1. The definition and properties of a strait line.—2. The definition and properties of a plane superficies.—3. Several sorts of crooked lines.—4. The definition and properties of a circular line.—5. The properties of a strait line taken in a plane.—6.. The definition of tangent lines.—7. The definition of an angle, and the kinds thereof.—8. In concentric circles, arches of the same angle are to one another, as the whole circumferences are.—9. The quantity of an angle, in what it consists. —10. The distinction of angles, simply so called.—11. Of strait lines from the centre of a circle to a tangent of the same. —12. The general definition of parallels, and the properties of strait parallels.—13. The circumferences of circles are to one another, as their diameters are.—14. In triangles, strait lines parallel to the bases are to one another, as the parts of the sides which they cut off from the vertex.—15. By what fraction of a strait line the circumference of a circle is made.—16. That an angle of contingence is quantity, but of a different kind from that of an angle simply so called; and that it can neither add nor take away any thing from the same.—17. That the inclination of planes is angle simply so called.—18. A solid angle what it is.—19. What is the nature of asymptotes.—20. Situation, by what it is determined.—21. What is like situation; what is figure; and what are like figures. [Sidenote: The definition end properties of a strait line.] 1. Between two points given, the shortest line is that, whose extreme points cannot be drawn farther asunder without altering the quantity, that is, without altering the proportion of that line to any other line given. For the magnitude of a line is computed by the greatest distance which may be between its extreme points; so that any one line, whether it be extended or bowed, has always one and the same length, because it can have but one greatest distance between its extreme points.