Turning a square into a rectangle of a given breadth
Narrowing square a b c d to the breadth e c and finding its new length (prop. 7)
This page closes one construction and opens a new proposition (7). The top text finishes forming the rectangle c o f m by a semicircle n b m drawn on centre d, cutting the breadth at n. The main proposition, "From a square to a rectangle," narrows the square a b c d to a given breadth e c and finds the length to which it stretches, using the fourth proposition and a semicircle f a n. A small semicircle construction with lettered points is drawn at the lower right.
On this page
Completing rectangle c o f m by a semicircle on centre d
Using the third proposition, the midpoint between a and m is taken on the line n m, the compass is opened to the space a d, and the semicircle n b m is drawn on centre d. Where the circle meets the indefinite line m g at n, the breadth of the long rectangle is cut off at n c and transferred to c o to form the rectangle c o f m.
From square a b c d to a rectangle of breadth e c
The square a b c d is narrowed into the given breadth e c, and the length to which it then stretches is sought. Leonardo sets the breadth e c on c f, draws the indefinite line f n, and by the fourth proposition sets a d equal to f d, opening the compass to a d to draw the semicircle f a n; where it cuts at n ends the length of the rectangle.
