Squaring the oval: a circle equal to an oval figure
Enclosing oval a b c d in a rectangle to build an equal circle a f e c
A geometry page in which Leonardo shows how to square the oval, drawing a large oval inscribed in a rectangle at the top and small squares and ovals in the margin. By the same rule used to square the sphere and the circle, he argues, one can square an oval body and an oval surface. He encloses the oval a b c d between parallel lines g h i K, erects the square L m g h on g h, and inscribes in it the circle a f e c, which he claims is exactly equal in capacity to the oval; a further note treats stretching a surface g h a c to a given length.
On this page
Squaring the oval as sphere and circle are squared
Leonardo states that by the same rule with which the sphere and the circle are squared, one can also square the oval body and the oval surface. He says this is done in the manner figured beside the text.
An oval as the circle's counterpart in an oblong
An oval figure, he explains, is one that does the office of the circle. Just as the circle touches the middle of the four sides of the square in which it is included, so the oval figure is made within its long rectangle.
A circle a f e c equal in capacity to oval a b c d
To square the oval figure a b c d, Leonardo encloses it between parallel lines on four sides, g h i K. He then builds the square L m g h on the line g h and describes in it the circle a f e c. This circle, he claims, is of capacity precisely equal to the proposed oval, and the same holds for oval bodies.
Stretching the surface g h a c to a given length f
Given the surface g h a c of unknown quantity, Leonardo wants to lengthen it to a given term f without knowing how much width to give it. If it lengthens from c to f it becomes of the thickness b e, the piece a b c being set upon d e f; conversely, to lower it to a given height he tells the reader to turn the page and read.