Division of Quantities into Equal Parts
The inverse of size and number, with a star-shaped flower drawn in a circle
Two columns of closely reasoned text turn on a single proportional law: when a given material or number is divided into equal parts, the size of the parts diminishes exactly as their number grows, and grows exactly as their number falls. The point is restated in several near-identical forms, and a small square of proportionality at the foot is said to be subdividable into unequal parts infinitely. Dominating the lower left, a large radiate flower with slender pointed petals is drawn within a ruled circle; this botanical study carries no transcribed text and appears in red-brown ink. Further untranscribed lines accompany the diagrams.
On this page
Parts grow as their number falls
Of equal quantities that grow or diminish equally, the parts grow by as much as their number falls short, and diminish by as much as the number grows. The same reciprocal law is repeated for divisible material and for a number divided into equal parts: the more it is divided, the more the parts grow while the count shrinks.
The law restated in the left column
A given quantity divided at different times with different numbers shows the parts growing as the number falls, and shrinking as it rises. When a number is successively divided into equal parts, the magnitude of each part diminishes by exactly as much as their number increases.
The square table of proportions
A small ruled square at the foot of the page is labeled the square table of proportions, which can be subdivided into unequal parts without end.
Radiate flower within a circle
A large flower with many slender, sharply pointed petals radiating from a small round center is drawn inside a compass-ruled circle at the lower left. It is rendered in reddish ink and carries no accompanying transcription, standing apart from the mathematical text around it.
