Doubling the cube, with plans for a palace and garden aviary
Geometric constructions for cube roots on one sheet; small architectural ground-plans on the mounted strip
Two folios are mounted side by side. The larger left sheet is a dense mathematical page on the doubling of the cube: constructions that yield the cube roots of 2, 8 and 16 'by sure science' rather than by mechanical trial, together with notes on the proportion of one triangle to another and on doubling a sphere as one doubles a cube. The narrow right-hand strip carries a column of small architectural ground-plans, among them a hall flanked by porticoes, a residence for a 'grand master' beside a bridged watercourse, and a garden with a 'Long Fountain' aviary covered by a copper net and full of birds. Numerous faint marginal jottings and further untranscribed notes accompany the drawings.
On this page
Doubling the cube by geometric construction
On the line a c d - b, b a is called the cause of the cube root of two cubes, b c the cause of the cube root of 8, and b d the cube root of 16. The first of these is admirable because it doubles a cube by 'sure science,' remote from the mechanical way, and a fourth method is promised below.
A cube and a sphere each doubled
Given a cube equal to two cubes, three lines a b, b d and g e are made equal to one another, each the root of a cube equal to the two given cubes. Leonardo adds that the proportion from sphere to sphere is the same as from cube to cube of their capacity.
Proportion of triangle to triangle
The proportion that the sides of one triangle bear to the sides of another is the same that the whole triangle bears to the whole triangle. It stands as the opening theorem of the sheet.
Palace for a 'grand master' beside a bridged watercourse
In this ground-plan a is the court of the grand master, b and e are his chambers, and e is his hall, which can be left entirely open at the front. A garden and a bridge over a watercourse adjoin the building.
Garden with a 'Long Fountain' aviary
A further plan sets a building, garden and river together, labelling a meadow ('Prato') and a 'Long Fountain.' The fountain is covered with a net of copper and full of birds.