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Seite 197 - IF two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz.
Seite 190 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Seite 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Seite 181 - ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754.
Seite 252 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Seite 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Seite 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...