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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.
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811

## Elements of Surveying

Charles Davies - 1830 - 390 pages
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle...

## A Concise System of Mathematics ...

Alexander Ingram - 1830 - 458 pages
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB is to their difference as the tangent of half the sum of the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan....

## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1831 - 656 pages
...lui(A-fB) sinx+sins v * This equation is readily converted into a very useful proportion, viz. Tin' sum of the sines of two arcs or angles, is to their...angles, is to the tangent of half their difference. 26. Operating with the third and fourth formula- of the preceding article, as we have already done...

## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - 1831 - 394 pages
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to...

## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 520 pages
...a - sin6~tan J(a — 6) ' sin a + sin b I sin a — sin b'. ;tan J(a+6) : tan J (a— b.) That is, The sum of the sines of two arcs or angles, is to the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent...

## Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - 1833 - 286 pages
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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. By help of this rule we may determine...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the 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. * PROP. IV. FIG. 8. In a plane triangle,...

## The Element of Geometry

John Playfair - 1836 - 148 pages
...three being given, the fourth is also given. PROP. III. i 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, the sum...