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C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages

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

Philip Ronayne - Algebra - 1717 - 478 pages
...Sum — ~ diff. is = lejje r of them. 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 i. s oppofite is to the Tangent of half their difference. ft. fD AXIOM 4.' • Me»»»- !-*- '"••...

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

William Hawney - Astronomy - 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...

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

Philip Ronayne - Algebra - 1738 - 458 pages
...= BC x S С j WhereforeAB"BC::SC"SA. QE.2). Axiom III. The Sum of th« Legs of any Angle of a Plane Triangle, Is to their Difference, As the Tangent of half the Sum of the Angles oppofite to thofe Legs, Is to the Tangent of half their Difference. 2)emonftration. which (by 8. i...

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

John Ward (of Chester.) - Mathematics - 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 Side...

## The Mathematician

Geometry - 1751 - 420 pages
...all 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...

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

John Ward - Mathematics - 1771 - 510 pages
...wherefore AB : BC : : Si. С : Si. A. ' & £• D. Axiom III. The Sum of the Leg« of any Angle of a Plane Triangle is to their Difference, as the Tangent of half the Sum of the Angles oppofite to thofe leg* is to the Tangent of half their Difference. SDcmoaírcatíon» In the Triangle...

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

Robert Gibson - Surveying - 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....

## Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...between either of them and 45°. PROP. 3oi PLANE TRIGONOMETRY. PROP. IV. HPHE fum of any two fides of a triangle is to their difference, as the tangent of half the fum of the angles oppolite to thofe fides, to the tangent of half their difference. Let ABC be any...