 | Philip Ronayne - Algebra - 1717 - 478 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. „... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Robert Gibson - Surveying - 1795 - 319 pages
...THEO. 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... | |
 | John Playfair - Euclid's Elements - 1804 - 470 pages
...becaufe BC is parallel to FG, CE : CF : : BE : BG, (2. 6.) ; that is, the fum of the two fides of the triangle ABC is to their difference as the tangent of half the v fum of the angles oppofite to thofe fides to the tangent of half their difference. Q ED PROP. 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... | |
 | Robert Gibson - 1808 - 440 pages
...II. 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.... | |
 | Sir John Leslie - Geometry, Plane - 1809 - 522 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 —... | |
 | Robert Gibson - Surveying - 1811 - 592 pages
...Fig. 11. In any Jilane 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 Che tangent of half their difference. Produce AB and make HB=BC,... | |
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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. 
