremiah Day - 1824 - 440 pages
...—sin b tan $(a — b) ' sin a+sin b : sin a— sin b::tan±(a+b) : tan ^(a—b.) Jt \.\ That is, **The sum of the sines of two arcs or angles, is to** the "ference of those sines j as th? tangent of half the sum of the or angle, to the tangent of half... | |
| Charles Hutton - 1826 - 682 pages
...i+ein. B' . . . (XXII.) The equation is readily converted into a very useful proportion, viz. Ttie **sum of the sines of two arcs or angles, is to their...tangent of half the sum of those arcs or angles, is to** Hie tangent of half thtir difference. 26. Operating with the third and fourth formulae of the preceding... | |
| Peter Nicholson - 1825 - 1046 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.... | |
| Nathaniel Bowditch - 1826 - 764 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 - 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 - 1826 - 732 pages
...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... | |
| Thomas Keith - 1826 - 504 pages
...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... | |
| Robert Simson - 1827 - 546 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... | |
| Dionysius Lardner - 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,... | |
| 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... | |
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