Squaring the circle: two tables of proportionality
Reducing curvilinear figures to a square via Euclid II; a large arc-rosette and grids
The sheet is devoted to the quadrature of curved figures—reducing a circle to an equal square. Leonardo sets out two 'tables of proportionality', one for a circle divided into four sectors (a b c d) and one into six (b e d f), argues they are of equal value in various numbers of parallels, and invokes the last proposition of the second book of Euclid's Elements to draw the greatest portions of a circle and reduce any curvilinear surface to a square. A large circle at the centre is filled with a symmetrical net of intersecting arcs forming a rosette, and small tilted squares and a ruled grid accompany the demonstration.
On this page
Two tables of proportionality for the circle
Leonardo labels two tables, a b c d serving a circle divided into four sectors and b e d f divided into six parallels for a circle in six sectors, and calls them of equal value in various numbers of parallels, the variety being infinite. From the four parallels the greatest portions of a great circle are drawn with the aid of the last proposition of the second book of the Elements.
Reducing any curvilinear surface to a square
By transmuting the six parallels b e d f into the four a b c d, Leonardo claims to reduce to a square whatever curvilinear surface is set before him. He judges it better to square the whole greater parallelogram a b c d at once and to build on one of its four sides an equilateral triangle.
Large circular net of intersecting arcs
A large circle dominates the centre of the sheet, filled with a dense, symmetrical mesh of intersecting arcs that form a star-like rosette, apparently a figure for the quadrature study. Small tilted squares sit at the upper corners and a ruled grid at the lower right.