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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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The Ohio Educational Monthly and the National Teacher: A Journal ..., Τόμος 32

1883
...finding the logarithm of a number having four places. 5. Show that 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. GENERAL HISTORY. 2. What colonies were...

A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - 1883 - 214 σελίδες
...: a : b : с = sin A : sin В : sin С ab с sin A sin В sin O 145. 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. 144, a : b = sin A : sinB Whence,...

Ohio Educational Monthly, Τόμος 32

1883
...finding the logarithm of a number having four places. 5. Show that 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. GENERAL HISTORY. 1. Before the Greeks,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 512 σελίδες
...principle, now to be demonstrated, viz. : In any plane triangle, the sum of the sides including any 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. Let ABC represent any plane triangle,...

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886
...10°, a = 23087, b = 7903.2. (25.) 37. Prove geometrically that the sum of 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. In a triangle ABC, given a = 3, b = 5,...

The Essentials of Plane and Spherical Trigonometry

Webster Wells - 1887 - 151 σελίδες
...be expressed more compactly as follows : , sin Л sin B sin (' 114. 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. Formula (45) of Art. 113 may be put in...

Plane Trigonometry

Webster Wells - 1887 - 103 σελίδες
...expressed more compactly as follows: ab с sin , I sin Б sin С 114. 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. Formula (45) of Art. 113 may be put in...

Trigonometry, Analytical, Plane and Spherical, with Logarithmic Tables

De Volson Wood - 1887
...'-ftThis reduced by (66) gives __ 0-6 tan | (1-5)' that is, The sum of two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. Toßnd A + Б we "have A + Б = 180° - G. (78)...

A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 302 σελίδες
...known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added...

Practical Surveying: A Text-book for Students Preparing for Examinations Or ...

George William Usill - 1889 - 272 σελίδες
...opposite angle. B. In a plane triangle the sum of the sides is to their difference in the same ratio as the tangent of half the sum of the angles at the base of the triangle is to the tangent of half their difference. C. In a plane triangle the base is to the...




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