ELEMENTS OF GEOMETRY... SUPPLEMEN T. BOOK III. DEFINITIONS. I. A SOL Book III! SOLID is that which has length, breadth, and thickness. II. Similar folid figures are fuch as are contained by the fame number of fimilar planes fimilarly fituated, and having like inclinations to one another. See N. IIL A pyramid is a folid figure contained by planes that are conftituted betwixt one plane and a point above it in which they meet. IV. A prifm is a folid figure contained by plane figures, of which two that are opposite are equal, fimilar, and parallel to one another; and the others are parallelograms. V. A parallelopiped is a folid figure contained by fix quadrilateral figures, whereof every oppofite two are parallel. VI. A cube is a folid figure contained by fix equal fquares, VII. A fphere is a folid figure described by the revolution of a femicircle about a diameter, which remains unmoved. VIII. The axis of a sphere is the fixed ftraight line about which the femicircle revolves, IX. The centre of a sphere is the fame with that of the femicircle, X. The diameter of a sphere is any straight line which paffes through the centre, and is terminated both ways by the fu perficies of the fphere. XI. A cone is a folid figure defcribed by the revolution of a right angled triangle about one of the fides containing the right angle, which fide remains fixed. XII. The axis of a cone is the fixed ftraight line about which the triangle revolves. 1 XIII. XIII. The base of a cone is the circle defcribed by that fide, containing the right angle, which revolves. XIV. A cylinder is a folid figure described by the revolution of a right angled parallelogram about one of its fides, which remains fixed. Book III. XV. The axis of a cylinder is the fixed straight line about which the parallelogram revolves. XVI. 'The bafes of a cylinder are the circles defcribed by the two revolving oppofite fides of the parallelogram. XVIII. Similar cones and cylinders are those which have their axes, and the diameters of their bafes proportionals, PROP, Supplement IF PROP. I. THEOR. F two folids be contained by the fame number of equal and fimilar planes, fimilarly fituated, and if the inclination of any two contiguous planes in the one folid be the fame with the inclination of the two equal, and fimilarly fituated planes in the other, the folids themfelves are equal and fimilar. Let AG and KQ be two folids contained by the fame number of equal and fimilar planes, fimilarly fituated, so that the plane AC is fimilar and equal to the plane KM, the plane AF to the plane KP; BG to LQ, GD to QN, DE to NO, and FH to PR. Let alfo the inclination of the plane AF to the plane AC be the same with that of the plane KP to the plane KM, and fo of the reft; the folid KQ is equal and fimilar to the folid AG. Let the folid KQ be applied to the folid AG, so that the bafes KM and are equal and fimilar, may a S. Ax. I. coincidea, the point N, coinciding with the point D, PROP. |
