| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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