Lunule construction and curvilinear surfaces
Squares with inscribed circles, a halving argument, and columns of figures
This geometrical sheet studies curvilinear surfaces: a lunule is built from a semicircle set within a circle, with the condition that the chord of the sub-double semicircle equal the chord of the double quarter-circle, namely the chord a b. A series of squares with inscribed circles accompanies an argument that a magnitude, repeatedly halved, always leaves a further divisible half. Columns of pen figures and sums run along the right and lower margins, some written with the sheet turned. Faint red-chalk spirals appear at the lower left.
On this page
Construction of a lunule from a semicircle within a circle
A lunule is constructed by setting a semicircle inside a circle. Leonardo states the governing condition that the chord of the sub-double semicircle be equal to the chord of the double quarter-circle, that is the chord a b.
Curvilinear surface
A brief heading names the subject of the study, the curvilinear surface. It ties together the lunule and the circle-in-square figures as an inquiry into areas bounded by curves.
Squares with inscribed circles and the endless half
A row of squares with inscribed circles is set beside an argument on continued halving: successive sub-doubles rejoined remake the first square, and in dividing there always remains a further divisible half. If a magnitude can be divided a half remains; if it cannot, no part remained, so it was never divided.
Columns of pen figures and sums
Along the right and lower margins stand columns of numbers written in pen, some read only with the sheet turned upside-down or onto its side. They record sums and doublings (16, 8, 8, 16, 4, 4, 8) and separate tallies such as 120, 89, 31, 36, 67.