A Treatise on Plane and Spherical Trigonometry

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B. Fellowes, 1842 - Plane trigonometry - 167 pages
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Page 114 - 4. Every section of a sphere made by a plane is a circle. Let AMB be the section made by
Page 91 - The square of the side of a pentagon inscribed in a circle is equal to the sum of the squares of the sides of a regular hexagon and decagon inscribed in the same circle.
Page 125 - For since the sum of the angles of a spherical triangle is greater than two right angles,
Page 91 - (8.) The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribed
Page 116 - 9. A spherical triangle is a portion of the surface of a sphere contained by three arcs of three great circles,
Page 54 - or the area of a triangle is equal to half the product of any two sides multiplied by the sine of the angle included by
Page 116 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. For
Page 146 - the area of a spherical triangle is proportional to the excess of the sum of its angles above two right angles. This is
Page 8 - The interior angles of a rectilinear figure are in arithmetic progression; the least angle is 120, and the common difference 5. Required the number of sides.
Page 91 - Three equal circles touch each other ; show that the space between them is nearly equal to the square described upon a fifth part of the diameter; find the area when the circles are unequal and the radii as the numbers

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