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In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Elements of Surveying - Page 25
by Charles Davies - 1830 - 300 pages

Elements of Plain and Spherical Trigonometry: Together with the Principles ...

John Harris - 1706 - 298 pages
...B. 3 Angles. 3 Sides. As the Sum of the Legs about the Angtt given, is to their Difference :: Soii the Tangent of half the Sum of the other two Angles, to the Tangent of half their Difference.. Now the Sum of the other two Angles is known, being what the given Angle wants of i80 Degrees and their...

A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 478 pages
...•• В С : : 5, С • S, A " - S,C: 3 D) == S, A, QED' AXIOM AXIOM. III. The Sum of che Legs of an Angle is to their Difference as the Tangent of half the Sum of the Angles oppofite to rhofe Legs, is to the Tangent of half their Difference. Demonßrütion. „ In the...

The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 504 pages
...the Tangent of half their Difference. But Wholes are as their Halves : Therefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the oppofite Angles, is to the Tangent of half their Difference. Which was, &c. From this Axiom the following...

The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - 1747 - 516 pages
...the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the Angles oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or greateu...

The Mathematician

1751 - 420 pages
...writers of Trigonometry, that the Sum of the Sides, including any given Angle Angle of a plain Triangle, is to their Difference, as the Tangent of half the Sum of the unknown Angles, is to the Tangent of half their Difference ; therefore, if the including Sides of two...

Henry Wilson - 1761 - 580 pages
...I, AXIOM III. In all Triangles, as tlie Sum of the Leg"; of any Angle is to their Difference, fo is the Tangent of half the Sum of the other two Angles, to the Tangent of half their Difle^ rencc; and therefore, When there are given two Sides, and ah Angle included, to find the other...

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

Robert Gibson - 1795 - 384 pages
...II. In any plane Triangle ABC, the Sum of the two given Sides AB and BC, including a given Angle ABC, is to their Difference ; as the Tangent of half the Sum ' of the two unknown Angles A and C is to the Tangent ef half their Difference. Fig. 1 1 . Produce Plate V....

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 pages
...given, the fourth is also given. ' PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. . * Let ABC be a plane triangle, live...