Solid Geometry Developed by the Syllabus Method

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American Book Company, 1918 - Geometry, Solid - 211 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 251 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Page 329 - The sum of the sides of any spherical polygon is less than the circumference of a great circle.
Page 288 - Two rectangular parallelepipeds are to each other as the products of their three dimensions.
Page 297 - Every section of a circular cone made by a plane parallel to the base is a circle.
Page 298 - The lateral area of a frustum of a right circular cone is one half the product of the slant height and the sum of the circumferences of the bases.
Page 398 - Bh where B is the area of the base and h is the height.
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 267 - Find the locus of a point such that the difference of the squares of its distances from two given points is equal to a given constant k-.

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