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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 Treatise of Practical Surveying: Which is Demonstrated from Its First ... - Σελίδα 103
των Robert Gibson - 1806 - 452 σελίδες
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Spherical trigonometry

Benjamin Martin - 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...

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

Robert Gibson - 1795 - 319 σελίδες
...Angles A and C : Now IG being parallel to AC ; AH : 1H : : CH : GH. (by Cor. i. Theo. 20. Sect, i.) But the Wholes are as their Halves, ie AH : IH : :...of the two Sides AB and BC, is to their Difference ; fo is the Tangent of half the Sum of the two unknown Angles A and C, • to the Tangent of half their...

Mathematics: Compiled from the Best Authors and Intended to be the ..., Τόμος 2

1801
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the...

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

Abel Flint - 1804 - 168 σελίδες
...this CASE 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 on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 σελίδες
...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,...

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

Isaac Dalby - 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...

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

Abel Flint - 1808 - 168 σελίδες
...this CASE 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, Τόμος 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...

Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - 1810 - 125 σελίδες
...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...

Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - 1813 - 534 σελίδες
...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....