A treatise on plane and spherical trigonometry

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B. Fellowes, 1848 - Trigonometry - 168 pages
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Page 13 - OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an...
Page 127 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 116 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Page 55 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.
Page 118 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 148 - The area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles (called the spherical excess).
Page 92 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 142 - By equating the results and transposing, cos a = cos b cos с — sin b sin с cos A cos b...
Page 118 - 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.
Page 118 - Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360. 49. The sum of the angles of a spherical triangle is greater than 180 and less tha'n 540.

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