The aliquot part of numbers; circles divided into portions
Why 24 divided by 6 is 4; a circle of twelve forked bi-angles worth six hexagon portions
Leonardo examines the 'aliquot part' of a number, asking whether the aliquot part of 24 is 4 or 6, and defining it as the multiplicative part that fits exactly into another number without leaving a fraction. He ties the arithmetic to geometry, showing a circle of twelve forked bi-angles that, halved, yield 24 portions divisible into four equal groups of six. Several rosette-like figures divide circles into lens-shaped 'bi-angles' and hexagonal portions, one 'pierced' circle being declared worth the greatest rectilinear hexagon the circle can contain. The lower half of the sheet carries further faint, largely rubbed text noted as present but not transcribed here.
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Definition of the aliquot part of 24
Dividing 24 by 6 gives 4 with no remaining fraction, so both 4 and 6 measure 24 exactly. Leonardo defines the aliquot part as the multiplicative part of a number that fits exactly with its equal parts into the equal parts of another number, as 6 does four times in 24.
Twelve forked bi-angles equal six hexagon portions
The figure is worth the greatest hexagon of the greatest circle. Make 12 of these forked bi-angles that are worth these six, or else double the circle as much again.
A pierced circle worth the greatest inscribed hexagon
This pierced (traforato) circle is worth the greatest rectilinear hexagon that can fit within the whole circle, drawn as a bi-angular star. Leonardo begins the demonstration ('it is proved thus').
