Euclid's definitions: point, line, surface, and angle
The opening definitions of the Elements, from point to figure
Folio 140v gives the opening definitions of Euclid's geometry: a point has no part, a line is length without breadth ending in two points, and a straight line is the shortest extension between two points. It defines surface and plane surface, then the plane angle formed where two lines meet without lying straight, naming rectilinear, right, obtuse, and acute angles and the perpendicular. The margin carries a labelled column of figures, from a point and line to the several kinds of angle.
On this page
Point, line, and surface defined
A point is that which has no part; a line is length without breadth ending in two points; a straight line is the shortest extension from one point to another. A surface has only length and breadth and is bounded by lines, and a plane surface stretches from one line to another.
Right, obtuse, and acute angles
A plane angle is the precise touching of two lines not laid straight. When a line stands on a line making its two angles equal, each is a right angle and the standing line is perpendicular. The angle greater than a right angle is obtuse, the lesser is acute; a figure is what is contained by one or more terms.