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" 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. "
A Course of Mathematics: For the Use of Academies, as Well as Private Tuition - Page 13
by Charles Hutton - 1831
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - Algebra - 1717 - 408 pages
...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 - Astronomy - 1725 - 479 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...
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The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

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

Geometry - 1751 - 399 pages
...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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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1795 - 319 pages
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...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 - Trigonometry - 1806 - 419 pages
...• 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 - Surveying - 1808 - 440 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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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Analytic - 1809 - 493 pages
...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 —...
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An Introduction to the Theory and Practice of Plane and Spherical ...

Thomas Keith - Navigation - 1810 - 420 pages
...THE DIFFERENCES OF ARCS. PROPOSITION xin. (Plate /. Fig. 2.) (P) The sum of the sines ofttvo arcs i: to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Let BA and BO be the two arcs ; draw the diameter nx, and...
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