Squaring the Lunes; Flame, Air, and a Note on the Medici
Geometric transformation of circular segments, with an optical passage and personal jottings
A near-circular fragment densely covered with semicircles bearing hatched lunes (falcate), working the transformation of circular segments into equivalent rectilinear areas by squaring and superposition. A central paragraph describes the air that rushes to a flame, condensing and turning blue as it refracts, while short lettered captions assert area-equalities such as "a b c equals d." At the foot stands Leonardo's terse aside that the Medici created and destroyed him, and, with the sheet inverted, columns of arithmetical figures. Many small captions around the diagrams remain beyond the transcribed blocks.
On this page
Squaring the lunes into the triangle
Two instructions govern the many diagrams: square that which lies outside the triangle and place it into the concavity, and let the lunes outside the triangle fill in within it. The repeated hatched semicircles work the reduction of circular segments to equal rectilinear figures.
Lune equivalences: a b c equals d
Small labelled semicircles carry area-equality formulae such as m n equals o, a b c equals d, and a b equals d, in which composite segments are declared equal to a stated figure. One note directs the reader to remove the equal part so that a b remains equal to d.
Air rushing to the flame turns blue and refracts
Air drawn toward the creation of the flame strikes it, is reflected back on itself, condenses, and becomes visible with a bluish cast. At the flame's sides a very thin air meets the light and refracts, is met by the oncoming air, and is thrown back in continual revolution and turning.
"The Medici created me and destroyed me"
A single line at the foot of the sheet states that the Medici created and destroyed him, one of Leonardo's terse autobiographical asides. A neighbouring fragmentary note reads "do not remain, and stay covered."
Arithmetical calculations (sheet inverted)
Turned upside down, the sheet carries columns of figures and multiplications, among them products such as 144 and 660. They are worked as running arithmetical operations rather than accounts of money.