The triangle as the most perfect figure; number tables
Building regular solids from triangles, with multiplication tables and jottings
Leonardo calls the triangle the most perfect figure and shows how taking it four times builds a solid whose angles are equidistant from the centre, then eight, thirty-two, and one hundred twenty-eight triangles, continuing to infinity. Extensive multiplication tables — powers of four, and columns set beside ten — fill the sheet, alongside wire-frame drawings of a cube and another solid. Lower down, a memorandum lists the names Antonio and Lionardo with figures and the word 'Pane' (bread), and a lettered note records that a b is one-sixth of the circle. The page mixes solid geometry, arithmetic, and everyday accounts.
On this page
The triangle builds the regular solids
The triangle is the most perfect figure there is: taken 4 times it makes a body whose angles are all equidistant from its centre. Taken 8 times it makes another such body, then 32, then 128, following the same rule and continuing successively to infinity.
Multiplication tables: powers of four to infinity
Beneath the text stand columns of numbers doubling and quadrupling — 4, 8, 32, 128, 512, 2048, 8192, 32768, 131072 — and a parallel column 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, each set beside 10, running on 'to infinity.'
Memorandum: Antonio, Lionardo, and bread
A short account in the middle of the page couples small figures with names — 7 Antonio, 4 Lionardo, 5 Pane (bread) — and repeats the pair Antonio and Lionardo, an everyday jotting amid the geometry.
a b is one-sixth of the circle
Beside an indeterminate geometric figure lettered b and a, Leonardo records his finding that the segment a b is one-sixth of the circle.