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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: With a Treatise on Surveying; in ... - Page 35
by Abel Flint - 1835 - 334 pages
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Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736
...Sides, Is to the Sine of their Difference, ( So is the Sine of the Sum of the Angles, to the Sine of their Difference ; ) So is the Tangent of half the Sum of the Angles, To the Tangent of halt their Différence. 14. That is, IK : IH: : AP :AO. Therefore IK+IH m...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801
...$ 07 21 feet. JROSLEM It. Given tiua sides and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to...difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 452 pages
...wholes are as their halves, ie 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 C, to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - Trigonometry - 1806 - 419 pages
...included angle are given, to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, is to their difference, so is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807
...triangles DRA, DGB will be similar; whence we have, DG : DR :: GB : RA; That is, as the sum of the sides, is to their difference, so is the tangent of half the sum of the unknown or opposite angles, to the tangent of half the difference of those angles. Examp. 1. Let CD...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pages
...wholes areas their halves, ie 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 C, to the tangent of half their difference. QED Plate V. THEO. III. In any right-lined...
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Mathematics, Volume 1

Samuel Webber - Mathematics - 1808
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : Is to their difference " : : So is the tangent of half the sum of their opposite angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem,...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Algebra - 1808 - 480 pages
...given. RULE 2. — As the sum of any two sides is to their difference ; so 5s the tangent of the half sum of the two opposite angles, to the tangent of half the difference of those two opposite angle* ; which hah" difference being added to the half sum, gives the greater...
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The British encyclopedia, or, Dictionary of arts and sciences, Volume 6

William Nicholson - 1809
...9.74198 To the sine DC .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 - Trigonometry - 1810 - 125 pages
...(AC + BC) : : BH (AC — 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,...of the two opposite angles, to the tangent of half their difference, For, let ABC (fig. 5.) be the triangle, and AB, AC the two proposed sides ; and from...
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