By Wilbur Richard Knorr
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Additional info for Ancient sources of the medieval tradition of mechanics: Greek, Arabic, and Latin studies of the balance
Kar. VII, a theorem missing from the Arabie; so also Exc. (4) agrees with V, even to the detail of considering specifically four equally distributed weights, while the comparable result does not have the status of a theorem in the Arabic. In Exc. (7) the notion of uirtus (" force ") is presented in the image of walkers traversing certain distances in given times; the same example appears in the Latin 1. Kar. I but is missing from the Arabie. Further, in the Excerptum two properties are stated of the beam which has been rotated out of equilibrium position: (8) that its endpoints trace out similar arcs and (9) that these arcs are proportional to the diameters (or rays) which have generated them.
M, n, And as each weight has resulted from an outward shift of the original part corresponding to it , each will now counterbalance a greater part of the weight R than it had at first. We now add another weight equal to each of these weights and suspended from e. By an earlier lemma (L. Qar. IV) , we may now combine all these weights and suspend them from j the midpoint of en without altering the state of balance or imbalance. Thus, these weights in sum overbalance the counterweight R suspended from the other end of the balance.
Kar. VII, 1. 408). Now, related expressions in Greek are not unknown (d. 0 't'~c:; Emcpcxvdcxc:; 1tpoc:; TIjv EmcpcXve:LcxV Myoc:; EO''t'LV 0 't'OU XOXAOU 1tpoc:; 't'OV XOXAOV, Archimedes, I, p. 216, 10; d . 216 . 21; II, 166, 12; III, 72, 27), but neither are they usual. How, then, does this seeming Arabicism affect our view, based on the extensive evidence of Greek-based usage, that L. Can. was translated from a Greek original? If we associate the author of the Latin L. Can. with the school of literal translators, typified by the Optics-translator, then we might be compelled to presume a Greek text which employed an idiosyncratic terminology of proportion.