By Wilbur Richard Knorr
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Additional resources for Ancient sources of the medieval tradition of mechanics: Greek, Arabic, and Latin studies of the balance
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.
VII: For the sake of example, let the line AB be divided into two different sections at point G, and let it be suspended from point G, and let there be set at point A the weight E suspended from it and in the part of the line Be (let there be) fixed a weight, plane, of equal continuity, in the manner of the beams of trutinae 5. And let that portion be RBQD and let it counterbalance weight E in the (downward) attraction of the beam, and let the length of the portion having mass be divided into halves at point U.
Prop QB LK Description and comments Pro Prologue on background and aims; missing from Arabic I E E X Postulate: forces are proportional to spaces traversed in equal times II E P E P X Sectors generated via rotation are similar; arcs are proportional to generating lines Cor Forces of motion are proportional to generating lines E P X Principle of equilibrium in massless beams; enunciation missing from Arabic; Latin amplifies proof via consideration of forces Scholium : (a) short remark on weightless vs.