Right angles from perpendiculars and crossing lines
Pen propositions: a perpendicular, two crossing lines, and the diagonals of a square
Four short pen propositions on the geometry of intersecting straight lines. Leonardo states that a line falling perpendicularly on another yields two right angles, that two crossing straight lines make four right angles about their intersection, and that when the four ends of two crossed diagonals are equidistant from the crossing they must also be equidistant from one another. A small square-with-diagonals and other geometric marks stand in the left margin.
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A perpendicular ends between two right angles
When a line falls perpendicularly upon another line, it terminates between two right angles. This is the base case from which the crossing-line propositions are built.
Crossing straight lines make four right angles
If one straight line passes over another and through their intersection, that intersection lies in the middle of four right angles. The point of crossing is thus surrounded equally on all sides.
Equidistant ends of two crossed diagonals
If the two straight lines that cross between four right angles have their four ends equidistant from the intersection, then those four ends are necessarily also equidistant from one another. This is illustrated by the small square carrying its two diagonals.