| Benjamin Martin - Plane trigonometry - 1736 - 414 pages
...Sides, Is to the Sine of their Difference, ( So is the Sine of the Sum of the Angles, to the Sine of **their Difference ; ) So is the Tangent of half the Sum of the** Angles, To the Tangent of halt their Différence. 14. That is, IK : IH: : AP :AO. Therefore IK+IH m... | |
| William Mudge, Isaac Dalby, Thomas Colby - Arc measures - 1801 - 690 pages
...angles of a spherical triangle, to find those angles : As the tangent of half the sum oj the sides, **Is to the tangent of half their difference ; So is the tangent of** halfibe sum of the angles, To the tangent of half their difference. Or thus. Let s and c represent... | |
| Abel Flint - Surveying - 1804 - 226 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to **their Difference ; So is the Tangent of half the Sum of the two** opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half... | |
| Robert Gibson - Surveying - 1806 - 486 pages
...are as their halves, ie 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... | |
| Isaac Dalby - Mathematics - 1807 - 476 pages
...DRA, DGB will be similar; whence we have, DG : DR :: GB : RA; That is, as the sum of the sides, is to **their difference, so is the tangent of half the sum of the** unknown or opposite angles, to the tangent of half the difference of those angles. Examp. 1. Let CD... | |
| Robert Gibson - 1808 - 482 pages
...wholes areas their halves, ie 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 Plate V. THEO. III. In any right-lined... | |
| Abel Flint - Surveying - 1808 - 190 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to **their Difference ; So is the Tangent of half the Sum of the two** opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half... | |
| William Nicholson - 1809 - 722 pages
................... l .75486 Axiom III. In every plane triangle it will bn as the sum of any two sides is to **their difference; so is the tangent of half the sum of the** angles opposite there, to the tangent of half their difference. Which lialf difference, being added... | |
| Robert Gibson - Surveying - 1811 - 580 pages
...as their halves, that is, AH: Iff : : CE : ED, that ia 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. 2. E. DK THEO. III. fig. 12. In any... | |
| George Adams - Geometry - 1813 - 648 pages
...angle CDB, and the side CD: to find CDB we use this proportion; as the sum of the two given aides is to **their difference, so is the tangent of half the sum of the two** unknown angles to the tangent of half their difference; the angle C'DB being found; the following projwrtion... | |
| |