Straight versus Curved Lines, and the Center of the World
Two definitions of line tested against a circle: the curve f b o and the chord a b c
This page offers a 'first' and 'second' definition of the straight and curved line, framed in terms of equal height from the center of the world, and then shows both to be false. A circle is drawn with radii and a tangent-like segment carrying the labels a b r s t c, n m o and f, so that the curve f b o would count as straight and the line a b c as curved. Leonardo is probing how straightness should be defined against the earth's center. The reasoning breaks off in mid-sentence.
On this page
First and second definitions of straight and curved line
The 'first' definition holds that a straight line is one whose every part is of equal height, and the 'second' that a curved line has a height uniformly uneven toward its extremes. Leonardo then declares both false, since equal height means equal distance from the center of the world.
Circle diagram: the curve f b o and the line a b c
A circle is drawn with radii and a tangent-like segment carrying the labels a b r s t c, n m o and f. By his own reasoning the curve f b o would count as straight and the straight line a b c as curved, on account of their distances from the center. The argument stops before it is finished.