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Libros Libros 1 - 10 de 180 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions...
" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Easy Introduction to Mathematics - Página 397
por Charles Butler - 1814
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 408 páginas
...Sum — ~ diff. is = lejje r 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 AXIOM 4.' • Me»»»- !-*- '"••...
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The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 479 páginas
...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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The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - 1747 - 480 páginas
...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 oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or greateu Side...
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The Mathematician

1751 - 399 páginas
...writers of Trigonometry, that the Sum of the Sides, including any given Angle Angle of 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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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1795 - 319 páginas
...II. In any plane Triangle ABC, the Sum of the two given Sides AB and BC, 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 ef half their Difference. Fig. 1 1 . Produce Plate V....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 páginas
.... * Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 páginas
...• Hence, since AC, OF are parallel, EcistocrasEA. is to AC; that is, the sum of the sides AB, B c 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 páginas
...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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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 páginas
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 páginas
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of -;' the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for...
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