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Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence .... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.
In J. Koenderink, Solid Shape, Cambridge Mass.: MIT Press, 1990.
Loci: Convergence
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Mathematical Treasures
Johann Kepler's Uralten Messekunst Archimedes
Johannes Kepler ( 1571—1630 ) was concerned that Austrian wine merchants were cheating their customers by gauging the volume of their barrels incorrectly. To correct the situation, he undertook a study of the volume of wine barrels. He published his findings, Nova Stereometria Doliorum vinarorum, in 1615. Forsaking classical techniques of volume calculation, Kepler produced solids of revolution, dissected them into an infinite number of circular laminae and obtained a volume summation. He applied this technique to consider solids other than wine barrels; in total studying the volumes of 92 different solids. Written in Latin this work was scholarly and had a limited audience. In order to increase his financial returns in 1616, he published a popular German language version of his work, Ausszag aus der Uralten Messekunst Archimedes. The page images are from the Messekunst. Page 27 contains a discussion on the volume of a torus. Page 28 returns to a consideration of the volume of wine barrels.