The Five Postulates of Geometry
Points, lines, circles, right angles and parallels defined
Under the heading 'On the five postulates' Leonardo sets out the elementary premises of geometry. He states that the boundaries of a line are points, of a surface lines, and of bodies surfaces; that a straight line can be drawn between two points and extended indefinitely; that many circles can be described over one point; that all right angles are equal; and that parallel lines make interior angles with a transversal equal to two right angles. A curved pen-stroke groups the lines belonging to each postulate.
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Boundaries, straight lines and their extension
The boundaries of a line are points, of a surface lines, and of bodies surfaces. From one point to another a straight line can be drawn, and that line can be extended beyond its points as far as one likes, though its boundaries will always be two points.
Circles, right angles and parallels
Over one same point many circles can be made, and all right angles are equal among themselves. Parallel lines are those which, when a transverse line is drawn across them, make two interior angles equal to two right angles.