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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. "
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 15
por William Findlay Shunk - 1908 - 345 páginas
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Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - 1810 - 168 páginas
...— BC) : BG (2ED), by 4. 6. ^ ED THEOREM V. In any plane triangle, it will be, 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 their difference, For, let ABC (fig. 5.) be the triangle,...
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Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - 1810 - 152 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 - 580 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...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - 1813 - 576 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...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - 1813 - 648 páginas
...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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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - 1814 - 398 páginas
...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 of the two unknown...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1814 - 558 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...
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - 1815 - 172 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 - 388 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

Olinthus Gregory - 1816 - 278 páginas
...PROP. XV. •. 15. In any plane triangle it will be, as the sum of the sides about the vertical angle, 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. By the preceding prop. AC : BC :: sin...
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