| John Potter - Mathematics - 1753 - 568 pages
...To the Sine of its oppofite Angle. Rule 2. When any two Sides with the Angle between them are given. **As the Sum of any two Sides Is to their Difference, So is the Tangent of** the Half-Sum of the two oppofite Angles " To the Tangent of Half the Difference of thofe two Angles.... | |
| Abel Flint - Surveying - 1804 - 226 pages
...Angles and Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every **Plane Triangle, As the Sum of any two Sides ; Is to...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... | |
| 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...angles, to the tangent of half their difference. Then** the half difference of these angles, added to their half sum, gives the greater angle, and subtracted... | |
| 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... | |
| Abel Flint - Surveying - 1808 - 190 pages
...Angles and Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every **Plane Triangle, As the Sum of any two Sides ; Is to...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... | |
| Nicolas Pike - Algebra - 1808 - 470 pages
...to the other side. When any ttvo sides luilh the angle included let-wen then are given. RULE 2. — **As the sum of any two sides is to their difference ; so** 5s the tangent of the half sum of the two opposite angles, to the tangent of half the difference of... | |
| William Nicholson - 1809 - 722 pages
...9.74198 To the sine DC .56.88 ................ 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 - 168 pages
...(AC + BC) : : BH (AC — BC) : BG (2ED), by 4. 6. ^ ED 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,... | |
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