Circle Sectors and Solid-Figure Studies
Portions a b equal a portion of d; the axiom that doubles minus doubles leave a double
Working with circle sectors labelled a, b, c, d, Leonardo shows that the two portions a b together equal a single portion of d, since d belongs to a circle double that of c, and states the axiom that if double parts are taken from double things the remainder is double. Around the text he draws a series of solid-geometry figures—curved lune and dome-like segments, a cone and a tall spike—matching the sheet's scholarly tags for cylinder and cone, prism, and the sphere and its lunes. Numerical workings accompany the diagrams, and further mirror-script text runs above.
On this page
Two circle sectors a b equal a portion of d
All of d equals all of c; and because d is one twelfth of a circle double the circle c, the portion b is likewise one twelfth of its circle and comes to be half the portion of d. Adding the second portion a, the portions a b together equal the single portion of d.
Axiom: doubles minus doubles leave a double
If from double things double parts are removed, the remainder is double.
Solid figures: lunes, cone and dome segments
The lower sheet is crowded with solid-geometry sketches: a series of curved lune and dome-like segments, a broad cone and a long tapering spike. The holding institution's index ties these to studies of the cylinder and cone, the prism, and the sphere and its lunes.
Numerical workings beside the figures
Columns of figures accompany the diagrams, including 200 over 12 and 12 into 5 into 60, supporting the portion-counting of the circle sectors and solids.