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" C' (89) (90) (91) (92) (93) 112. 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. "
A Treatise on Practical Surveying: Which is Demonstrated from Its First ... - Σελίδα 116
των Robert Gibson - 1818 - 478 σελίδες
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A Treatise on Land Surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1855 - 524 σελίδες
...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane...

Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1855 - 178 σελίδες
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Dividing formula (3) by (4), and considering...

Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1856 - 235 σελίδες
...(2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin. B...

Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 σελίδες
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the...

A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1856 - 464 σελίδες
...to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane...

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

Adrien Marie Legendre, Charles Davies - 1857 - 432 σελίδες
...AC :: sin C : sin B, THEOREM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let A CB be a triangle : then will AB +...

A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1857 - 524 σελίδες
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane...

Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - 1859 - 150 σελίδες
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. .Dividing formula (3) "by (4), and considering...

Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 σελίδες
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin....

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and...




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