 | William Nicholson - Natural history - 1821 - 358 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 - 706 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 - 394 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 - 518 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 - 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)... | |
 | 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 =... | |
 | Peter Nicholson - Mathematics - 1825 - 1058 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 - 504 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... | |
| |
In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
