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 Llibres Llibres 1 - 10 de 180 sobre In any plane triangle, the sum of any two sides is to their difference as the tangent.... 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. By Theorem II. we have a : b : : sin. A : sin. B. A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pàgina 114
per Jeremiah Day - 1815 - 126 pàgines
Visualització completa - Sobre aquest llibre ## A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 408 pàgines
...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. „ In the...
Visualització completa - Sobre aquest llibre ## The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 479 pàgines
...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...
Visualització completa - Sobre aquest llibre ## The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - 1747 - 480 pàgines
...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...
Visualització completa - Sobre aquest llibre ## The Mathematician

1751 - 399 pàgines
...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...
Visualització completa - Sobre aquest llibre ## A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1795 - 319 pàgines
...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....
Visualització completa - Sobre aquest llibre ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 pàgines
...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 difference. . * Let ABC be a plane triangle, live...
Visualització completa - Sobre aquest llibre ## A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 pàgines
...• 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....
Visualització completa - Sobre aquest llibre ## A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volum 2

Charles Hutton - 1807
...be as BE : BD : : AE : DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. EXAMPLE I. In the plane triangle ABC, C AB 345 yards Given < AC 174-07 yards / / A 17° <?(Y I f- AOI...
Visualització completa - Sobre aquest llibre ## A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pàgines
...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....
Visualització completa - Sobre aquest llibre ## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 pàgines
...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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