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 Bøker Bok 71–80 av 191 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. A Treatise of Practical Surveying, ... - Side 94
av Robert Gibson - 1808 - 440 sider
Uten tilgangsbegrensning - Om denne boken Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 sider
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are...
Uten tilgangsbegrensning - Om denne boken A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - 1848 - 153 sider
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making...
Uten tilgangsbegrensning - Om denne boken Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 359 sider
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin...
Uten tilgangsbegrensning - Om denne boken A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...AH : IH : : CE :ED, that is, as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED THEO. III. In any plane triangle A BD ; the base AD, will...
Uten tilgangsbegrensning - Om denne boken A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - 1851 - 372 sider
...: tan £ (A + B) : tan ^ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 76 This proportion is employed when two...
Uten tilgangsbegrensning - Om denne boken A course of mathematics: containing the principles of plane trigonometry ...

Jeremiah Day - 1851
...the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan...
Uten tilgangsbegrensning - Om denne boken ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...AC :: sin 0 : sin jR THEOEEM 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 ACB be a triangle: then will AJ3 + AC...
Uten tilgangsbegrensning - Om denne boken A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane 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, by the preceding article, a : b =...
Uten tilgangsbegrensning - Om denne boken Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1886 - 324 sider
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...
Uten tilgangsbegrensning - Om denne boken A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1853 - 5 sider
...therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to...
Uten tilgangsbegrensning - Om denne boken