On Time, the Point, the Line, the Angle and the Surface
Geometry's first principles applied to time: the instant as point, with definitions of angle and surface.
These two densely written leaves set out a meditation on time and geometry. Leonardo argues that time, though counted among continuous quantities, submits only to geometry's first principles, the instant answering to the point and the length of time to the line, and is divisible to infinity in the same proportionable way. A series of definitions follows: the point has no part, the line is the transit of the point, the angle is a line broken at a point, and the surface is the motion of the line. He closes with 'level' lines whose extremities stand equidistant from the centre of the world.
On this page
Time is caused by the motion of the instant
Time, being invisible and without body, does not fall wholly under geometry, agreeing only with its first principles. The instant answers to the point and a length of time to the line; the instant has no time, and time is caused by the motion of the instant.
Time divisible to infinity and proportionable like the line
Just as points are the beginning and end of the line, instants are the end and beginning of a span of time. If the line is divisible to infinity, so is time; and if the divided parts of the line are proportionable among themselves, so too are the parts of time.
Definitions of point, line, angle and surface
The point has no part; the line is the transit of the point; the angle is a line broken at a point, or the contact of the extremities of two lines. The surface is the motion of the line, has no body, and the boundaries of bodies are surfaces.
Level lines equidistant from the centre of the world
A short list of named lines closes the leaf: line of equality, line of the horizon, lying (level) line, equally-lying line. These are the lines whose extremities stand equidistant from the centre of the world.