| Philip Ronayne - 1717 - 408 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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... | |
| Robert Simson - 1806 - 518 páginas
...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 páginas
...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 páginas
...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 páginas
...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... | |
| |