Books Books 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... A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 74
by Charles Hutton - 1811 ## Nine Geometricall Exercises: For Young Sea-men, and Others that are Studious ...

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... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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... ## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

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... ## Easy Introduction to Mathematics, Volume 2

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... ## Elements of Plane and Spherical Trigonometry: With Their Applications to ...

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... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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... ## A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 2

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... ## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

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... ## New Series of The Mathematical Repository, Volume 4

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... 