Theory of proportion; the four powers and the nature of gravity
Ratios classed as multiple, superparticular and superpartient; gravity and lightness as accidental powers of motion
The left folio sets out the classical theory of ratios in a tabulated scheme, naming the multiple, superparticular and superpartient classes with worked examples (dupla, sesquialtera, superbipartient and so on) and defining each. The right folio turns to physics, listing gravity, force, material motion and percussion as the four accidental powers behind all mortal works, then giving several definitions of gravity as an invisible power created by motion and infused into displaced bodies. Small diagrams accompany the physics text, and Leonardo concludes that gravity and lightness are so alike that they are almost one and the same.
On this page
The classes of ratio, tabulated
Leonardo tabulates simple inequality as multiple (2:1 double, 3:1 triple, 4:1 quadruple), superparticular (3:2 sesquialtera, 4:3 sesquitertia, and so on) and superpartient (5:3, 8:5, 9:5, 11:6), then compound inequality such as 5:2 double sesquialtera. He explains that the greater term either contains the lesser an exact number of times, or with an aliquot part, or with a non-aliquot part composed of aliquot parts.
The four accidental powers and definitions of gravity
Gravity, force, material motion and percussion are named as four accidental powers by which all the manifest works of mortals have their being and death. Gravity is defined as an invisible power created by motion and infused into an element drawn or thrust into another, living as long as that element takes to return home. Lightness differs from gravity only in the opposite lines along which each is born and dies.
Gravity and lightness transmuted
Beside three small figures, Leonardo repeats that invisible gravity is an accidental power created by motion and infused into bodies outside their natural place. He states that gravity and lightness are two elements transmuted one into the other, so alike in every function except in the motions of their creation and privation that they may almost be called one and the same.