Squaring of figures and transformation of quadrilaterals

Curvilinear triangles equal to circles and squares

The curvilinear triangles a b and d are worth the circles c f and also half the greatest circle. Removing the a d portions and the four greatest portions of each circle leaves two squares equal to the b and the triangles.

Stretching a quadrilateral and restoring it

Let a be the given quadrilateral and b the length to which it is to be extended; adding b to the lower side and drawing the touching line h n makes a surface S equal to a, since n d multiplied by g h equals L p multiplied by r K. The elongated parallelogram then shortens back into the original square without any change of quantity.

Squares on the sides of a right triangle

The right-angled triangle a is worth each of the other triangles, and the square f g h i is worth the other two squares d b c e together. The figure sets out the equality of the square on the hypotenuse with those on the legs of an isosceles right triangle.

Right angles inscribed in a semicircle

The sides of the right angles made in a semicircle are always of equal value in the squares created by their multiplications. Four right angles are drawn within the semicircle to demonstrate the relation.

Dated heading: Amboise, 24 June 1518

On the 24th of June, the day of St John, 1518, at Amboise in the palace of Cloux. Leonardo then states his plan to extend the given quadrilaterals according to their lengths and give the due reductions of their widths.

Marginal plan: Rooms of the lions of Florence

A small building plan near the margin is labelled Rooms of the lions of Florence. It stands apart from the surrounding geometry as a jotted architectural note.

Facciata destra. Figura di due cerchi in un cerchio, con:

Figura di due cerchi in un rettangolo, con:

Figura sottostante, con:

Figura: Terza.

Figura sottostante:

Figura analoga:

Presso la piega mediana, figura con:

Presso il margine, pianta d'edificio:

Sul margine inferiore, due quadrati divisi in quadratini, con:

Facciata sinistra.

Due figure di rettangolo e segmento rettilineo, con:

Tre figure con:

Doppia figura con:

Sotto la terza figura:

Quadrati costruiti sui lati di un triangolo rettangolo isoscele e suddivisi in triangoli eguali, con:

Quattro ortogonii in un semicerchio:

Lungo il margine inferiore, figura di parallelo grammo:

A sinistra della figura:

Right-hand face. Figure of two circles within a circle, with:

Figure of two circles in a rectangle, with:

Figure below, with:

Figure: Third.

Figure below:

Analogous figure:

Near the middle fold, a figure with:

Near the margin, plan of a building:

In the lower margin, two squares divided into little squares, with:

Left-hand face.

Two figures of a rectangle and a straight segment, with:

Three figures with:

Double figure with:

Beneath the third figure:

Squares built on the sides of an isosceles right triangle and subdivided into equal triangles, with:

Four right angles in a semicircle:

Along the lower margin, figure of a parallelogram:

To the left of the figure: