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 Bøker Bok 41–50 av 192 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 ## Elements of Surveying

Charles Davies - 1830 - 300 sider
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;...
Uten tilgangsbegrensning - Om denne boken ## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 sider
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the...
Uten tilgangsbegrensning - Om denne boken ## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1832 - 348 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 THEOREM III. Fig. 12. In any right-lined' plane triangle...
Uten tilgangsbegrensning - Om denne boken ## Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - 1833 - 264 sider
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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 help of this rule we may determine the...
Uten tilgangsbegrensning - Om denne boken ## The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 sider
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. * PROP. IV. FIG. 8. In a plane triangle,...
Uten tilgangsbegrensning - Om denne boken ## Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 sider
...c=2p — 2c, a+c — 6=2p — 26; 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 ## The Element of Geometry

John Playfair - 1836 - 114 sider
...three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides 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 a plane triangle, the sum of...
Uten tilgangsbegrensning - Om denne boken ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...BC is parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sum of the angles opposite to those sides to the tangent of half their difference. 325 PROP. V. THEOR. If a perpendicular...
Uten tilgangsbegrensning - Om denne boken ## Elements of Surveying: Including a Description of the Instruments and the ...

1837 - 249 sider
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:...
Uten tilgangsbegrensning - Om denne boken ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 sider
...sine of a right angle is equal to the radius. PROP. III. THEOR. THE sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, is to the tangent of half their difference. Let ABC be a triangle,...
Uten tilgangsbegrensning - Om denne boken