On the Nature of Heat: Power Concentrated on a Smaller Base
How a pyramid's force quadruples as its base shrinks, tabulated up to 4,194,304
Headed 'On the nature of heat', the note argues that when the base of a pyramid of power is reduced, its force and heat multiply: reduce the base fourfold and the heat grows four times; reduce it to a quarter of a braccio and the power gains sixty-four degrees. Leonardo lays out the rule as a long descending table of powers of four, running 1, 4, 16, 64, 256, 1024 and on to 4,194,304. A side note states plainly that as the base diminishes the power of the pyramid increases, and reversely; the main column concludes that reducing a base of four braccia in diameter to the size of a vetch seed yields a power of 4,194,304. The sheet is filled with columns of these numbers.
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Force and heat concentrated onto a smaller base
A base of four braccia sending its power into one braccio of space multiplies its heat fourfold; reduce that base to a quarter of a braccio and the power gains sixty-four degrees. As the base diminishes the power of the pyramid grows, and as the base grows the power fails.
The quadrupling table of powers up to 4,194,304
The successive diminutions of base and increases of power are tabulated as a geometric progression multiplying by four: 1, 4, 16, 64, 256, 1024, and onward to 4,194,304. Reducing a base of four braccia in diameter to the size of a vetch seed acquires a power of 4,194,304.
