Weights on Oblique Supports and Centres of Gravity
A load shared between two inclined props; bodies seeking the centre of the world
A sequence of statics studies. In the first, a weight a resting on two props b and c of equal obliquity and length gives an equal share of its weight to each. Reasoning only with "mathematical lines" (so that the instrument's own weight is annulled), Leonardo argues that a load's gravity avails as much at one prop's end as at the other because the plumb-lines converge to the centre of the world in balance. A hinged window-"pole" figure shows a centre of gravity that "desires to descend" toward the centre of the world by the shortest path, descending where it can if not where it wishes, with impetus consumed in one motion and increased in another. A jointed instrument and several plumb-line sketches accompany the text.
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A weight shared equally between two equal props
In the first figure a weight a rests on two supporting rods b and c. Because the supports are of equal obliquity and length, the weight gives an equal share of itself to each.
Gravity effective at either end; plumb-lines to the world's centre
Considering only mathematical lines, so the instrument's own weight is annulled, the gravity of weight b avails as much at c, the end of support a c, as at b, the end of support a b. This is proved because the straightness of the potential pendant m o and the semi-potential pendant n c b converge to the centre of the world, in balance with arms equidistant from the centre of rotation n m.
The window-pole and the descent to the world's centre
a, the pole (pivot) of the window a d c b, has its centre of gravity at e, which desires to descend to the line a c and below the pole c, its principal intent being to reach the centre of the world by the shortest way; if it cannot descend where it wishes, it descends where it can. He asks whether the weight c weighs more to a or to c, noting that in motion e S the impetus is consumed while in motion c e it increases.
Jointed instrument and plumb-line figures
At the top centre a jointed, articulated instrument is drawn, and several plumb-line / pendant figures (marked o) trail down the left and right of the sheet. These illustrate the "instrument" whose own weight the text sets aside, reasoning only with mathematical lines.