Square Numbers and Continued Proportion
Squares split by their diagonals paired with the square numbers 4→16, 5→25, and a continued proportion
Several small squares are sketched at the inner margin, each divided by a diagonal and lettered (diagonal e, side f; g, h; K), and set beside columns of numbers. The notes pair roots with their squares — 4 and 5 give 16 and 25, 3 and 4 give 9 and 16 — labelled "squares" and marked odd or even. A final group headed "continued proportion" runs p, 2, m, 4 ("square"), K, 8, tying the numerical squares to the drawn geometric ones.
On this page
Roots paired with their squares (4→16, 5→25)
Beside a square lettered with diagonal e and side f, the figures 4 and 5 are set against 16 and 25, with a further label K and 32, pairing each number with its square.
Odd squares: 9 and 16
A second square, its diagonal halved (2) and a side marked 4, carries the pair 3 and 4 against 9 and 16, tagged "odd" and "squares".
A continued proportion p, m, K
The lowest group, headed "continued proportion", runs p, 2, m, 4 (labelled "square"), and K, 8, drawn against two adjacent squares with a smaller square superposed on a half-diagonal.
Squares divided by their diagonals
At the inner margin each numerical pair is illustrated by a small square cut by its diagonal, one of them with a smaller square set on a half of the diagonal, giving a geometric picture of the squaring operation.