Inscribed Hexagon and the Squaring of Circle Portions
Hexagon side as radius and a sixth of the circumference; six squares equal to one maximum square
A dense sheet of geometry on the hexagon and the squaring of circular portions. It notes that the straight line a c equals the semidiameter of the circle and also the sixth part of its circumference, so that the side of the triangle a b c (a sixth of the circumference and half the diameter) can be used to open the compass and describe the circle a b n m. Six parallels reduced to six squares are shown to equal the maximum square a c S t, each square's side becoming the semidiameter of a circle sub-sextuple to the greatest circle, and the proportion between similar portions of two circles is likened to that between the squares raised on their sides. A faint pencil note adds that equal surfaces may be treated 'by numbers', and further small diagrams — a spiral, squares and a hemisphere at the top of the sheet — are present but untranscribed.
On this page
Hexagon side as radius and a sixth of the circumference (a c, a b c)
The line a c equals both the semidiameter of the circle and the sixth part of its circumference; the portion a b c has its straight side worth a sixth of the circumference and half the diameter, so the compass opened to a b describes the circle a b n m.
Six squares summing to the maximum square (a c S t)
Six parallels reduced to six squares are worth the maximum square a c S t, each square's side serving as the semidiameter of a circle sub-sextuple to the greatest one. The squares into which the maximum square is resolved always equal their whole, whatever their number or variety.
Equal surfaces reckoned by numbers
A faint pencil addition notes that the equal surfaces may be handled 'by numbers', extending the geometric equalities toward numerical proportion.