Publisher's Synopsis
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. 1820 edition. Excerpt: ... pyramids, and each face will Lave a rectangle described on it by these lines, each of which rectangles will be equal to the base of a rectangular pyramid; their sides are to each other as 1: DEGREES/2, the same as the two diagonals of the face on which they are drawn. The edges of the cuboctahedron must be all bisected, and lines must be drawn connecting the adjacent points of bisection; these lines will form a triangle on the middle of each triangular face, and a square in the middle of each square face: the angular extremities marked off by them will become rectangular pyramids, which pyramids, if they were removed, and placed on the rectangular spaces marked off on the faces of the rhomboidal dodecahedron, would convert it into an exact representation of fig. 71, or if the triangular and square pyramids were removed, from the rhomboidal dodecahedron and placed on the triangular and square spaces, marked off on the faces of the cuboctahedron, they would produce exactly the same effect OF THE LONGEST AXIS. A plane passing through the acute solid angle at right angles to the longest axis, bisects that axis, if it pass through an obtuse solid angle at right angles to the same axis, it cuts off one fourth: if it pass through an intermediary solid angle at right angles to the same axis, it cuts off one sixth. OF THE SHOETtST AXIS. If a plane pass through one of the long diagonals of the face of a trapezohedron at right angles to the shortest axis farthest distant, it will bisect that axis; if it pass through an obtuse angular extremity at right angles, to the same axis, it will rut off one third; if it pass through an acute angular extremity at right angtas, to the same axis, it will cut off one sixth: and through an intermediary angular.
