In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... Easy Introduction to Mathematics - Pagina 361door Charles Butler - 1814Volledige weergave - Over dit boek
| Philip Ronayne - 1717 - 408 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
.... * Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce **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 side for... | |
| John Bonnycastle - 1806 - 419 pagina’s
...• 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 pagina’s
...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 pagina’s
...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 pagina’s
...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 side for... | |
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