C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| 1824
...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... | |
| Peter Nicholson - 1825 - 372 sider
...: 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 - 617 sider
...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 - 442 sider
...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 - 1826 - 165 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 - 617 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 - 513 sider
...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 - 317 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
...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,... | |
| Alexander Ingram - 1830
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB **is to their difference as the tangent of half the sum of the** opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B... | |
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