Distributing four pounds among three cords on a beam
A worked proof of load-sharing, with a marginal note on dividing 4 into 7 parts
Marked "tested by experiment," the leaf sets out two diagrams of a beam (its points labelled a, b, c, d) hung from three cords, and a long procedure for finding how a 4-pound load is shared. Leonardo sums the spaces spanned by the cords (b to c with c to d, then a to c with c to d) to get 7 parts, divides the 4 pounds by 7 so each part is 4/7, and then dispenses the shares among a, b and d. A marginal note gives the reciprocal arithmetic: dividing 4 into 7 parts yields 4/7 each, and dividing 7 into 4 parts yields 7/4, that is 1 3/4.
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Proof of how three cords share a four-pound load
Hanging the stick from three cords so that it weighs 4 pounds is equivalent to hanging three cords from the stick and loading them with 4 pounds at the same place. Adding the spaces b-c with c-d, and then a-c with c-d, gives seven parts of proportion, and 2 parts are given to b against one to d before the remainder is dealt to a and d.
Dividing 4 into 7 parts and its reciprocal
If you divide 4 into 7 parts, each part is 4/7 and every whole is 7. And if you divide 7 into 4 parts, each part is 7/4, that is 1 3/4.