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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 ... - Página 27
por Abel Flint - 1804 - 168 páginas
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Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - 1810 - 125 páginas
...co-sine AC : : tang. C : co-tang. A. £>. E, D. LEMMA. 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* the co-sines is to their...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 páginas
...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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Geometrical and Graphical Essays: Containing a General Description of the ...

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

John Gummere - 1814 - 346 páginas
...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 - 1814 - 508 páginas
...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 - 1815 - 126 páginas
...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 - 1815 - 96 páginas
...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 - 1816 - 244 páginas
...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

Olinthus Gregory - 1816 - 244 páginas
...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 páginas
...: 0.37044=60° 30'. CASE III. Two Sides and their contained Angle given, to find the ether Jingles and Side. Fig. 49. The solution of this CASE depends...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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