“A bird makes the same use of wings and tail in the air as a swimmer does of his arms and legs in the water.”

The Notebooks of Leonardo Da Vinci (1938), XVII Flight

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Leonardo Da Vinci 363
Italian Renaissance polymath 1452–1519

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His collected works contain no riddle about dog legs, but George W. Julian recounts Lincoln using a similar story about a calf in Reminiscences of Abraham Lincoln by distinguished men of his time (1909), p. 241: "There are strong reasons for saying that he doubted his right to emancipate under the war power, and he doubtless meant what he said when he compared an Executive order to that effect to 'the Pope’s Bull against the comet.' In discussing the question, he used to liken the case to that of the boy who, when asked how many legs his calf would have if he called its tail a leg, replied, 'Five,' to which the prompt response was made that calling the tail a leg would not make it a leg."
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The Notebooks of Leonardo Da Vinci (1938), XVII Flight

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