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" C' (89) (90) (91) (92) (93) 112. In any plane triangle, 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. "
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Pągina 54
per Elias Loomis - 1855 - 178 pągines
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 478 pągines
...С : : 5, С • S, A " - S,C: 3 D) == S, A, QED' AXIOM AXIOM. III. The Sum of che Legs of an Angle is to their Difference as the Tangent of half the Sum of the Angles oppofite to rhofe Legs, is to the Tangent of half their Difference. Demonßrütion. „...
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The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 504 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...
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The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - 1747 - 516 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 oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or...
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The Mathematician

1751 - 420 pągines
...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...
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An Account of the Life, Writings, and Inventions of John Napier, of Merchiston

David Stewart Erskine Earl of Buchan, Walter Minto - 1787 - 164 pągines
...difference. Cof af-cof b : cof a — cof b : : cot ^ : tang t±?. (4) Lem. 3. The fum of the fines of two arcs is to their difference as the tangent of half the fum of thofe arcs is to the tangent of half their their difference. * Sin a + fin b : fin a — fin...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1795 - 384 pągines
...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...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801 - 658 pągines
...side by the first problem. NbT* tile sum of the sines is to the difference of the sine: of two arcs, as the tangent of half the sum of those arcs is to the tangent of half their difference : in order to which, let ED, CE, be the sines of the arcs AB, AC ; produce BD to the circumference...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 pągines
...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 difference. . * Let ABC be a plane triangle, live...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 464 pągines
...• 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 - 482 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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