B. II. pr. 3. 1. 5. før AC, CD, r. AF, CE; pr. 10. 1. 15. for DEF r. DFE. B. III. pr. 23. note, for def. 11. r. def. 10; pr. 28. for def.14.1 r. def. 4.1. pr. 37. cor. I. 1 2. for point A. r. point D. m på mi B. V. pr. 9. l. 5. for it has to C, r. A has to C; the fame pr. 10. 1. 6. B. VI. pr. 12. p. 88. 1. 1. för EF r. DF. pr. 29. l. 17. for KL r. EL. B IV. pr. 15 p. 64. 1. 8. for CG, GF r. CG, GD. Q A4 A D M Prop. 23 B G E A I K ME Prop. 28 G O F M D EA M ML S BK N Book XI. A Solid, is that which hath length, breadth, and thick- II. The term of a folid, is a fuperficies. III. A right line is perpendicular to a plain, when it makes right angles with all the lines that touch it, and are drawn in the fame plain. IV. A plain is perpendicular to a plain, when all the right lines in one plain, drawn at right angles to the common section of the two plains, are at right angles to the other plain. V. The inclination of a right line to a plain, is the acute angle contained under that line, and another right one drawn in the plain, from that end of the inclining line, which is in the plain, to the point where a right line falls from the other end of the inclining line, perpendicular to the plain. VI, The inclination of a plain to a plain, is the acute angle contained by the right lines drawn in both plains, to the fame point of their common fection, and making right angles with it. VII. Plains are inclined fimilarly, when their angles of inclination are equal. VIII. Parallel plains are fuch, which being produced, never meet. IX. Similar folid figures are fuch as are contained under an equal number of fimilar plains. X. Equal and fimilar folid figures are fuch as are contained by an equal number of fimilar and equal plains. XI. A folid angle is the inclination of more than two right lines that meet in one point, but are not in the fame fuperficies. XII. A pyramid is a folid figure, contained by more than two plains fet upon one plain, and meeting at one point in the vertex. XIII. A prifm is a folid figure contained by plains, whereof the two oppofite are equal, fimilar, and parallel; and the other parallelograms. XIV. A fphere is a folid figure, defcribed by a femicircle revolving about its diameter, which remains fixed in the fame poftion. XV. The axis of a sphere is that fixed right line about which the femicircle revolves. XVI. The centre of a fsphere is the fame with that of the femicircle. XVI. XVIII. The diameter of a fphere is a right line drawn through the cone; cone; if less, an obtufe angled cone; and if greater, an a- Book XI. cute angled cone. XIX. The axis of a cone is that fixed right line about which the tri angle is moved. XX. The base of a cone is the circle described by the revolving line. XXI. A cylinder is, a figure described by a right angled parallelogram, revolving about one of the fides, containing the right angle, remaining fixed. XXII. The axis of a cylinder is that fixed right line about which the parallelogram is moved. XXIII. The bases of a cylinder are the circles defcribed by the motion of the two opposite fides of the parallelogram. XXIV. Similar cones and cylinders are fuch, whofe axes and diameters of their bafes are proportional. XXV. A cube is a folid figure contained by fix equal fquares. XXVI. A tetrahedron is a folid figure contained by four equal equilateral triangles. * XXVII. An octahedron is a folid figure contained by eight equilateral triangles. XXVIII. A dodecahedron is a folid figure contained by twelve equal equilateral and equiangular pentagons. XXIX. An icofahedron is a folid figure contained by twenty equal equilateral triangles. XXX. A parallelopipedon is a folid figure contained by fix quadrilatėral figures, whereof thofe that are oppofite are parallel. Ο PROP. I. THEOR. NE part of a right line cannot be in a plain superficies, and For, |