Solid Geometry, Volumes 6-9

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Page 372 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.
Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 383 - 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 250 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 246 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 245 - 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 46 INTERCEPTS BY PARALLEL LINES.
Page 295 - An oblique prism is equivalent to a right prism whose base is equal to a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. r Let FI be a right section of the oblique prism AD', and PI" a right prism whose lateral edges are equal to the lateral edges of AD'.
Page 280 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 395 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.

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