 | Philip Ronayne - Algebra - 1717 - 478 pages
...Sum — ~ diff. is = lejjer of them. But Wholes are as their Halves : Wherefore the Sum of the Legs is to their Difference as the Tangent of half the Sum of the i. s oppofite is to the Tangent of half their difference. ft. fD • Me»»»- !-*- '"•• AXIOM... | |
 | William Hawney - Astronomy - 1725 - 504 pages
...the Tangent of half their Difference. But Wholes are as their Halves: Therefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the oppofite Angles, is to the Tangent of half their Difference. Which was, &c. From this Axiom the... | |
 | Philip Ronayne - Algebra - 1738 - 458 pages
...В С : : S С •• S A. QE.Z). Axiom III. The Sum of the Legs of any Angle of a Plane Triangle, Is to their Difference, As the Tangent of half the Sum of the Angles oppofite to thofe Legs, Is to the Tangent of half their Difference. 2)emonfiratiott. D (by... | |
 | Geometry - 1751 - 420 pages
...writers of Trigonometry, that the Sum of the Sides, including any given Angle Angleof a plain Triangle, is to their Difference, as the Tangent of half the Sum of the unknown Angles, is to the Tangent of half their Difference ; therefore, if the including Sides... | |
 | Geography - 1867 - 878 pages
...sines, and may be thus written :— sin. A _ ein. B _ gin. С abc .(66) 2. The sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By the lost proposition, Then, componenda... | |
 | John Ward - Mathematics - 1771 - 510 pages
...the Tangent of half -their Difference: But Wholes are as their Halves ; wherefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the Angles oppofite is to the Tangent of half their Difference. J. ED Axiom IV. The Bafe, or greateft... | |
 | John Hamilton Moore - Nautical astronomy - 1791 - 578 pages
...Tangent of half their Difference : but Wholes are as their Halves ; wherefore the Sum of the Leg« is to their Difference, as the Tangent of half the Sum of the «ppofite Angles, is to the Tangent of half their Difference, E* The . Tp find the Angles D and... | |
 | John Bonnycastle - Trigonometry - 1806 - 464 pages
...• Hence, since AC, OF are parallel, EcistocrasEA. is to AC; that is, the sum of the sides AB, Bc is to their difference, as the tangent of half the sum of their opposite angles B AC, BCA is to the tangent of half their difference. , QE u. THEOREM III. 95.... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...difference ; and since BC FG are parallel (2. 6.) EC is to CF, as EB to BG ; 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. PROP. IV. FIG. 18. cess of this angle... | |
 | Robert Gibson - 1808 - 482 pages
...la any plane triangle ABC, the sum of the two. given sides AB and £C, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY.... | |
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&c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half 
