Dividing a circular sector; a note on lightning
An eighth part of a circle's portion, made similar; why the thunderbolt tapers
Two short notes share this fragmentary sheet. On the right, with the page turned, a figure of a subdivided portion asks that a sector of a circle be divided into eight smaller portions similar to the whole, or that its eighth part be given as a smaller but similar portion. On the left a single line reasons that the thunderbolt runs narrow because the vaporization of the air, which sheaths its motion and turns to fire, forms a sheath around it. Small geometric sector and lens shapes are drawn at the foot of the sheet.
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Dividing a circular portion into eight similar parts
Leonardo asks that a portion of a circle be divided into eight smaller portions similar in figure to the whole, or that its eighth part be supplied as a smaller portion geometrically similar to the original. It is a problem of proportional subdivision of a circular sector.
Why the thunderbolt runs narrow
The thunderbolt goes narrow, Leonardo notes, because the vaporization of the air becomes the sheath of its motion; that vapor, converting into fire, forms a sheath about it. The idea ties the bolt's slender form to the behavior of heated, moving air.