The impossibility of perpetual motion; jets from pipes
Four buckets cannot raise eight: a proof against accidental perpetual motion, with questions on water-jets
Folio 151r opens with the heading 'On the impossibility of perpetual accidental motion.' Leonardo analyses a bucket-wheel where 4 full buckets stand against 8: although a bucket poured onto the shorter arm weighs double by its leverage, its descent must be twice the rise it produces, so 4 buckets can never raise 8 to the same height, as his treatise's fifth proposition already denied. Any real motion here would be natural (driven by a fall of water), not the promised accidental kind. Two further water figures pose the questions of which pipe expels its water with greater force and which of four pipes throws it farthest.
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Why four buckets cannot raise eight: no perpetual motion
Four full buckets stand against eight, but the eight have eight braccia of leverage against the four. A bucket poured onto the four weighs as two of the eight through its leverage, yet its descent must be twice the height it raises. So four buckets can never raise eight to the same height; they rest in equal resistance, as the fifth proposition of the treatise shows. Any motion would be natural, driven by falling water, not accidental.
Which pipe expels its water with greater force
A figure of water-filled pipes labelled a b c d e f g asks which of these pipes will send out its waters with the greater impetus.
Which of four pipes throws its water farthest
A second water figure labelled o, m, n, a poses the question of which of these four pipes will drive its waters farthest from itself.