 | 1829 - 530 pages
...shewn to depend on the theorem, that, " the sum of two sides of a triangle is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference." This half difference added to half the sum, gives the greater, and subtracted from the half sum, gives... | |
 | Jeremiah Day - Measurement - 1831 - 394 pages
...angle greater than 45° : And radius is to the tangent of the excess of this angle above 45° ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. In the triangle ABC, (Fig. 39.) let the sides AC and AB, and the angle A be given. Through A draw DH... | |
 | Jeremiah Day - Logarithms - 1831 - 418 pages
...angle greater than 45° : And radius is to the tangent of the excess of this angle abort 45° ; os the tangent of half the sum of the opposite angles, to the tangent of ha1f their difference. In the triangle ABC, (Fig. 39.) let the sides AC and AB, and the an<rle A be... | |
 | Jeremiah Day - Measurement - 1831 - 520 pages
...difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference; as the tangent of half the sum of the opposite angles, to the tangent <if half their difference. Therefore, R :tan(ACH-45°)::tan|(ACB + B) : tan iHACB^B) Ex. In the triangle... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...difference . / .19 ARTIcLE. PAGE. 19. In a plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference . . . .21 •20. Formulas for determining an angle in terms of the sides . 22 21. Remarks on these... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...the two sides and contained angle are given. I. As the sum of the given sides Is to their difference; So is the tangent of half the sum of the opposite angles To the tangent of half their difference. Half the difference added to half the sum of those angles gives the greater, and subtracted from half... | |
 | Mathematics - 1836 - 488 pages
...sides. Theorem II. In any plane triangle, As the sum of any two of the sides, to their difference ; so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. .Theorem III. As the largest side, to the sum of the two others ; so is the difference of the latter,... | |
 | Jeremiah Day - Measurement - 1836 - 418 pages
...19.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES j To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to their difference... | |
 | Jeremiah Day - Geometry - 1838 - 416 pages
..... THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE J So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the... | |
 | Jeremiah Day - Geometry - 1839 - 434 pages
...119.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference... | |
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DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. 
