Wheel Diameter in Vitruvius

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Archimedes
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Wheel Diameter in Vitruvius

In his De architectura (10.9.1-4), Vitruvius gives the diameter of a wheel. Extant manuscripts give this diameter as pedum quaternum et sextantes, pedum quaternum et sextantis, or pedum quaternum et sextante. Is this supposed to be "four feet and a sixth (of a foot)"? Why the variation in declension?

Aetos
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Re: Wheel Diameter in Vitruvius

I'm sure there's someone out there that knows this for sure, but after a little research, I'm guessing that sextans is being used to express "linear unit". Here's Pliny's usage of it and Vitruvius' definition:
¶ 6. De aliis. Plin. 13. Hist. nat. 15. 29. (94). Tiberio principi mensam fuisse quatuor pedes sextante et sicilico excedentem, tota vero crassitudine sescunciali. ¶ 7. Mathematici sextantem appellant sextam partem numeri sex, quod est unum. Vitruv. 3. 1. ante med.
It appears that Pliny is using sextante for length, excendentem for width, and crassitudine for thickness.
It goes back to six being a perfect number, hence a perfect "unit".
The only other use of sextans that I could find was as a measurement of the area of a rectangular field (jugerum).
So the diameter of the wheel was 4 linear units (quaternum pedum et sextantes) and with one full rotation, covered a distance of 12 linear units (XII S).
This is pretty cool-I didn't know he constructed the first odometer!