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Bøker Bok 6170 av 73Plane 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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Mathematics for Practical Men: Being a Common-place Book of Principles ...

1863
...180°, the remainder will be the sum of the 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. Then, secondly, say, — As the cosine...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

1865 - 428 sider
...angle from 180° : the remainder will be the sum of the remaining angles. Then, 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. This half difference added to the half sum...
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Land and marine surveying

William Davis Haskoll - 1868 - 184 sider
...greater side, the required angle will be acute. When two sides and their included angle are given. — 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 the half difference of these angles,...
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The Theory of Navigation and Nautical Astronomy; Together with the Elements ...

William Thomas Read - 1869 - 154 sider
...= Therefore Sin A DC BC DC 0 DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ...
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Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

1875
...41' 36" i sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between D and...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1880 - 318 sider
...remainder will be the sum of the other two angles. Then, by proposition 3, — 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 sum of the remaining angles added...
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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - 1882 - 104 sider
...last section. But there is a more convenient method founded on the following theorem : THEOREM IV. As the sum of any two sides is to their difference, so is the tangent of half the sum of the angles opposite these sides to the tangent of half their difference. Proof. From the equation b : o...
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Land and Marine Surveying in Reference to the Preparation of Plans for Roads ...

William Davis Haskoll - 1886 - 230 sider
...greater side, the required angle will be acute. When two sides and their included angle are given. — 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 the half difference of these angles,...
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Philosophical Transactions of the Royal Society of London

1828
...the following method : As the tangent of half the sum of the co-latitudes is to the tangent of half their difference ; so is the tangent of half the sum of the observed angles, to the tangent of half their difference. The triangle is thus reduced to a spherical...
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Manual of Rules, Tables, and Data for Mechanical Engineers: Based on the ...

Daniel Kinnear Clark - 1889 - 1011 sider
...sides and the included angle are given. RULE 4. 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 — add this half difference to the half...
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