 | John Potter - 1753 - 568 σελίδες
...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 - 1804 - 226 σελίδες
...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 - 1806 - 464 σελίδες
...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 - 1806 - 486 σελίδες
...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 - 1807 - 476 σελίδες
...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 - 1808 - 190 σελίδες
...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 σελίδες
...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 - 1808 - 470 σελίδες
...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 σελίδες
...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 - 1810 - 168 σελίδες
...(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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To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference... 
