Circles in Quadruple Proportion and 'Shield' Figures
More area equivalences of lunes and shields, with a jotted 'Tuesday'
The verso continues the area-equivalence studies with roundels of interlocking circles and two-angled stars. Leonardo states that among circles in quadruple proportion the 21 portions of the greatest equal the 84 of the least (one great worth four small), and lists the halving series 84, 42, 21. Further figures reduce lunes and eight shield-shaped pieces to the greatest square of the greatest circle, and a group of ten portions to the four greatest portions of the circle. On the left page a single stray word, 'Tuesday,' is jotted among the diagrams.
On this page
Circles in quadruple proportion: 21 great equal 84 small
Among circles standing in quadruple proportion, the 21 portions of the greatest are worth the 84 of the least; that is, one of the great portions equals four of the small. An inverted column lists the halving series 84, 42, 21.
Eight 'shields' equal to the greatest square
In a figure of circles double one another, the sub-double circle receives the 8 greatest portions of the greatest circle, split into 16 halves but reshaped into shield forms; the whole is worth the greatest square of the greatest circle.
Outer lune as a quarter of the circle
With four internally tangent circles, the outer lune is the fourth part of the whole circle; removing a single one of its portions leaves a square equal to the quarter of the square of the greatest circle.
'Tuesday' written on the left page
Among the geometrical figures on the left-hand page Leonardo has jotted the single word 'Tuesday,' a stray day-of-the-week note unrelated to the demonstrations around it.