| Philip Ronayne - Algebra - 1717 - 408 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 - 479 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 - 480 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
...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... | |
| Euclid, Robert Simson - Euclid's Elements - 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 - 419 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 - Surveying - 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.... | |
| Sir John Leslie - Geometry, Analytic - 1809 - 493 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 —... | |
| Thomas Keith - Navigation - 1810 - 420 pages
...THE DIFFERENCES OF ARCS. PROPOSITION xin. (Plate /. Fig. 2.) (P) The sum of the sines ofttvo arcs i: **to their difference, as the tangent of half the sum of those arcs** is to the tangent of half their difference. Let BA and BO be the two arcs ; draw the diameter nx, and... | |
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