The four elements weighed, with number tables and water chapters
Axioms on the gravity and levity of the elements, a section of the elemental spheres, and columns of squares and cubes
The verso of the same double sheet, again filled with mirror script. It continues the theory of the gravity and levity of the four elements with a set of axioms, and carries a diagram of a section through the elemental spheres (fire, air, water, earth) annotated with rules of which element needs another's aid to remain within it. A block of computed figures (squares and cubes) and a small circle divided into four quadrants sit lower down, while a further list of chapters extends the projected book on the percussion of water.
On this page
Axioms on the gravity and levity of the elements
Each element has gravity or levity only outside its own element, greater or less as the surrounding element is lighter or heavier. No element receives or retains the element above or below it without the aid of a third. Adding light to light makes greater levity, heavy to heavy greater gravity, and joining heavy with light destroys both.
Section through the elemental spheres
A figure of the elemental spheres labelled Foco, Aria, Acqua, Terra (fire, air, water, earth) with rules: fire in air wants the aid of water; water in fire has no place; earth in water wants the aid of air; earth in fire is nothing. The letter a marks the penultimate sphere, said to gain two degrees of levity and one of gravity.
Columns of squares and cubes
A block of computed figures set transversely on the sheet, chains of multiplications running from small numbers up to values in the tens and hundreds of thousands, related to Leonardo's comparisons of square and cube roots.
Further chapters on the percussion of water
The right side extends the book on water: the power of water impeded in its course; impacts of water descending by curved lines, in stair-like steps, and through conduits, spouts and tapering channels; and water interrupted by the blades of mill wheels turning uprightly or flat.
Circle divided into four quadrants
At the bottom a circle is divided into four quadrants, annotated "Igna, in 4 pieces" — a division of the figure into equal parts.
