Summary of the Ratio Types, with a Multiplication Table
Recap of multiple / superparticular / superpartient and the 'sub-' names; a 10x10 product grid
Folio 48v gives a summary ('nota bene') of the ratio taxonomy just developed: a greater quantity that contains a lesser several times without remainder is multiple; once with an aliquot remainder is superparticular; once with a non-aliquot remainder is superpartient; and several times with a further part is multiple-superparticular or multiple-superpartient. Leonardo adds that the corresponding species of lesser inequality are formed simply by prefixing 'sub', as submultiple. At the foot of the page he draws a ruled 10x10 multiplication table, its rows labelled with the ratio names (dupla, tripla, quadrupla, sesqui...). The grid is clearly ruled in ink.
On this page
Summary of the four ratio classes
A greater quantity containing a lesser several times with no fractional remainder is 'multiple' (double, triple, etc.); containing it once with an aliquot remainder is 'superparticular'; with a non-aliquot remainder made of equal aliquot parts is 'superpartient'. Containing it several times with a further part gives 'multiple-superparticular' (aliquot) or 'multiple-superpartient' (non-aliquot).
Naming lesser inequality with the prefix 'sub-'
The species of lesser inequality, where comparison runs from the lesser to the greater, are named by adding the syllable 'sub', so that a multiple becomes submultiple and likewise for all the species. Leonardo notes there are exactly as many species of lesser inequality as of greater.
Ten-by-ten multiplication table
A ruled grid at the foot of the page tabulates products from the rows labelled dupla, tripla, quadrupla and the superparticular sesqui-series: the double row runs 2 4 6 8 ... 20, the triple row 3 6 9 ... 30, on down to the tenth row 10 20 30 ... 100. It serves as a ready reckoner for the ratio classes just defined.