 | Abel Flint - Surveying - 1804 - 226 pages
...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.... | |
 | 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... | |
 | 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... | |
 | Abel Flint - Surveying - 1808 - 190 pages
...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... | |
 | 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... | |
 | Thomas Simpson - Trigonometry - 1810 - 152 pages
...(2ED), by 4. 6. ®. ED •f THEOREM V. In any plane triangle, it -will be, 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 their difference. For, let ABC (fig. 5.) be the triangle,... | |
 | Robert Gibson - Surveying - 1811 - 580 pages
...wholes are 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.... | |
 | George Adams - Geometry - 1813 - 648 pages
...the 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... | |
 | Robert Gibson - Surveying - 1814 - 558 pages
...wholes are as their halves, that is, 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 G, to the tangent of half their difference. QED THEO. III. Fig. 12. In... | |
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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. 
