Squaring a square with curved figures; ornament and a pulley
Resolving a square into equal curvilinear parts; interlace and tile patterns; a pulley scheme and sums.
The sheet works a geometric problem repeatedly: resolving a square into equal and similar parts bounded by curved lines, each part itself squarable, with figures lettered b a, e and d c. A reflective note argues that a method is valid only if it can both divide a whole into parts and recompose that whole, and that a science which restores a figure to the form it altered has perfection. Around the geometry the page carries many decorative squares filled with interlace and scale or tile patterns, a faint large pencil study of a roofed, arcaded structure, and a small pulley scheme (16, 16 - 8, 8, 8) with the multiplication 16 x 8 = 128. Further untranscribed jottings are present at the margins.
On this page
Resolving a square into equal curved parts
A square is to be resolved into parts that are equal and similar among themselves, each bounded by curved lines. The problem is stated more than once, with the requirement that each curvilinear part be in itself squarable.
Squarable curvilinear parts b a, e, d c
A figure lettered b a, e and d c accompanies the rule that the whole square be resolved into equal, similar curvilinear-sided parts, each of which is itself squarable. A companion note on the opposite margin repeats that the surface of a square be resolved into similar curvilinear figures.
Pulley scheme and its numbers
A scheme of pulleys is marked 16, 16 - 8, 8, 8, and a small pencil calculation gives 16 multiplied by 8 as 128. The figures distribute a load across the sheaves of a block-and-tackle.
Interlace and scale-tile patterns
Several small squares are filled with decorative motifs, including interlaced knot patterns and overlapping scale or fish-scale tiling. They read as design studies for surface ornament.
Faint pencil study of a roofed structure
A large, faint pencil drawing crosses the centre of the sheet, sketching a roofed and arcaded structure. Smaller arched forms and further pencil lines appear toward the lower right.