The Four Operations on a Proportion (Series 191)
Alternation, conversion, composition and separation applied to divided line-segments
The note instructs the reader to carry out the four classical operations on a proportion: permutation (impromutata, alternando), conversion (eversa), composition (congiunta, componendo) and separation (disgiunta, dividendo). Beneath it the magnitudes are laid out as a 12, e 4 and b with the whole 16, and c 6, f 2 and d with the whole 8, together with a further set a 8 / b 4, c 6 / d 3, e 6. Line-segments split at the lettered points illustrate the transformations.
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Permute, convert, compound and divide the proportion
Leonardo directs: make an alternation, a conversion, a composition and a separation. These are the standard manipulations of a proportion (permutando, convertendo, componendo, dividendo), by which a given ratio yields its derived forms.
Line-segments split at interior points
The magnitudes are drawn as horizontal segments, one bearing a 12 and e 4 within the whole 16, another c 6 and f 2 within the whole 8. Cutting each line at the lettered point makes the additive relations of composition and separation visible as lengths.