| William Nicholson - Natural history - 1821 - 362 pages
...difference of the same arches. In any spherical triangle, ABC (fig. 27,) it will be, as the co-tangent **of half the sum of the angles at the base is to the tangent of half their difference,** so is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD... | |
| Nautical astronomy - 1821 - 704 pages
...difference of the same angles, (to the same radius,) and therefore (by art. :<:».) as the tabular **tangent of half the sum of the angles at the base is to the** tabular tangent of half the difference of the same angles. LX. I ed in it M : ABC, if the Hoe CD be.... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...44. And from this, the principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal **triangle, the sum of two sides is to their difference, as the tangent of half the sum of the angles** opposite those sides is to the tangent of half the difference of those same angles. From the proportion... | |
| 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...the base is to the tangent of half their difference.** Let ABC be a triangle ; then, of the two sides, CA and CB, let CB be the greater. Produce CA to E,... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...angle. Shew that radius is to the tangent of the difference between this angle and half a right angle, **as the tangent of half the sum of the angles at the base is to the** tiuigcnt of half their difference. ELEMENTARY PRINCIPLES OP SPHERICAL TRIGONOMETRY. 1. A SPHERE is... | |
| Jeremiah Day - Geometry - 1824
...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)... | |
| Industrial arts - 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 + DA =... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...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
...chords of 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... | |
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