Plane Geometry Developed by the Syllabus Method

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American Book Company, 1909 - Geometry, Plane - 192 pages

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Page 343 - 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 329 - The sum of the sides of any spherical polygon is less than the circumference of a great circle.
Page 297 - Every section of a circular cone made by a plane parallel to the base is a circle.
Page 260 - The acute angle which a straight line makes with its own projection upon a plane is the least angle it makes with any line of that plane.
Page 389 - 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.
Page 48 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 73 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 212 - To prove the conclusion, it is necessary to use the additional geometrical principle that but one parallel to a given line can be drawn through a given point.
Page 304 - The volume of a circular cone is equal to one third the product of its base by its altitude.
Page 311 - The greatest right circular cylinder that can be inscribed in a right circular cone is one whose altitude is one third that of the cone.

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