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Bøker Bok 110 av 59TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES',...
" TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 32
av Thomas Simpson - 1810 - 125 sider
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1804 - 168 sider
...this CASE depends on the following PROPOSITION. In every 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. Add this half difference...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 sider
...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 the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 452 sider
...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....
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volum 1

Isaac Dalby - 1807
...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...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 sider
...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...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - 1808 - 168 sider
...this CASE depends on the following PROPOSITION. In every 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. Add this half difference...
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The British encyclopedia, or, Dictionary of arts and sciences

William Nicholson - 1809
...co-sine of the hypothemiie, so is the tangent of either angle to the co-tangent of the other angle. A* the sum of the sines of two unequal arches is to their ditlereiice, so is the tangent of half the sum of those arches to the tangent of half their difference...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 sider
...wholes are as their halves, that is, AH: Iff : : CE : ED, that ia 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. 2. E. DK THEO. III. fig. 12....
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - 1813 - 534 sider
...the angle CDB, and the side CD: to find CDB we use this proportion; as the sum of the two given aides is to their difference, so is the tangent of half the sum of the two unknown angles to the tangent of half their difference; the angle C'DB being found; the following...
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