Geometry.

f - g a - h o L - p r

Let the fifth part of a circle be given with a single opening of the compasses, because — fifth — 'Such proportion holds from circumference to circumference as holds from diameter to diameter of the same circles.' And if you wish to divide the circumference of a given circle into five equal parts, divide its quarter part into five. Thus, if the said circle was first divided into sixteen, it had four partitions for each of those four parts; then, this circumference being divided into twenty, each of those parts remains divided into five other parts. Now, to return to the demonstration of this practice, I say that I shall take the diameter of the given circle, which is p r, and set it five times along the line h L; and so I shall have 2 diameters, p r and h L, in fifth proportion one to the other, and the 2 circles will do the same; and the like will be found in their quarters a p and f h. And from this it follows that, with the same opening of the compasses with which the smaller circle was made, you divide the greater circle's quarter part into five other equal parts, of which four parts are the fifth part of the greater circle. And if all such parts are drawn with straight lines to the centre of their circle, they will cut the smaller circle into five other parts equal among themselves. But so as not to have to open the compasses to make the greater circle, place the ruler upon the centre of the circle and draw the line o h divided by the given compass-opening, then draw the other line and divide it by the same opening; and you will do the like to all the other similar lines, and so the line f g h will be produced for you, and so on.

And if you wish to divide the periphery of a circle into three equal parts, divide its half into three, which will be six parts in the whole, of which the two parts are a third of the whole. And if you wish to divide it into seven, divide its third into 7, and you will have 21/7, of which 3/7 are the seventh part of that whole circumference. And so always keep as a rule to divide each partition of a circle into one more than all the partitions of that circle number; and that 'one' is what does as was seen in dividing the half of a circle into 3, which made 6 in the whole circle, of which the third, being 2, was the third of that circle.