Dividing the circle, a geared mechanism, a lamp and a violet
Compass constructions splitting a circle into 9, 6 and 18 parts, with a water-driven gear train and a bright glass lamp
The page mixes geometry, mechanism and nature. Its main text explains how to divide a circle into 9, 6 and 18 equal parts without moving the compasses, with a supporting list of ratios and a diagram whose one line is marked 'false' because it is not a third of the pyramid's height. In the margins are a mechanism of toothed wheels that can be turned by water or by living motion, and a lamp made from a cut glass ball that gives a great light. A finely drawn stem of violet with flower and leaves occupies the centre; a small star within an octagon sits at the top.
On this page
Dividing a circle into 9, 6 and 18 parts
With the diameter c d fixed, arcs struck from d, c, i and h build lines e f and e g so that the space a b is a ninth of the circle, a r an eighth and f g a sixth. The reasoning turns on the half-diameter fitting six times into the circle, so the diameter divided into three parts yields the ninth. The line n m is flagged 'false' for not being a third of the pyramid's height.
Toothed-wheel mechanism turned by water
A cluster of geared wheels mounted on a round table is drawn at the upper left. The note says part a can be turned by water or by living motion, and that it is good for the s p c.
Lamp from a cut glass ball
A standing lamp holds a glass sphere. The note directs cutting the glass ball below and above and fitting back a vessel with the light in the middle, so that it gives a great light.
Stem of a violet with flower and leaves
A drooping stem of violet with its flower and leaves is drawn at the centre of the sheet, a naturalistic plant study set among the geometric and mechanical notes.