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 Bøker Bok 91–100 av 187 på C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides... 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. The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ... - Side 479
av John Ward - 1771 - 480 sider
Uten tilgangsbegrensning - Om denne boken ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...|(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...
Uten tilgangsbegrensning - Om denne boken 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 C denote...
Uten tilgangsbegrensning - Om denne boken Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 sider
...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....
Uten tilgangsbegrensning - Om denne boken Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 sider
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides 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. 6. Observers on two ships a mile apart find...
Uten tilgangsbegrensning - Om denne boken Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...£ (^l — " B) (R7\ smA—maB ~ <^rt1[ (A + B) ' *•"' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to tlie tangent of half their difference, or as the cotangent of half their difference is to tfie...
Uten tilgangsbegrensning - Om denne boken Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...B = —-, therefore b = p cot -4, p = b cot 5. 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. For, by (90), a : 6 : : sin A : sin B;...
Uten tilgangsbegrensning - Om denne boken Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1862 - 393 sider
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will...
Uten tilgangsbegrensning - Om denne boken Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 sider
...a sin A sin B sin 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. For, by (90), a : b : : sin A : sin B;...
Uten tilgangsbegrensning - Om denne boken A Treatise on Plane and Spherical Trigonometry

1863 - 256 sider
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»...
Uten tilgangsbegrensning - Om denne boken Elements of Plane Trigonometry: And Their Application to the Measurement of ...

1864
...the first proportion in Theorem I. THEOREM III. 41. 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. Let ABC be a triangle ; then AB + BC:BC—...
Uten tilgangsbegrensning - Om denne boken