Quadrature studies and the plan of the Stable of the Magnifico

Ground plan of the Stable of the Magnifico

Two planimetries describe the Stable of the Magnifico as 110 braccia long and 40 braccia wide. It is divided into 4 rows of horses, each row split into 32 spaces called intercolumns, every intercolumn holding two horses separated by a bar, so the stable can hold one hundred and twenty-eight horses.

Euclid: circle is to circle as square is to square

Two squares double one to the other stand with their centres on the centre of one circle, which touches the angles of the lesser square and the sides of the greater. The circles are double in proportion, one touching the angles and the other the sides of the same square, and from this Euclid said the proportion from circle to circle is as that from square to square built on the diameters.

The four maxima and the greatest square

Across many figures Leonardo repeats that where the four maxima are missing the remainder is worth the greatest square of the greatest circle. Biangles are shown worth the four maxima, and a labelled circle abcdfegn is declared worth the greatest square of the greatest circle.

Equal figures: remove equals, leave equals

Because the first and second figures are one same value, Leonardo removes equal parts from each: taking the four portions bcde from the first and hg from the second leaves the curvilinear aLm of the first equal to the square rectilinear nmpq of the second. A parallel figure fills the voids fg with ab so the reintegrated second figure stays square and equal to the first.

Prima colonna a destra

Planimetria:

Altra planimetria:

Figura con due cerchi e due quadrati:

Seconda colonna, figura biffata:

Cerchio colle lettere:

Due figure unite alla precedente con tratto di penna:

Più in basso:

Sotto la precedente, figura con:

Sul margine inferiore, cerchio con otto divisioni:

A sinistra della precedente:

Terza colonna. Due figure biffate

Sotto due figure biffate, altre due figure3) con:

Figura con:

Cerchio con:

Sotto la precedente:

Ultima colonna, due figure con

Due figure con:

Semicerchio con:

Cerchio con:

First column on the right

Ground plan:

Another ground plan:

Figure with two circles and two squares:

Second column, cancelled figure:

Circle with letters:

Two figures joined to the preceding by a pen-stroke:

Further down:

Below the preceding, figure with:

On the lower margin, circle with eight divisions:

To the left of the preceding:

Third column. Two cancelled figures

Below two cancelled figures, two other figures with:

Figure with:

Circle with:

Below the preceding:

Last column, two figures with

Two figures with:

Semicircle with:

Circle with:

On this page

Ground plan of the Stable of the Magnifico

Euclid: circle is to circle as square is to square

The four maxima and the greatest square

Equal figures: remove equals, leave equals