Flame, Rising Air and the Geometry of Narrowing Triangles
Convection around a flame likened to water in cisterns, with triangle proportions
The verso couples a study of fire and air with a study of triangles. Leonardo argues that air entering a furnace from below rises rather than falls, that the flame heats and thins the air clothing it until that air, weakened, sinks back to feed the flame, so the air stays in continual revolution and issues as smoke. He likens this to water in cisterns, where a conduit driven by the weight above raises water into the air. The lower diagrams treat triangles whose sides narrow toward the apex, one inverted figure losing three-quarters of its width, with equidistant motions yielding equal gains and losses.
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Air rises in a furnace and circulates around the flame (a c b)
Air entering a furnace from below rises rather than falls. The flame heats and thins the surrounding air, which then resists the cold air above it less, so it sinks back into the consuming flame; thus the air is in continual revolution and finally issues as smoke.
Cistern and jet: water raised by the weight pressing above
Leonardo compares the circulating air to water-cisterns from which a conduit descends and, at its far end, raises the water up into the air, driven by the weight that presses down upon it from above. A vent is given to the flame so it may rise and make smoke.
Inverted triangle loses three-quarters of its width (b a p o r)
In the inverted triangle, a b coming to o p loses three-quarters of its width; while r p, moving away just as much in the opposite direction, rises to a b and in the same distance gains three-quarters of its size.
Equidistant motions give equal gains and losses (o b a f d e c m)
If the line a b descends to e d it loses three-quarters of its quantity, and if it rises from c d to f b it gains three-quarters; being equidistant, such motions make equal gains and equal losses.