Geometry of lunes and surfaces, with a note on safe falling
Postulates of the first book, proportions of triangles, and cushioning a fall with straw or wool
The sheet is filled with geometric figures — concentric semicircles, triangles on a common base, circular sectors and lune-shaped portions — supporting Leonardo's study of squaring curvilinear surfaces by removing and restoring equal parts. A left-hand column sets out numbered 'postulates of the first book' and 'conceptions', concluding that a curvilinear surface is squarable only if an equal square can be given to it. A separate note at the top reasons about a safe descent: leaping onto a great bundle of straw or wool is like falling joined to it, and one should hold a light branch so the head stays uppermost, since in any falling body the heavier part guides the motion. Further mirror-script text is present on the sheet but not transcribed here.
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Breaking a fall on a bundle of straw or wool
Leaping upon a great bundle of straw or a ball of wool is treated as equivalent to descending joined to it onto hard ground. Leonardo advises carrying a branch or other light thing in the hand so that the descent keeps the head uppermost, because in every falling body the heavier part becomes the guide of the motion.
Equal remainders from equal figures (a c d and b n m)
Since a c d equals b n m, the half-portions c d are removed from a c d and the two whole portions n m from b n m, the latter being worth the two half-portions c d. Equal things removed from equal quantities leave the remainders a b equal to one another.
Triangles on one base proportional to their axes
For triangles standing on an equal base, the proportion from triangle to triangle is as the proportion from axis to axis. The figure carries the letters e d a and h g f c b.
Postulates and conceptions on squaring curved surfaces
A numbered column gives the 'postulates of the first book': that a part may be taken from one side of a surface and restored on another side of the same surface, and that parts of two surfaces may be superimposed. Its 'conceptions' state that a part regains its whole when the removed quantity is restored, and that a curvilinear surface is squarable only if an equal square can be given to it.
A curved side taken from a straight-sided equal surface
When the curved side of one surface takes away from the straight side of another surface of equal value, the first is left with a straight side and yields its curved side to the other. The figure is lettered p o a.