Gravity toward the centre; balls falling by different slopes
Motion of falling balls proportioned to the chord; spiritual arms of the balance
Leonardo opens with a cosmological principle: a body resting at the centre of the world weighs nothing on its support, and every heavy body seeks its support toward the centre. A quarter-circle diagram then shows balls falling by different obliquities, the proportion of their motion and weight following the parts of the ball cut off between the perpendicular of contact and the start of the fall - weight v descending freely, t lacking the part m c n, S lacking b, and r where the power M equals the resistance o. A closing note corrects those who think equal weights on equal balance-arms simply rest in equilibrium, insisting one must reckon the 'spiritual' arms, the distances of the weights' centres from the centre of the balance.
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A body at the centre of the world weighs nothing
The body that rests at the centre of the world weighs nothing on its support; every ponderous body seeks its support toward the centre, and every opposition presses according to its heaviness. Weight is defined relative to the centre toward which bodies tend.
Balls falling by different obliquities
The quality of motion and weight of these balls falling by different slopes is shown; the proportion of their velocity along straight lines equals the proportion of the parts lying between the perpendicular of their contact and the beginning of their motion. Motion is tied to how the descent line cuts the sphere.
What each weight lacks: v, t, S, r
The descending weights keep the same proportion in their motions: v descends freely with no exception; t lacks the part m c n; S lacks the part b; and in r the power M equals the resistance o. Where M o are equal the motion is not, and a b are unequal.
Spiritual arms of the balance, not the material arms
Some believe that equal weights hung at the ends of equal balance-arms rest in equilibrium, but they are much deceived: one must reckon, in place of the material arms, the 'spiritual' arms - the distances of the weights' centres from the centre of the balance. A simple beam with two weights of 8 is drawn alongside.