 | William Leybourn - 1704 - 432 pages
...Oblique-angled Spherical Triangles, whofe Three Sides together are lefs than -a Semicircle, or 1 80 Degrees. As the Sine of half the Sum of the Angles at the Is to the Sine of the half Difference ofthofe Angles ^ . So is the Tangent of half the Bafe, To the... | |
 | Robert Simson - 1806 - 546 pages
...6.) EC is to CF, as EB to BG ; that is, the sum of the sides is to their diffcrence, as the tangent of half the sum of the angles at the base to the tangent of hal£ their difference. PROP. IV. FIG. 18. In any plane triangle BAG, whose two sides are... | |
 | Sir John Leslie - 1809 - 522 pages
...S,C: S,A. PROP.X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB + AC : AB— AC : : T, : f ., ( ,— [ t... | |
 | Charles Butler - 1814 - 568 pages
...: AE:: FB : ED (16. 5.) ; that is, the sum of the 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. QED When two sides and the included angle are given, the remaining... | |
 | Olinthus Gregory - 1816 - 276 pages
...will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin B : sin A, .•. by comp. and... | |
 | Euclides - 1816 - 588 pages
...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 any two sides AB, AC will... | |
 | Charles Hutton - 1816 - 618 pages
...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. JLx. 14. How must three trees, A, B, c, be planted, so that the... | |
 | Sir John Leslie - 1817 - 456 pages
...the same. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difi ference. In the triangle ABC, AB+AC : AB— AC : : From the vertex A, and... | |
 | Thomas Leybourn - 1819 - 430 pages
...geometrically, that in any plane triangle, the sum of the 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. 9. Shew that tan.3 60 = 3 tan. 60 to rad. == i. 10. P and W being... | |
 | Charles Hutton - 1822 - 680 pages
...and the tangent of half its complement. Ex. 13. Prove that, in any plane triangle, the base is to tbe difference of the other two sides, as the sine of half the "• " l ' " " v' ' 1 ' ' ' ' ~ ' sum of the angles at the base,* to the sine of half their difference... | |
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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... 
