Multiple and Submultiple Ratios on Divided Lines
Magnitudes grouped as multiplici and sub multiplici, with a rule for handling three lines at a time
The page classifies ratios as multiplici (multiple ratios) and sub multiplici (submultiple ratios), tabulating paired magnitudes such as g 16 / h 24, K 8 / L 12, and a 8 / b 4. A closing note advises keeping only three lines (a b c) in hand at once and, to add a fourth d, cancelling the second b. Faint mirror-script above and horizontal line-segments divided into proportional parts below fill the sheet.
On this page
Multiple and submultiple ratios tabulated
Leonardo groups magnitudes under the headings multiplici (multiples) and sub multiplici (submultiples), pairing values such as g 16 with h 24, K 8 with L 12, and a 8 with b 4. The scheme rehearses how one quantity contains another a whole number of times, or is contained in it as a fraction.
Rule for keeping three lines at a time
A prose note states that it is enough to take three lines one after another, such as a b c; and if one wishes to set down the fourth, d, the second, b, is to be cancelled. The remark keeps the running comparison of proportional terms to a manageable set.
Line-segments divided in proportion
The lower half of the sheet carries ruled horizontal segments marked off at interior points and joined by curved brackets, realising the tabulated ratios as proportional divisions of a line. The construction turns the numerical ratios into lengths.