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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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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1811 - 508 pages
...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. In any...
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A SYSTEM OF GEOMETRY AND TRIGONOMETRY

Abel Flint - Surveying - 1813 - 168 pages
...its opposite Angle, 0.72537; the other given side 240. As 200' : 0.72337 : : 240 : 6.87044=50 3<X. CASE III. Two Sides and their contained Angle given,...the Angles and you will have the greater Angle; and substract the half Difference Sfom the half Sum and you will have the lesser Angle. In the Triangh...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 534 pages
...triangle and the included angle are given, to find the other angles and side. 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. Half the difference thus found, added to half...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 534 pages
...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 projwrtion...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 346 pages
...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 of the two unknown angles,...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Electronic books - 1814 - 508 pages
...wholes are as their halves, that is, 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 G, to the tangent of half their difference. QED THEO. III. Fig. 12. In any right...
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - Logarithms - 1815 - 126 pages
...radius. (Art. 11 9.) THEOREM II. ..* 144. In a plane triangle, Jl 3 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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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - Measurement - 1815 - 96 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, !o the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - Plane trigonometry - 1816 - 244 pages
...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 - Plane trigonometry - 1816 - 244 pages
...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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