 | John Harris - Geometry - 1706 - 253 pages
...B. 3 Angles. 3 Sides. As the Sum of the Legs about the Angtt given, is to their Difference :: Soii the Tangent of half the Sum of the other two Angles, to the Tangent of half their Difference.. Now the Sum of the other two Angles is known, being what the given Angle wants of i80 Degrees and their... | |
 | Philip Ronayne - Algebra - 1717 - 478 pages
...•• В 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 - Astronomy - 1725 - 506 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 following... | |
 | John Ward (of Chester.) - Mathematics - 1747 - 516 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 greateu... | |
 | 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 of two... | |
 | Henry Wilson - Navigation - 1761 - 528 pages
...I, AXIOM III. In all Triangles, as tlie Sum of the Leg"; of any Angle is to their Difference, fo is the Tangent of half the Sum of the other two Angles, to the Tangent of half their Difle^ rencc; and therefore, When there are given two Sides, and ah Angle included, to find the other... | |
 | 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 V.... | |
 | Robert Simson - Trigonometry - 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... | |
 | John Bonnycastle - Trigonometry - 1806 - 464 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.... | |
 | Robert Gibson - 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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In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 
