| Philip Ronayne - 1717 - 408 sider
...difference of any two Quantities is = greater of them. And ± Sum — ~ diff. is = lejje r of them. **But Wholes are as their Halves : Wherefore the Sum...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
...oppofite Angles is to 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 - 1738 - 421 sider
...parallel to the Bafe, being ( by Schol. to 2. 6 End. El. ) proportional ; E С » EB : : FA •• FG 5 **that is in Words, half the Sum of the Legs, Is to...oppofite, Is to the Tangent of half their Difference.** ,§>. E Û). Axiom IV. The Bafe , or greateft v „ Side of any Plane Trian- ..--Ч gle, Is to the... | |
| 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
...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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