In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. Elements of Geometry and Trigonometry - Side 241av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
| Philip Ronayne - 1717 - 408 sider
...Sum — ~ diff. is = lejje r of them. 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** i. s oppofite is to the Tangent of half their difference. ft. fD AXIOM 4.' • Me»»»- !-*- '"••... | |
| William Hawney - 1725 - 479 sider
...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.) - 1747 - 480 sider
...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 Side... | |
| 1751 - 399 sider
...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... | |
| Robert Gibson - 1795 - 319 sider
...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.... | |
| Euclid, Robert Simson - 1806 - 518 sider
...three being 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 sura of... | |
| John Bonnycastle - 1806 - 419 sider
...• 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 sider
...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 - 1809 - 493 sider
...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 — S,B... | |
| Euclid - 1810 - 518 sider
...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 greater... | |
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