 | Henry Wilson - Astronomy - 1720 - 218 pages
...HI. , • , j In all Triangles, as the Sum of the Legs including any Angle is to their Difference, fo is the Tangent of half the Sum of the unknown Angles, to the Tangent of half th«ir Difference. •' . .; v ,. : "'. • -I AXIOM IV. In all right lined Triangles ; as the Bafe... | |
 | 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... | |
 | Henry Wilson - Navigation - 1761 - 580 pages
...find the other Angles, the Proportion is, As the Sum of the Sides, to the Difference of the Sides, fo is the Tangent of half the Sum of the unknown Angles, to the Tangent of half their Difference ; which half Difference added to the half Sum, is the greater Angle, and fubtradted leaves the letter.... | |
 | Mathematics - 1801 - 658 pages
...sides and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the... | |
 | Abel Flint - Surveying - 1804 - 226 pages
...solution of this CASE 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... | |
 | Robert Gibson - Surveying - 1806 - 486 pages
...wholes 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... | |
 | John Bonnycastle - Trigonometry - 1806 - 464 pages
...included angle are given, to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, is to their difference, so is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
 | Isaac Dalby - Mathematics - 1807 - 476 pages
...triangles 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 = 4100... | |
 | Abel Flint - Surveying - 1808 - 190 pages
...solution of this CASE 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... | |
 | 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... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
