Sharing two weights along a beam hung from three cords
A statics problem worked out in fractions, amid many beam-and-balance diagrams and columns of figures.
This transmitted-light spread is filled with balance diagrams: horizontal beams marked off in parts, weights hung from cords, and dense columns of fractions. In the main note Leonardo shares two unequal weights (7 and 5) hung at the ends of a beam a, f suspended at three points, dividing the beam into 12 parts and reducing the three cords to proportions that total twenty-one, to find each cord's share (2 18/21 and 6 6/21). A brief adjoining note reads 'divide the 12 at n into the 24 of the proportions.' Much of the surrounding numeric working and several small diagrams on both leaves are left untranscribed.
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Sharing two weights along a beam hung by three cords
Two unequal weights, 7 and 5, hang at the ends a and f of a beam suspended at three points. Leonardo divides the loaded span into as many parts as the sum of the weights (12), then takes the center of the two weights by setting 5 opposite 7, so that the twelve spaces balance in equal weight.
Twelve parts, twenty-one proportions: the reckoning
Taking the proportions of the three cords in the usual way, he finds them to total twenty-one, and reduces each part to 12/21. Summing, he obtains the loads carried by the two cords on that side as 2 18/21 and 6 6/21, and declares the weight exactly shared out.