Thinning a Board Without Changing Its Volume
A geometric construction, dated 'begun 12 July 1505'
A dated note in the upper corner records that Leonardo began this work on 12 July 1505. The main problem asks how to reduce a board (a b c d) to a given thickness without changing its width, and how much its length must grow to conserve the material. Using three lines intersecting at g, Leonardo lays off the original thickness at c e and the length at n f, narrows the lines, and adds the resulting difference to obtain the new length b f. A large construction of converging lines and a rectangle fills the sheet.
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Reducing a board's thickness, finding its new length
Leonardo wishes to lower the thickness of a board to a given value without altering its width, and asks how much longer it becomes. Taking the board a b c d with thickness c e d f, he uses three lines intersecting at g, placing the first thickness at c e and the length at n f; narrowing the lines to o a and m f gives the elongation n m, which added at h n yields the new length b f.
Dated note: begun 12 July 1505
An inscription in the upper corner records that the work was begun by Leonardo da Vinci on the 12th of July 1505. It fixes a date for this part of the notebook.