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" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 117
των Dennis M'Curdy - 1846 - 138 σελίδες
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Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - 1889 - 284 σελίδες
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations...

Elements of Plane and Spherical Trigonometry

Edwin Schofield Crawley - 1890 - 159 σελίδες
...can show and sin B sin C ca sin C sin A. abc sin A sin 5 sin C . ч (82) or PLANE TIUGONOMETKY. 62. In any triangle the sum of two sides is to their difference ae the tangent of half the sum of the opposite angles is to the tangent of half their difference. From...

The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1890 - 339 σελίδες
...any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half the difference...

Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 172 σελίδες
...difference, provided the right order is maintained. 57. Law of Tangents. — In any 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 Art. 55, a : b = sin A : sin B. By composition...

A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 368 σελίδες
...difference, provided the right order is maintained. 97. Law of Tangents. — In any 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 Art. 95, a : b = sin A : sin B. By composition...

The Ohio Educational Monthly and the National Teacher: A Journal ..., Τόμος 41

1892
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle is to their difference as the tangent of half the sum of the two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms...

A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - 1894 - 193 σελίδες
...multiplied (1) by a, (2) by b, and (3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin...

Plane and Spherical Trigonometry

Alfred Hix Welsh - 1894 - 206 σελίδες
...CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, 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. Scholium. — The half difference added...

New Plane and Spherical Trigonometry

Webster Wells - 1896 - 126 σελίδες
...с = sin В : sin C, and с : a = sin (7 : sin A. (48) (49) 108. In- a iti/ 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 (47), a:b = sin A : sin B. Whence by...

Elements of Plane and Spherical Trigonometry

Charles Winthrop Crockett - 1896 - 295 σελίδες
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For we have b _ sin ß с sin y By composition...




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