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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. "
A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... - Page 34
by Abel Flint - 1825 - 241 pages
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - Deeds - 1818 - 168 pages
...: 0.37044=60° 30'. CASE III. Two Sides and their contained Angle given, to find the ether Jingles and Side. Fig. 49. The solution of this CASE depends...Tangent of half the Sum of the two opposite Angles ; To th« Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 478 pages
...wholes are as their halves, ie AH : IH : : CE : ED, that is, as the snm 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 THEOREM HI. In any right-lined...
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American Practical Navigator

Nautical astronomy - 1821
...same angle*. Thus, in the triangle ABC, if we call AB the base, it will he as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, BAG', to the tangent of half their difference. Dem. With the longest leg CB as radius,...
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British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volume 12

William Nicholson - Natural history - 1821
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum of their co-sines a to their...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 12

William Nicholson - Natural history - 1821
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum of their co-sines is to their...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 617 pages
...THEOREM HI. . In every plane triangle, it will be, as the sum of any two sides is to their difference, su is the tangent of half the sum of the two opposite angles to the tangent 'tif half their difference (by art. u'J, Geom.) THEOREM IV. As the base of any plane triangle is to...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 617 pages
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their difference. Dan. With the longest leg CB as radius,...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 322 pages
...45. In a plane triangle when 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...
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 120 pages
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sura of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference. Having thus found the half difference, add...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - Measurement - 1831 - 370 pages
...other radius. (Art. 1 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; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to...
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