| Rev. John Allen - Astronomy - 1822 - 516 pages
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC **is to their difference, as the tangent of half the sum of the angles** CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If to half the... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of the angles** at the base is to the tangent of half their difference. Let ABC be a triangle ; then, of the two sides,... | |
| Industrial arts - 1824 - 492 pages
...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 + DA = 9, = 0.954243... | |
| Jeremiah Day - Geometry - 1824 - 440 pages
...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 - Nautical astronomy - 1824 - 572 pages
...= 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 AB... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...R 42. From the 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... | |
| Thomas Keith - Navigation - 1826 - 442 pages
...of triangles are to each other as the chords of double their opposite angles. PROPOSITION IV. (E) 1. **In any plane triangle, the sum of any two sides is...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... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 710 pages
...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,... | |
| Silvestre François Lacroix - Geometry, Analytic - 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 - Nautical astronomy - 1826 - 782 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... | |
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