VI. The inclination of a plane (A B) (Fig. 1) to a plane (PL); is the acute angle (D E F) contained by two straight lines (E D & E F) drawn in each of the planes, (that is D E in the plane AB & EF in the plane PL) from a fame point (E), perpendicular to their common fe&tion (A N). VII. Two planes are said to have the same or a like inclination to one another, wbieb two otber planes bave, when their angles of inclination are equal. VIII. IX. Similar solid figures are those which are contained by the same number of surfaces, fimilar and homologous. X. Equal & similar Solids are those which are contained by the same number of equal, similar and homologous furfaces. XI. A solid Angle (A) is that which is made by the meeting of more than two plane angles (B A C, CAD & BAD), which are not in the same plane, in one point (A). XII. A Pyramid (E BADF) (Fig. 3) is a solid contained by more than two triangular planes (B A D, B A E &c.) having the same vertex (A), and whole bases (viz. the lines EB, B D &c.) are in the same plane (EB D F). DEFINITIONS, XIII. A Prism is a folid figure (AHE) (Fig. 1.) contained by plane figures , of which two that are opposite (viz. GHIKF & BCD A) are equal similar, and parallel to one another; and the other sides (as GA, AK, KD, &c.) are parallelograms. If the opposite parallel planes be triangles, the prism is called a triangular one, (and it is only of those prisms that Euclid treats in the XIth and XIIth Book), if tbe opposite planes are polygons, they are called polygon prisms. XIV. A Sphere is a solid figure (A EBD) (Fig. 2.) whose furface is described by the revolution of a semicircle (AEB) about its diameter, which remains un moved. XV. Tbe Axis of a Spbere is the fixed diameter (A B) about which the semicircle revolves whilft it describes the superficies of the sphere. XVI. The Center of a Spbere is the same with that of the semicircle which described its superficies. XVII. The Diameter of a Spbere is any straight line which passes thro' the center, and is terminated both ways by the superficies of the sphere. A Cone is a folid figure (A B CD) (Fig. 1, 2, & 3.) described by the revolution of a right angled triangle (ABE), about one of the fides (BE) containing the right angle, which fide remains fixed. It the fixed fide (B E) of the triangle (A BE) (Fig. 2.) be equal to the other fide (A E) containing the right angle, the cone is called a right angled cone ; if (BE) be less than (A E) (Fig.3.) an obtuse angled, and if (BE) be greater than (AE) (Fig. 1.) an acute angled cone. XIX. The Axis of a Cone is the fixed straight line. (B E) about which the triangle (A B E) revolved whilft it described the superficies of the cone. XX. The Base of a Cone is the circle (AGCD) (Fig. 1.) described by that fide (BE) containing the right angle, which revolves. A Cylinder is a folid figure (EB D F) (Fig. 1.) described by the revoluti on of a right angled parallelogram (A NMC) about one of its fides (AC) which remains fixed. XXII. The Axis of a Cylinder is the fixed straight line (A C) about which the parallelogram revolved, whilft it described the superficies of the cylinder. XXIII. The Bases of a Cylinder (viz. E N B, & FMD) are the circles described by the two opposite sides (N A, M C) of the parallelogram, revolving about the points A & C. XXIV. Similar Cones and Cylinders are those which have their axes and the diameters of their Bases proportionals. XXV. A Cube or Exabedron (Fig. 2.) is a solid figure contained by six equal squares. XXVI. A Tetrahedron is a pyramid (B DCA) (Fig. 3.) contained by four equal and equilateral triangles (viz. ABD Ç, BAD, ADC & BAC). DEFINITIONS. XXVII. AN N O flabedron (Fig. 1.) is a solid figure contained by eight eqaul and equilateral triangles. XXVIII. A Dodecbabedron (Fig.2.) is a solid figure contained by twelve equal pentagons which are equilateral and equiangular. XXIX. An Icofabedron (Fig. 3.) is a solid figure contained by twenty equal and equilateral triangles. XXX. A Parallelepiped is a solid figure contained by fix quadrilateral figures wbereof every opposite two are parallel. XXXI. A Solid is said to be inscribed in a Solid, when all the angles of the inscribed folid touch the angles, the sides, or the planes of the solid in which it is inscribed. 1 XXXII. A Solid is said to be circumscribed about a Solid, when the angles, the fides, or the planes of the circumscribed folid touch all the angles of the inscribed folid EXPLICATION of the SIGNS. . . Similar. Parallelepiped. |