| Jeremiah Day - 1824
...the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 1 44.] 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+B)... | |
| 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... | |
| 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... | |
| 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... | |
| 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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