| 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. „ 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 - 420 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... | |
| David Stewart Erskine Earl of Buchan, Walter Minto - Logarithms - 1787 - 164 pages
...difference. Cof af-cof b : cof a — cof b : : cot ^ : tang t±?. (4) Lem. 3. The fum of the fines **of two arcs is to their difference as the tangent of half the** fum of thofe arcs is to the tangent of half their their difference. * Sin a + fin b : fin a — fin... | |
| Robert Gibson - Surveying - 1795 - 386 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 - 548 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 - 488 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.... | |
| Euclid - Geometry - 1810 - 554 pages
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be **to their difference as the tangent of half the sum of -;' the** angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the... | |
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