Proportional rectangles with root magnitudes
Continuous proportionals: surface is to surface as base is to base
The page studies rectangles whose sides and areas are square-root magnitudes, arranged as continuous proportionals. Two segments meeting at a right angle (labelled c, b, a) generate rectangles marked Root 12 and Root of Root of 48, and rows of compounded rectangles carry the values Root 3, Root 12, Root 48. Leonardo states the rule that surface is to surface as base is to base, illustrated by the geometric sequence 16, 8, 4, 2, and cites 'the first of the sixth' (Euclid) as authority.
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Rectangles built on segments c, b, a with root areas
Two segments meet at a right angle with endpoints labelled c, b and a. A rectangle constructed on them is marked Root 12, with Root of Root of 48 below, justified 'by the first of the sixth.' Further rows compound rectangles labelled Root 3, Root 12 and Root 48, and a paired figure adds Root of Root of 48 and Root of Root of 3.
Continuous proportionals and the sequence 16, 8, 4, 2
Leonardo states the rule of continuous proportionals: surface is to surface as base is to base. Beneath it he writes the geometric sequence 16, 8, 4, 2, each term half the last. The numbers give an arithmetical model of the proportional rectangles drawn above.