 The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.  Plane Trigonometry - Pągina 71906 - 188 pąginesVisualització completa - Sobre aquest llibre
 | 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. „ In the... | |
 | 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 following... | |
 | Philip Ronayne - 1738 - 458 pągines
...= BC x S С j WhereforeAB"BC::SC"SA. QE.2). Axiom III. The Sum of th« 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)emonftration. which (by... | |
 | 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 greateu... | |
 | 1751 - 420 pągines
...all 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... | |
 | John Ward - 1771 - 510 pągines
...wherefore AB : BC : : Si. С : Si. A. ' & £• D. Axiom III. The Sum of the Leg« of any Angle of a Plane Triangle is to their Difference, as the Tangent of half the Sum of the Angles oppofite to thofe leg* is to the Tangent of half their Difference. SDcmoaķrcatķon» In the... | |
 | 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 V.... | |
 | John Playfair, Euclid - 1804 - 468 pągines
...between either of them and 45°. PROP. 3oi PLANE TRIGONOMETRY. PROP. IV. HPHE fum of any two fides of a triangle is to their difference, as the tangent of half the fum of the angles oppolite to thofe fides, to the tangent of half their difference. Let ABC be any... | |
 | 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... | |
 | 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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