Squaring the circle, with cylinders, cones and spheres
Solid-geometry equalities, a recipe for hollow gold wire, and a note on embrasures
The sheet opens with a goldsmith's recipe for making hollow silver or gold wire by cladding a lead core, drawing it thin as straw, then heating it upright so the melted lead can be poured out (text 1). Most of the page is geometry: statements of equal figures with a shared 'black portion,' and, on the facing folio, an attempt to construct a rectangle equal to a given circle alongside relations among the surfaces of cylinders, cones and the largest inscribed sphere (texts 4, 6). A single line on fortification notes that embrasures thick enough that a man cannot pierce them will prevent mines (text 6). Numerous small geometric sketches and further untranscribed writing surround the text (text 7).
On this page
Making hollow gold or silver wire over a lead core
To make hollow silver wire as thick as straw: draw the lead a finger thick and clothe it with gold or silver; when it is thinned like straw, heat it upright so the melted lead can be poured out, and thus you can work the gold like straw. He adds the practical reminder, 'Help yourself by borrowing.'
Equal figures and a common portion
The figure a c b n is equal to d e, and the black portion is common to both quantities. Removing b from a b c n and e from d e leaves a c n above equal to d below; a companion note states a b equal to c so that n equals c.
Squaring the circle; cylinder, cone and inscribed sphere
Let there be given a rectangle equal to a given circle. Leonardo then relates a cylinder whose thickness is double its height to the circle of its face, converts a semicircle whose semidiameters touch into a cone with a base one-quarter of the greater circle, and equates a cylinder's lateral surface to four base-circles and to the surface of the largest sphere it can contain.
Thick embrasures that prevent mines
Embrasures thick enough that a man cannot penetrate them will prevent mines. The remark stands as a single line within the geometrical passage on folio 197r.