C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Philip Ronayne - 1717 - 408 sider
...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 - 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... | |
| 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
...AH : IH : : CE : ED, that is, as the Sum of the two Sides AB and BC, is to their Difference ; fo is **the Tangent of half the Sum of the two unknown Angles A and C,** • to the Tangent of half their Difference. QED THEO. Plate V. <THE 0. III. In any right-lined plane... | |
| Robert Gibson - 1806 - 452 sider
...AH : IH : : CE : ED, that is .as the sum of the two sides AB and BC, is to their difference ; so is **the tangent of half the sum of the two unknown angles A and C,** to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate V. THEOREM JII. In any right-lined... | |
| 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... | |
| John Bonnycastle - 1806 - 419 sider
...circle is to the radius of the tables. THEOREM II. 94. The sum of any two sides of a plane triangle **ABC, is to their difference, as the tangent of half the sum of** their opposite angles is to the tangent of half their difference. . &> For about one of the angular... | |
| 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... | |
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