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" Plane Triangle, 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 the Difference between them. "
A System of Geometry and Trigonometry: With a Treatise on Surveying; in ... - Page 35
by Abel Flint - 1838 - 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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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - Geometry - 1804 - 168 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum...the Angles and you will have the greater Angle ; and subtract the half Difference from the half Sum and you will have the lesser Angle. In the Triangle...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 452 pages
...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 Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807
...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 System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - Geometry - 1808 - 168 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum...the Angles and you will have the greater Angle ; and subtract the half Difference from the half Sum and you Will have the lesser Angle V * In the Triangle...
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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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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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The British encyclopedia, or, Dictionary of arts and sciences, Volume 6

William Nicholson - 1809
................... 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
...(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 AB, AC the two proposed sides ; and from...
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Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - Trigonometry - 1810 - 125 pages
...- J -- : tang -- - - ; that is, As the sine of the sum of the tivo perpendiculars is to the sine of their difference, so is the tangent of half the sum of the two bases to the tangent of half their difference. PROP. XXVI. The product of the square of radius and...
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