Truncated pyramids and wedges: volumes and weights
Letter-labelled solids valued in parts, balance figures, and a column reducing the whole to twelfths of an ounce
The left half of the sheet studies the geometry of a truncated pyramid and related solids whose lettered parts are assigned numerical values (e worth 6, others worth 3 or 2), and it states that a wedge (bisconio) equals one-third of its pyramid. Small balance figures pair the parts as weights, one balancing 12 against 12 and another setting 1-1-6 against 1-1-12. The right half carries long arithmetic columns that reduce the total to twelfths of an ounce and to a single sum labelled 'the whole'. A closing note tallies eight pyramids, one cylinder and four wedges, playfully likening the wedge shapes to men's little boots.
On this page
Frustum of a pyramid divided into valued parts
The lettered frustum a b c - d e f - g has its parts weighted: e is worth 6, while b, d, h, f are worth 3 each and a, c, g, i are worth 2 each. A companion figure adds that, by the same reasoning, h is worth 2 so that L remains one.
A wedge equals one-third of its pyramid
The figure lettered b e - a d - f e states that the wedge (bisconio) abcf is worth one-third of the pyramid a b d e c. It ties the smaller solid directly to the pyramid from which it is cut.
Balance figures weighing the parts
Two small scales set the solids against one another as weights: one balances 12 against 12, and the other pairs 1-1-6 against 1-1-12. The figures treat the measured volumes as quantities to be brought into equilibrium.
Reducing the whole to twelfths of an ounce
The right half works long multiplication columns (288, 2880, 576, 10736, 42944, up to 1545984) and labels intermediate results 'a twelfth of an ounce' and 'the whole', converting the measured solids into a single numerical total.
Eight pyramids, a cylinder and four wedges
A concluding note counts the solids on the sheet: eight pyramids, one cylinder and four wedges, the wedge forms fancifully called 'men's little boots'.