 | Enoch Lewis - Conic sections - 1844 - 240 pages
...cos CAD : cos CAB : : tan AD : tan AB. QED ART. 72. As the sum of the sines of any two unequal arcs is to their difference, so is the tangent of half the sum of those arcs, to the tangent of half their difference. Let AB, AC be the arcs ; L the centre of the circle... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also-, that the base is to the sum of the other two sides as the cosine... | |
 | Nathan Scholfield - 1845 - 894 pages
...sine of half their difference: also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...sine of half their difference : also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...same angles. Thus, in the triangle ABC, if we call AB the base, it will l>e, As the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their dinerence. DH Dem. With the longest leg, CB, as radius, describe... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...then will the radius be to the tangent of the difference between that angle and half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of two sides 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. Given the triangle ABC, the side AB being greater than... | |
 | Jeremiah Day - Logarithms - 1848 - 354 pages
...other radius. (Art. 119.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...angle between them, to find the other two angles and the third side. RULE. As the sum of the two given sides, is to their difference, so is, the Tangent of half the sum of the unknown angles, to the Tangent of half their difference. Half the difference thus found added to half... | |
 | Alexander Ingram - 1851 - 202 pages
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sum of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference (Theor. 4. Trig.) Having thus found the half... | |
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AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
