Squares, triangles and circles inscribed and circumscribed
Doubling of figures and the 3:1 ratio of a triangle's circumscribed to inscribed circle
A stained fragment carrying geometric propositions on inscribed and circumscribed figures, drawn with squares, triangles and circles. Two notes state that a square touching a circle at its angles is double the one touching it at its sides, and correspondingly that the two circles related to one square are double one another. Further propositions give the largest inscribed circle of a triangle a diameter equal to two-thirds of the triangle's axis, and make the circle through an equilateral triangle's three vertices triple the circle touching its three sides. A small tally in the upper corner records cash 25 and expenses 72, totalling 97.
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Inscribed and circumscribed squares are double one another
Two squares are said to be double one another when one is tangent to the same circle by its angles and the other by its sides. The proposition is stated as provable but the demonstration breaks off.
The two circles of one square are double one another
Likewise the two circles are double one another when the greater touches one square by its angle and the lesser touches the same square by its side. The similar parts of several circles are said to share the same proportion as their wholes.
Inscribed circle of a triangle: diameter = 2/3 of the axis
The diameter of the largest circle inscribed in a triangle is stated to be worth two-thirds of the axis (altitude) of that triangle.
Circumscribed circle triple the inscribed circle of an equilateral triangle
The circle touching the three angles of an equilateral triangle is said to be triple the circle that touches its three sides, with the note on the inscribing equilateral triangle breaking off.
Corner tally: cash, expenses, total
A small reckoning in the upper right corner sets cash at 25 against expenses of 72, summing to 97.