 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.  The Mathematician - Side 1571751 - 399 siderUten tilgangsbegrensning - Om denne boken
 | Philip Ronayne - 1717 - 478 sider
...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 sider
...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 sider
...= 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 sider
...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... | |
 | John Ward - 1771 - 510 sider
...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. SDcmoaírcatíon» In the... | |
 | Robert Gibson - 1795 - 384 sider
...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.... | |
 | Alexander Ewing - 1799 - 512 sider
...triangles, as alfo the l1t and :u Cafes of oblique angled triangles. 2. Since the fum of any two fides of a plain triangle is to their difference, as the tangent of half the fum of the oppolire angles is to the tangent of half their difference ; hence we can folve the 1ft... | |
 | Robert Simson - 1806 - 546 sider
...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 sider
...• 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.... | |
 | Robert Gibson - 1808 - 482 sider
...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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