Angles Around a Point Equal Four Right Angles
Spherical right angles, and why all angles about a point or within a circle sum to four right angles
The folio gathers several results about angles summing to four right angles. Leonardo notes spherical angles equal to right angles, illustrated by a sphere on which two perpendicular meridians cross; states that the four angles made within a circle, filling all its space, equal four right angles whether their sides are curved, straight, or mixed; and generalises that any number of lines crossing at one point make as many angles about that point as there are lines, together equal to four right angles. Two small figures show three straight lines and three curved lines meeting at a single point.
On this page
Spherical angles equal to right angles
The note states that spherical angles can be equal to right angles. A sphere at the top of the page carries two perpendicular meridians crossing on its surface to picture such right angles on a curved body.
The four angles within a circle equal four right angles
Every four angles made within a circle, together filling all the space of the circle, are equal to four right angles. This holds whether their sides are of curved and straight lines, of all straight lines, or of all curved lines.
Any number of lines about a point make as many angles, equal to four right angles
Any number of lines intersecting over a given point make about that point the same number of angles as there are lines departing from it. Joined together, these angles are equal to four right angles.
Three straight lines and three curved lines meeting at one point
Two small figures at the right of the page show three straight lines crossing at a single point and, below, three curved lines crossing at a single point. They illustrate that the angles formed about the shared point, whether the lines are straight or curved, still sum to four right angles.