# Rational geometry: a text-book for the science of space based on Hilbert's foundations.

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Pages: 66

Language: English

Book format: An electronic version of a printed book that can be read on a computer or handheld device designed specifically for this purpose.

Publisher: RareBooksClub.com (21 May 2012)

By: George Bruce Halsted (Author)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 Excerpt: ...to another point equals the sum of the sq's of the three Xs from that point to the st's. Ex. 505. Draw a st' to cut three given non-intersecting st's so that the intercepts may be as two given sects. Ex. 506. If a plane cut a tetrahedron in a g'm, the plane is to two opposite edges. Ex. 507. The aggregate of all points is divided by four planes into (in general) fifteen regions. Ex. 508. The medians of a skew quadrilateral bisect one another. Ex. 509. If two medians of a skew quadrilateral be X the diagonals are =, and sections to them are llg'ms of = perimeter. CHAPTER XII. POLYHEDRONS AND VOLUMES. Polyhedrons. 376. Definition. A tetrahedron is the figure constituted by four non-coplanar points, their sects and triangles. The four points are called its summits, the six sects its edges, the four triangles its faces. Every summit is said to be opposite to the face made by the other three: every edge opposite to that made by the two remaining summits. A point is within the tetrahedron if it is within any sect made by any summit and a point within its opposite face. Points not within or on are without. The faces taken together are called the surface of the tetrahedron. 377. A polyhedron is the figure formed by n plane polygons such that each side is common to two. The polygons are called its faces, and taken together, its surface. Their sects are its edges: their vertices its summits. A convex polyhedron is one through no edge of which pass more than two faces, and which has no summits on different sides of the plane of a face. A polyhedron of five, six, eight, twelve, twenty faces is called a pentahedron, hexahedron, octahedron, dodecahedron, icosahedron. 378. A pyramid is a polyhedron of which all the faces, except one, are copunctal. This one face is called...

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