This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 edition. Excerpt: ...Similar polyhedrons are polyhedrons which have the same number of faces similar each to each and similarly placed, and which have their homologous polyhedral angles equal. Proposition XXIX. Theorem 630. There can exist no more than five kinds of regular polyhedrons. Proof: The faces must be equilateral ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 edition. Excerpt: ...Similar polyhedrons are polyhedrons which have the same number of faces similar each to each and similarly placed, and which have their homologous polyhedral angles equal. Proposition XXIX. Theorem 630. There can exist no more than five kinds of regular polyhedrons. Proof: The faces must be equilateral A, squares, regular pentagons, or some other regular polygons. (629.) There must be at least three faces at each vertex. (565.) The sum of the face A at each vertex is 360. (549.) I. Each Z of an equilateral A = 60 (?). Hence we may form a polyhedral Z by placing 3, 4, or 5 equilateral A at a vertex, but not 6 (?). That is, only three regular polyhedrons can be formed having equilateral triangles for faces. II. Each Z of a square = 90 (?). Hence we may form a polyhedral Z by placing 3 squares at a vertex; but not 4. That is, only one regular polyhedron can be formed having squares for faces. III. Each Z of a regular pentagon = 108 (155). Hence we may form a polyhedral Z by placing 3, but not 4 regular pentagons at a vertex. That is, only one regular polyhedron can be formed having regular pentagons for faces. IV. Each Z of a regular hexagon = 120 (?).. no polyhedral Z can be formed by hexagons (?). Consequently there can be no more than five kinds of regular polyhedrons, --three kinds bounded by triangles, one kind by squares, and one by pentagons. Q.e.d. Directions For Construction.--Mark on cardboard larger figures similar to the drawings. Cut the dotted lines half through and the solid lines entirely through. Fold along the dotted lines, closing the solids up and forming the figures. Paste strips of paper along the edges. Historical Note. Pythagoras knew about the existence of all the regular polyhedrons except the dodecahedron. This was..
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Add this copy of Robbins's New Solid Geometry to cart. $41.63, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2018 by Palala Press.
Add this copy of Robbins's New Solid Geometry to cart. $58.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2015 by Palala Press.
