A catalogue of lunes: the quadrature demanded without arithmetic
Dozens of numbered lune and sector figures ranked by their fractional value
The sheet is filled with rows of tiny lune, sector and quadrant figures, each tagged with a number, a letter or a fraction-name such as 'an eighth and a half', 'a quarter and a half' or 'a sixteenth and a quarter'. A heading demands that the quadrature be demonstrated by continuous quantity, without any help from arithmetic, for the case of double diameter. Scattered notes mark individual figures ('Note', 'Double', a lune equal to its semicircle or to a portion), and one records the operation 'take m from a b; there remains p equal to b'. A concluding rule states that once two equal right-angled figures of equal sides are reduced, they may be made similar to one another since their value is the same.
On this page
Quadrature by continuous quantity, without arithmetic
The upper margin sets the programme of the whole sheet: to demonstrate the squaring by reason of continuous quantity, without any aid of arithmetic, for circles of double diameter.
A lune equal to its semicircle
Among the small figures one shows a circle within a semicircle and is annotated that the lune is equal to the semicircle. Another notes a lune equal to the portion.
Subtracting parts to leave equal remainders
A struck-through figure carries the working: take m away from a b, and there remains p equal to b, labelled b p – a – m with a note.
Reducing equal right-angled figures to one form
The bottom row, above mutilated figures, states the rule: when two equal right-angled figures with equal sides have been reduced, make them similar to one of them, since the value is one and the same.