Division of the Greater Inequality: Ratio Theory
Simple and composite proportions—multiple, superparticular, superpartient
A page of classical ratio theory setting out the 'greater inequality' in the Boethian manner, dividing it into simple and composite kinds. The simple has three members—multiple, superparticular and superpartient—and the composite two, multiple-superparticular and multiple-superpartient, each illustrated with tables of named ratios such as dupla, sesquialtera and superbipartiens and their fractional values. The lower half is blank and carries the red British Museum crown ownership stamp.
On this page
Greater inequality: simple and composite
The greater inequality is of two kinds, simple and composite. The simple has three members—multiple, superparticular, and superpartient—while the composite has two, multiple-superparticular and multiple-superpartient.
Table of the simple inequality
Under 'della semplice inequalità' three columns list the ratios: multiples 2:1, 3:1, 4:1, 5:1; superparticulars such as 3:2 sesquialtera (1 1/2) and 4:3 sesquitertia (1 1/3); and superpartients such as 5:3 superbipartiens (1 2/3) and 8:5 supertripartiens (1 3/5).
Table of the composite inequality
Under 'della composita inequalità' the multiple-superparticular ratios (5:2 dupla sesquialtera, 2 1/2; 7:3 dupla sesquitertia, 2 1/3) stand beside the multiple-superpartient ratios (8:3 dupla superbipartiens; 15:4 tripla supertripartiens), down to 29:4 quadrupla sesquisettima.