\chapter{Definitions}

\begin{enumerate}
    \item \label{def:1} A point is that of which there is no part.
    \item \label{def:2} And a line is a length without breadth.
    \item \label{def:3} And the extremities of a line are points.
    \item \label{def:4} A straight-line is (any) one which lies evenly with points on itself.
    \item \label{def:5} And a surface is that which has length and breadth only.
    \item \label{def:6} And the extremities of a surface are lines.
    \item \label{def:7} A plane surface is (any) one which lies evenly with the straight-lines on itself.
    \item \label{def:8} And a plane angle is the inclination of the lines to one another, when two lines in a plane meet one another, and are not lying in a straight-line.
    \item \label{def:9} And when the lines containing the angle are straight then the angle is called rectilinear.
    \item \label{def:10} And when a straight-line stood upon (another) straight-line makes adjacent angles (which are) equal to one another, each of the equal angles is a right-angle, and the former straight-line is called a perpendicular to that upon which it stands.
    \item \label{def:11} An obtuse angle is one greater than a right-angle.
    \item \label{def:12} And an acute angle (is) one less than a right-angle.
    \item \label{def:13} A boundary is that which is the extremity of something.
    \item \label{def:14} A figure is that which is contained by some boundary or boundaries.
    \item \label{def:15} A circle is a plane figure contained by a single line [which is called a circumference], (such that) all of the straight-lines radiating towards [the circumference] from one point amongst those lying inside the figure are equal to one another.
    \item \label{def:16} And the point is called the center of the circle.
    \item \label{def:17} And a diameter of the circle is any straight-line, being drawn through the center, and terminated in each direction by the circumference of the circle. (And) any such (straight-line) also cuts the circle in half.
    \item \label{def:18} And a semi-circle is the figure contained by the diameter and the circumference cuts off by it. And the center of the semi-circle is the same (point) as (the center of) the circle.
    \item \label{def:19} Rectilinear figures are those (figures) contained by straight-lines: trilateral figures being those contained by three straight-lines, quadrilateral by four, and multilateral by more than four.
    \item \label{def:20} And of the trilateral figures: an equilateral triangle is that having three equal sides, an isosceles (triangle) that having only two equal sides, and a scalene (triangle) that having three unequal sides.
    \item \label{def:21} And further of the trilateral figures: a right-angled triangle is that having a right-angle, an obtuse-angled (triangle) that having an obtuse angle, and an acute-angled (triangle) that having three acute angles.
    \item \label{def:22} And of the quadrilateral figures: a square is that which is right-angled and equilateral, a rectangle that which is right-angled but not equilateral, a rhombus that which is equilateral but not right-angled, and a rhomboid that having opposite sides and angles equal to one another which is neither right-angled nor equilateral. And let quadrilateral figures besides these be called trapezia.
    \item \label{def:23} Parallel lines are straight-lines which, being in the same plane, and being produced to infinity in each direction, meet with one another in neither (of these directions).
\end{enumerate}