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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. "
An elementary course of practical mathematics - Página 282
por James Elliot - 1851
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The British encyclopedia, or, Dictionary of arts and sciences, Volumen6

William Nicholson - 1809 - 722 páginas
....56.88 ................ l .75486 Axiom III. In every plane triangle it will bn as the sum of any two sides is to their difference; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which lialf difference, being added...
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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, and...
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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 any...
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A Course of Mathematics: In Three Volumes : Composed for the Use of the ...

Charles Hutton - 1811 - 494 páginas
...sum of the two other angles ; then divide that by 2, which will give the half sum of the said unknown angles. Then say, As the sum of the two given sides, Is to the difference of the same sides ; So is the tang, of half the sum of their op. angles, To the tang,...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - 1813 - 576 páginas
...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 found, the following proportion...
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Geometrical and Graphical Essays: Containing a General Description of the ...

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

John Gummere - 1814 - 398 páginas
...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...,. % 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 - 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 right...
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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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