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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.
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 69
by Thomas Simpson - 1810 - 125 pages

## Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736 - 414 pages
...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...

## An Account of the Operations Carried Out for Accomplishing a ..., Volume 2

William Mudge, Isaac Dalby, Thomas Colby - Arc measures - 1801 - 690 pages
...angles of a spherical triangle, to find those angles : As the tangent of half the sum oj the sides, Is to the tangent of half their difference ; So is the tangent of halfibe sum of the angles, To the tangent of half their difference. Or thus. Let s and c represent...

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

Abel Flint - Surveying - 1804 - 226 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 of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half...

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

Robert Gibson - Surveying - 1806 - 486 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...

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

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

## 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 any right-lined...

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

Abel Flint - Surveying - 1808 - 190 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 of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half...

## The British encyclopedia, or, Dictionary of arts and sciences, Volume 6

William Nicholson - 1809 - 722 pages
................... 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...