Squaring surface a b c d in ten staged figures
Lending and subtracting a circular portion to leave an equal square
Leonardo lays out a ten-figure procedure, drawn as a column of small diagrams down the right margin, for squaring the surface a b c d. He lends the circular portion e f g to complete the square e g h i, then squares that portion and subtracts it, so the remainder is the figure e f g h i. Through the ten numbered figures — completing the rectangle, dividing the sector, spreading and doubling triangles, then halving repeatedly — he shows that the tenth surface is a square equal to the first figure. A closing note remarks that this same demonstration is given more briefly on folio 33.
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Completing the square by lending portion e f g
To square surface a b c d one must lend the circular portion e f g, forming the square e g h i; then square that portion and subtract it from the square, leaving the figure e f g h i. The first and second right-margin figures show the rectangle first lacking, then completed with, the lent portion.
Spreading and doubling the sector triangles
The third figure holds the portion plus a lent triangle whose apex is equidistant from the opposite curvature; the fourth spreads the triangles' vertices apart; the fifth doubles the surface by lending an equal set of triangles. These stages appear as the fan and sawtooth figures in the margin column.
Halving down to a square equal to the first figure
The sixth figure holds the original with all lent parts; removing half leaves the seventh (the fourth and third combined), and removing the lent triangle leaves the ninth, equal to the circular portion, which is subtracted from the tenth. Thus the tenth surface is a square equal to the first figure, a result repeated more briefly on folio 33.