| 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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