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" DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. "
A Course of Mathematics ...: Composed for the Use of the Royal Military ... - Page 13
by Charles Hutton - 1811
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A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 2

Charles Hutton - Mathematics - 1807
...same radius AD, by the definition of a tangent. But the tangents AE, DF, being parallel, it will be as BE : BD : : AE : DF; that is, as the sum of the...difference. EXAMPLE I. In the plane triangle ABC, C AB 345 yards Given < AC 174-07 yards / / A 17° <?(Y I f- AOI &\) Required the other parts. 1. Geometrically....
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - Logarithms - 1815 - 126 pages
...THEOREM II. ..* 144. In a plane triangle, Jl 3 the sum of any two of the sides, To their difference; So is the tangent of half the sum of the opposite angles, To the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the...
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - Measurement - 1815 - 96 pages
...THEOREM II. 144. In a plane triangle, As the sum of any two of the sides, To their difference; • • So is the tangent of half the sum of the opposite angles, !Ło the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference...
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A Course of Mathematics in Two Volumes for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816
...radius AD, by the definition of a tangent. Bui the tangents AK,, or, being parallel, it will be as BŁ : BD : : AE : DF ; that is, as the sum of the sides...EXAMPLE I. In the plane triangle ABC, f AB 345 yards €liven< AC 1 74-0? yards I ^A 37° 20' Required the other parts. 1. Geometrically. Draw AB = 345...
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A Course of Mathematics: For the Use of Academies, as Well as Private Tuition

Charles Hutton - Mathematics - 1818
...the definition of a tangent, but the tangents AE, DF, being parallel, it will be as BE : BD : : AR : DF ; that is, as the sum of the sides is to the difference...difference. EXAMPLE I. In the plane triangle ABC, t AB 345 yards Griven < AC 174-07 yards f /.A 37° 20' Required the other parts. 1. Geometrically....
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822
...same radius AD. by the definition of a tangent. But the tangents AE, DF, being parallel, it will be as BE : BD ;; AE : DF ; that is, as the sum of the...angles, to the tangent of half their difference. EXAMPLE J. In the plane triangle ABC, i AB .145 yards Given < AC 174-07 yards I Z. A 37° 20' Required the...
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - Geometry - 1824
...119.) THEOREM II. lit. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDE*. To THEIR DIFFERENCE J SO IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25) is to their difference ; as the tangent of half the sum of the...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825
...the detinition of a tangent. But the tangents AK. DF, being parallel, it will be as BE : BD : : AG : DF ; that is, as the sum of the sides is to the difference...angles, to the tangent of half their difference. EXAMPLE f. In the plane triangle ABC, l AB J-15 yards Given ? AC 1 7-1 -07 yards . ( ^A :i7° ,'tf Required...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 322 pages
...two sides and contained angle are given. I. As the sum of the given sides, Is to their difference ; So is the tangent of half the sum of the opposite angles, To the tangent of half their difference. Half the difference added to half the sum of those angles gives the greater, and subtracted from half...
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 317 pages
...sines of the opposite angles. (73.) The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine, tangent, and cotangent of half the difference of any two...
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