Dividing Circles Between Parallel Lines

A fourth or third part of a circle between parallels

A numbered series of figures poses the problem: 'Give me the fourth part of the first circle between two parallel lines,' and 'Give me the fourth part of a half circle between two parallel lines.' To the right, in a b c d, Leonardo delivers the third part of a semicircle between two parallels, claiming he can give infinitely whatever part is asked.

Six sectors of a semicircle made equal

The six portions of the six sectors of the semicircle are said to equal the portion of the larger sector; gathered into one, they fill the concavity n, and the outer part is left straight-sided and equal to c.

Euclidean common notion

A marginal note states the axiom: if from equal things you take equal things, and so on. It underwrites the equalities Leonardo claims when he removes matching portions from paired curved figures, as in the last figure where taking the portion o from each leaves the remainders equal.

Spoked wheel and small devices

The large browned fragment carries several small mechanical sketches, among them a spoked wheel and a compact framed device. These are drawn but not covered by the transcribed captions.

Balance-beam frames

Both the left fragment and the large fragment show slender balance-beam or steelyard frames pivoting on a support. They appear as physical apparatus alongside the geometric figures and are not transcribed.

a)

b)

Parte di un settore di cerchio colla lettera:

Settore di cerchio su un semicerchio con:

c)

In alto a sinistra, figura:

Figura:

Figura:

Seguendo il tratto di penna, figura

A destra, figura con:

A sinistra:

Figura colle lettere:

a)

b)

Part of a circle sector with the letter:

A circle sector on a semicircle with:

c)

Top left, figure:

Figure:

Figure:

Following the pen-stroke, a figure:

On the right, figure with:

On the left:

Figure with letters: