 | Charles Hutton - 1807 - 464 ページ
...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 - 1815 - 172 ページ
...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 - 1815 - 388 ページ
...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, !£o the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference... | |
 | Charles Hutton - 1816 - 610 ページ
...radius AD, by the definition of a tangent. Bui the tangents AK,, or, being parallel, it will be as B£ : 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 - 1818 - 646 ページ
...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 - 1822 - 616 ページ
...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 - 1824 - 440 ページ
...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 - 1825 - 608 ページ
...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 - 1827 - 412 ページ
...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 - 1828 - 434 ページ
...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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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. 
