Continuous and Discontinuous Proportionality
Least terms 1 2 4 and 1 2 8 16; antecedents and consequents
Folio 46v sets out the theory of geometric proportionality with rows of numbers bracketed to show their ratios. Continuous proportionality is said to need at least three terms, 1 2 4, which form two double proportions and make the smallest continuous series; discontinuous proportionality needs at least four, 1 2 8 16. A closing note observes that within the extremes of a continuous proportion every figure serves as both antecedent and consequent, taken from either side. A small pen tetrahedron is drawn at the upper right.
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The least continuous proportion is 1 2 4
In continuous proportionality at least three terms are required, that is 1 2 4, which make two double proportions. This is called the least, or smallest, continuous proportionality.
Discontinuous proportion needs four terms
In discontinuous proportionality at least four terms are required, namely 1 2 8 16, and in this way the discontinuous proportionality is composed.
Every term is both antecedent and consequent
Within the extremes of a continuous proportionality all the figures are antecedents and consequents, taken from whichever side one reads them.
Pen tetrahedron
A small tetrahedron is drawn in pen at the upper right of the sheet, a lone solid figure set apart from the columns of proportion numbers.