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" 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... "
Elemento of Geometry, Theoretical and Practical: Containing a Full ... - Page 197
by George Clinton Whitlock - 1848 - 324 pages
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 576 pages
...BD, and the angle CBD, to find the angle CDB, and the side CD: to find CDB we use this proportion ; as the sum of the two given sides 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 CDB being...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 648 pages
...proportion must begin with an angle ; and when an angle is wanted, it must begin with a side. As the sun, of the two given sides is to their difference ; so is the tangent of half the sum of the two 3. When two sides of a triangle and the included angle are given, to find the...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 398 pages
...from 180°, and the remain' der will be the sum of the two unknown angles. Then ; • * * * * • * As the sum of the two given sides, „• Is to their difference ; ,. % So is the tangent -of half the sum of the two uuknown angles, To the tangent of half their difference.* This half difference...
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New American Practical Navigator

Nautical astronomy - 1821 - 708 pages
...from 90°, the remainder is half he sum of the other angles Then say, as the sum of the sides AC, AB is to their difference, so is the tangent of the half sum of the other angles to the tangent of half their difference; which added o and subtracted Ciom the half sum,...
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A complete treatise on practical land-surveying

Thomas Holliday - Surveying - 1838 - 404 pages
...Case When two sides and the angle contained between them are given, to find the rest. u2 Rule.—As the sum of the two given sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference: this half difference being...
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An Encyclopędia of Architecture: Historical, Theoretical, and Practical

Joseph Gwilt - Architects - 1842 - 1114 pages
...which will give the half sum of the said unknown angles ; and using the following ratio, we have — 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 the difference of the same angles. Now...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 854 pages
...90° ; the remainder is half the sum of the other angles. Then say, As the sum of the sides, AC, AB, is to their difference, so is the tangent of the half sum of the other angles to the Uingentof half their difference ; which added to and subtracted from the half sum,...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...3rd. Having two sides, and the angle between them, to find the other two angles and the third side. RULE. As the sum of the two given sides, is to their difference, so is, the Tangent of half the sum of the unknown angles, to the Tangent of half their difference. Half the difference thus...
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An elementary course of practical mathematics, Part 3

James Elliot - 1851 - 162 pages
...the given angle from 180° : the remainder will be the sum of the two required angles. Then say,— As the sum of the two given sides is to their difference, so is the tangent of half the sum of the two required angles, to the tangent of half their difference. Having found the...
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A Complete Epitome of Practical Navigation ...

John William Norie - Nautical astronomy - 1852 - 838 pages
...from the nature of the triangle. II. When two Sides and the Angle contained between them are given. As the sum of the two given sides Is to their difference, So is the tangent of half the sum of the unknown angles To the tangent of half their difference : This half difference added...
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