| 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. „ In the... | |
| William Hawney - 1725
...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 - Algebra - 1738 - 421 pages
...= R x BD) = 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.) - 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 greateu... | |
| Mathematics - 1751 - 399 pages
...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 - Mathematics - 1771 - 480 pages
...С ; 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 - 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.... | |
| John Playfair - Euclid's Elements - 1795 - 400 pages
...radius to the tangent of the difference between either of them and 45°. PROPTHE fum of the fides of any **.plane triangle is to their difference, as the tangent of half the** fum of the angles at the bafe of the triangle, to the tangent of half their difference. Let ABC be... | |
| 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.... | |
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