How Infinite Lines Can Meet at a Single Point
A circle enclosing a fan of converging line-sectors, on the point as origin and end of lines
This page of Notebook M's geometry sequence treats the angle as the meeting, or contact, of two lines. Because every line terminates in a point, Leonardo reasons that an infinite number of lines can begin from one point and, conversely, an infinite number can end together there, so a single point may be common to the beginning or the end of innumerable lines. A circle at the head of the sheet encloses a fan of straight sectors converging to one point, illustrating the idea. The lower part of the sheet carries further mirror-script geometry not transcribed here.
On this page
A single point as the common origin or end of innumerable lines
If an angle is the contact of two lines, then since lines terminate in a point, an infinite number of lines can begin from that point. Conversely, an infinite number of lines can terminate together at that point. So one point can be common to the beginning or the end of innumerable lines.
Fan of converging sectors within a circle
At the top of the page a circle encloses a bundle of straight lines that fan out from, and converge upon, a single point near its lower centre. The drawing pictures the many lines sharing one common point that the text describes.