Plane And Spherical Trigonometry in Three Parts

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Each side of a spherical triangle must be less than a semicircle (art. 23).
2. Each angle must be less than two right angles (art. 24).
3. Any two sides of a spherical triangle are together greater than the third (art. 29).
4. If two sides of a spherical triangle are equal, the angles opposite to them are equal, and conversely (arts. 32, 33).
5. The greater side is opposite to the greater angle, and con- versely (arts. 34, 35).
6. A — B and a — b have the same sign (art. 35).
7. The three sides
... of a spherical triangle are together less than four right angles.
8. The three angles of a spherical triangle are greater than two right angles and less than six right angles (art. 31).
Ul CHAPTER in.
ON FOKMULiE CONNECTING FUNCTIONS OF THE SIDES AND ANGLES OF A SPHE.RJCAL TJ^JANGLE.
87. The sines of the angles of a spherical triangle are "pro- portional to the sines of the opposite sides.
Let ABC be a spherical triangle, and the centre of the sphere.
Take any point D in OA, and from D let fall DE perpendicular to the plane BOC.


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