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To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Mathematics: Compiled from the Best Authors and Intended to be the Text-book ... - Page 17
1801

## A System of Practical Mathematics: ... With a Plain Account of the Gregorian ...

John Potter - Mathematics - 1753 - 568 pages
...To the Sine of its oppofite Angle. Rule 2. When any two Sides with the Angle between them are given. As the Sum of any two Sides Is to their Difference, So is the Tangent of the Half-Sum of the two oppofite Angles " To the Tangent of Half the Difference of thofe two Angles....

## A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - Surveying - 1804 - 226 pages
...Angles and Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to...Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference...

## A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - Trigonometry - 1806 - 464 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...angles, to the tangent of half their difference. Then the half difference of these angles, added to their half sum, gives the greater angle, and subtracted...

## A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 486 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....

## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...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...

## A System of Geometry and Trigonometry: Together with a Treatise on Surveying ...

Abel Flint - Surveying - 1808 - 190 pages
...Angles and Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to...Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference...

## A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 482 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...

## A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Algebra - 1808 - 470 pages
...to the other side. When any ttvo sides luilh the angle included let-wen then are 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...