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Llibres Llibres 1 - 10 de 180 sobre in any triangle, the sum of two sides is to their difference as the tangent of half....
" in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. "
ELEMENTS OF TRIGONOMETRY, PLANE AND SPHERICAL - Pągina 71
per LEFEBURE DE FOURGY - 1871
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 408 pągines
...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...
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The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 479 pągines
...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 following...
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1738 - 421 pągines
...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 8. iJSuA&m.)...
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The Mathematician

1751 - 399 pągines
...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 of two...
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The popular educator, Volums 5-6

Popular educator - 1767
...the rule of 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...
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The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward - 1771 - 480 pągines
...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 Side of...
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The Practical Navigator, and Seaman's New Daily Assistant: Being an Epitome ...

John Hamilton Moore - 1791 - 296 pągines
...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 C,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 pągines
...three being given, the fourth is also given. ' 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 differcnce. • •• Let ABC be n plane triangle, tl>e...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 pągines
...• 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....
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pągines
...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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