Elements of Geometry with Exercises for Students: An an Introduction to Modern Geometry

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Wilson, Hinkle & Company, 1876 - Geometry - 372 pages
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Page 59 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 72 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 322 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.
Page 58 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 336 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 329 - Theorem.—If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.
Page 316 - The centre of the sphere is the vertex of the pyramid, and the spherical polygon is the base of the pyramid.
Page 79 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 85 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 331 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.

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