Squaring lunes and dividing semicircles, with flight notes

Dividing the semicircle and the lune into equal parts

A semicircle lettered a b c d is divided into four parts equal in quantity, of which two are alike; by the same rule the crescent 'lune' (falcata) is divided into three equal parts. Neighbouring figures subdivide the lune further into one, 2, 4 and 8 parts.

Three semicircles in the proportion 1 : 2 : 4

A large diagram sets three semicircles in the ratio 1:2:4, lettered b, d, n, e, f, h, K, m, c, L, a. Leonardo argues that a lune equals a sector and both equal the same semicircle, so that things equal to a third are equal to one another.

A prognostic on halving circles to infinity

From small figures of semicircles set upon sectors he draws the 'manifest prognostic' that a semicircle equals an eighth of a circle, and that a sixteenth of the greater circle equals a quarter of the smaller, continuing so to infinity.

The descent of a bird and the direction of the winds

Two small bird sketches accompany a note that the bird's descent shifts from right to left, passing from above the north wind (tramontano) toward the northwest (maestro), and entering below the wind toward the northeast (greco). A further note observes that between mountains and clouds the winds are eddying and changeable.

A body's motion and equal opposing powers

The motion of every moving body follows the direction of its greater length, and if one descends with a power of 10 against a power of 10 the moving body remains motionless.

Why the bell-tower sways when its bells are rung

Beside a small circular tower Leonardo writes a reminder to himself: to explain why the campanile sways when its bells are rung.

Colonna destra, lungo il margine. Cerchio entro semicerchio, con :

Doppio semicerchio, con:

Semicerchio diviso con:

Due settori di cerchio, con:

Due figure collegate, con:

Triplo semicerchio biffato, con:

A sinistra delle tre precedenti, quattro figure con:

Semicerchio con:

Quattro semicerchi concentrici, con:

Cerchio diviso in falcate, con:

Sul margine destro e inferiore, semicerchio diviso, con:

Grande figura di tre semicerchi nella proporzione 1 :

Entro la predetta figura, due piccoli disegni d'uccello:

Sul margine inferiore.

Colonna sinistra.

Rjferito alla grande figura dei tre semicerchi:

Piccole figure di semicerchi sovrapposti a settori o settori a settori, con:

Margine sinistro, torre circolare:

Right column, along the margin. Circle within a semicircle, with:

Double semicircle, with:

Semicircle divided, with:

Two circular sectors, with:

Two connected figures, with:

Triple crossed-out semicircle, with:

To the left of the three preceding, four figures with:

Semicircle with:

Four concentric semicircles, with:

Circle divided into lunes, with:

On the right and lower margin, a divided semicircle, with:

Large figure of three semicircles in the proportion 1 :

Within the aforesaid figure, two small drawings of a bird:

On the lower margin.

Left column.

Referring to the large figure of the three semicircles:

Small figures of semicircles set on sectors, or sectors on sectors, with:

Left margin, circular tower: