Cones from cylinders and the ballistics of bombards
Greatest cone and triangle inscribed in solids, with sections of straight and curved bombards
The upper part of the sheet is filled with geometric solids — cones, cylinders, pyramids, spheres and a woven square — that illustrate the accompanying notes: the greatest cone that can be cut from a cylinder, and the largest triangle inscribable in a rectangle. The lower half turns to artillery, comparing two bombard barrels (marked a and b), giving a cross-section of a bombard, and reasoning about how the enclosed flame drives the shot and makes the piece recoil. A final small figure of a bent tube introduces 'the curvilinear bombard'.
On this page
Greatest cone inscribed in a cylinder
Leonardo states that the greatest cone that can be drawn from a cylinder stands in a threefold relation to the whole cylinder, and that the surface of that greatest cone is double the surface of the cylinder from which it was taken. The solids drawn above the note illustrate the comparison.
Largest triangle within a rectangle
A short note on triangles set within quadrilaterals: the largest triangle that can be made inside a right-angled quadrilateral is equal to the remainder of that rectangle.
Two bombard barrels a and b
Comparing two barrels labelled a and b (10 and 20), Leonardo says the shot from a will travel little and that from b far, because the bombard recoils away from a and runs behind b.
Cross-section of a bombard: motion of the enclosed flame
In a cross-section marked a d b c he argues that a rectangular bombard would act as if rectilinear. Every simple motor that drives its projectile away runs a little behind it after separation, whereas the composite motion of the flame enclosed in the bombard pushes in every surrounding direction and follows the easiest path.
The curvilinear bombard
A small figure of a bent, curved tube is captioned as belonging to the curvilinear bombard.