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Bøker Bok 2130 av 75Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the...
" 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. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 5
av Thomas Simpson - 1810 - 125 sider
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - 1816 - 244 sider
...180°, the remainder will be the sum of th£ other two angles. Then say, — As the sum of the given sides, Is to their difference ; So is the tangent of half the sum of the remaining angles, To the tangent of half their difference. Half the difference added to half the sum...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - 1816 - 244 sider
...AC; whence the proposition is manifest. PROP. XI. 1 1 . As the sum of the sines of two unequal arcs, is to their difference, so is the tangent of half the sum of those two arcs, to the tangent of half their difference. Let AE and AB be two unequal arcs, of which...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1818 - 168 sider
...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 their Difference...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 - 1818 - 478 sider
...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

1821
...opposite angle, so is either of the other sides to the sine of its opposite angle. THEOREM III. In every plane triangle, it will be, as the sum of any two sides is to their difference, so is the tangtnt of half the sum of the two opposite angles to the tangent 'of half their difference (by art....
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volum 12

William Nicholson - 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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British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volum 12

William Nicholson - 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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A treatise on navigation, and nautical astronomy

Edward Riddle - 1824
...triangle. Or the angles opposite the given sides may be determined as follows. As the sum of the given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half the difference of the same angles, (Trig. Prop. 6.) And...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1825 - 241 sider
...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 their difference,...of the two opposite Angles to the Tangent of half the difference between them. Add this half difference to half the sum of the Angles and you will have...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 617 sider
...opposite angle, so is either of the other sides to the sine of its opposite angle. 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...
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