Counterweight demonstrations, cubes, and artillery bores
Balance fractions worked to unity, doubling the cube, gun bores, and after-images of the sun
A continuation of the balance calculations from the facing leaf: two worked examples reduce the counterweight problem to fractions (8/64 back to 1, and 2/2 to 1) beside small balance schemas. A strip at upper right treats the geometry of cubes, seeking a length d that stands to b as the cube's diameter c stands to a. Other notes describe three shapes of artillery bore and the three positions for igniting the charge, and a final line records the coloured after-images left in the eye by staring at the sun.
On this page
Counterweight worked to unity on the balance
For an arm a b eight times the length of b c, the weight 8 at c multiplied gives 64, then 8 divided by 64 and multiplied back by 8 returns one whole at a. A second example with arm ratio 2 to 1 likewise reduces the balancing weight to one whole placed at a.
Doubling the cube by proportion
Four sectioned cubes are compared: a has c as the diameter of its cube, while b has d, which is not the diameter but must be constructed so that d is to b as c is to a.
Bore shapes and where to ignite the powder
There are three kinds of gun bore — wide at the bottom and narrow at the mouth, the reverse, or of uniform width — and three positions for firing the charge: at the bottom, at the front, or somewhat away from the bottom. Front ignition at the centre of the powder, closing below where the piece rests in recoil, is judged best, and Leonardo calls for tests with varied powder.
After-images of the sun
A closing note describes how an eye that has quickly and repeatedly looked at the body of the sun sees a dark place strewn with luminous spots and a luminous place strewn with dark round spots.