a — n m — b

ab is equal.

1000 braccia — 1,000,000 braccia.

Thousand — Million.
The proportion of these two squares is millions to the … it follows that the …

1 100
1 10000
That proportion, from circle to circle, is as from square to square made of their diameters. If one circle is a thousand and another circle is a million, a thousandth of the greater circle equals the lesser circle. Make then a pyramid of the length of the semidiameter of that greater circle, whose base is such a quantity that the base multiplied by half its length gives five hundred thousand of quantity, and you will have the quadrature of the lesser circle, plus one imperceptible trifle, of which, by the rule of Archimedes, you will have fewer than 999 of such trifles, which you can then make of a size near to the mathematical point. Therefore do not remove the portion from the circle, but remove it only from the pyramid, and you will say that the circle is the quantity of that pyramid, plus the portion that was removed from that pyramid.

24

b d c a

If from equal things equal parts are removed, the remainders will be equal. It follows that, the circle a being equal to the sector b, and removing the portion d from both, the triangle b is equal to the circle a.
Make of the triangle b its square, and see what proportion one of its sides has with the diameter of the circle to which that square was made equal; then look at what proportion that diameter has with the circumference of that circle, and make a rule of it.

The sides of a figure having 96 equal sides are to the diameter as 3 and 1/7 to one, or a little more.

a a — b b —

c c — d d

a equal.
b equal.
c equal.
d equal.

If you wish to work with arc and chord, that is to square every portion of a circle, you must see, of that portion, what part its curve is of the periphery of that circle (Figure of a portion), and then complete the sector of the circle to that portion (Figure of a sector), and detach that portion from the said sector. But first detach from the quadrature of the circle that part of it which is the sector of the whole circle, and place it under the sector (Figure of a sector). Then detach the portion from the sector, and there remains a rectilinear triangle, which you will take from the square f (Figure of a rectangle with f); and the remainder of that f will be equal to that portion. And here arithmetic is of no use.

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