Geometry, calculations and machine studies
Circles with lunes and tetrahedra, columns of figures, and gears, jacks and lifting gear
A varied working sheet combining geometry, arithmetic and mechanics. The upper half carries circles divided into hatched lunes and semicircles together with several triangular (tetrahedral) frames drawn in perspective. Columns of figures at the left and centre step through squares, cubes and higher powers, while the lower half is filled with gears, screw jacks, cranes and other lifting mechanisms; a note along the central fold sets the tooth-spacing of a wheel.
On this page
Circles divided into lunes and semicircles
Near the top a large circle is split by chords into hatched crescent-shaped areas (lunes), flanked by a semicircle and further part-circles. These are studies in the areas of curved figures, of a kind associated with squaring-the-circle and lune problems. The construction lines run faintly across the sheet.
Tetrahedra drawn in perspective
At the upper right and again lower right are triangular pyramids (tetrahedra) sketched as transparent frames with internal edges shown. They read as trials of a solid figure seen from different angles. One is reinforced with darker ink.
Columns of powers and working figures
Columns of numbers run down the left and centre of the sheet, among them 25, 125, 625 and 36, 216, 1296 — successive powers of five and of six — together with further groups involving 22, 7 and 11. They are calculation columns rather than continuous prose.
Gear-tooth spacing note
A note written above a toothed wheel on the central fold specifies its pitch: every two ounces (unit-lengths), one tooth and two spaces. It fixes how the teeth are laid out around the rim.
Screw jacks, gears and lifting frames
The lower third of the sheet is crowded with mechanical trials: geared shafts, a toothed disc, screw jacks and heavy timber frames apparently for raising loads. The perspective sketches overlap one another. They accompany the sheet's more finished geometry above.