Squaring the circle, an inheritance problem, and perspective studies

Remove the four greatest portions and the remainder equals the square

Repeated beside several crossed circles is the rule that here the four greatest portions are lacking, and the remainder equals the greatest square of the greatest circle. In one case the r S bi-angle is added as equal to the n p portions, tying the quadrature figures together.

Inheritance-and-debt word problem

A puzzle sets you as heir of Attilio while owing your father twice what you inherit from Attilio, and as heir of your father to half of that debt along with your brothers. Taking the inheritance as 4 and the debt as 8, the note works through what each heir must draw, with the figures 8, 4, 4 written out beside it.

Squares on the sides of a right triangle: 2, 4, root of 20

Three squares are built on the sides of a right triangle and labelled 2, 4 and root of 20, a Pythagorean figure in which the squares on legs 2 and 4 sum to the square on the hypotenuse, root of 20.

Constructions in the lower half of the sheet

The lower half is occupied by larger drawings, a curved ramped or vaulted structure with hatched steps at the left, a framed rectangular grid, and a triangular wireframe crossed by internal diagonals. No transcription accompanies these, so they are recorded here only from the drawing.

Facciata destra. Angolo superiore sinistro.

A destra del primo scritto, cerchio biffato:

In basso a sinistra, tre cerchi concentrici:

A destra del precedente, tre quadrati costruiti sui lati d'un triangolo rettangolo, con:

Capovolto il foglio, sul margine sinistro, cerchio biffato:

Angolo inferiore sinistro, figura con:

Verso il centro, cerchio con quattro bisangoli:

Sotto il precedente:

A destra dei precedenti, cerchio biffato con:

Sotto il precedente, figura con:

Right side. Upper left corner.

To the right of the first writing, a crossed circle:

Lower left, three concentric circles:

To the right of the preceding, three squares built on the sides of a right triangle, with:

Sheet turned upside down, on the left margin, a crossed circle:

Lower left corner, figure with:

Toward the centre, a circle with four bi-angles:

Beneath the preceding:

To the right of the preceding, a crossed circle with:

Beneath the preceding, figure with:

Squaring the circle, an inheritance problem, and perspective studies

On this page

Remove the four greatest portions and the remainder equals the square

Inheritance-and-debt word problem

Squares on the sides of a right triangle: 2, 4, root of 20

Constructions in the lower half of the sheet