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
To see this, let us set out in parallel the steps of the two proofs 4. Each casts the terms of the theorem with reference to a diagram: 4 The two texts appear in parallel in App. B. The translations, here as throughout this study, are my own. I aim at a literal rendition, even where this turns out to be extremely awkward. For this will enable the reader to see the parallels in phraseology linking two texts which are in literal correspondence. SOLUTION OF THE PROBLEM OF THE WEIGHTED BEAM 8 o Fig.
This suggests that although the Excerptum itself is derived from an Arabic text, that text in its turn was drawing from Greek sources. (For an alternative explanation of binatim, see App. C, note 14). H H H 46 THE MEDIEVAL TRADITION OF MECHANICS their results easily available is one which we know Arabic editors often did undertake. In particular, al-Khazinl provides summaries of this kind for a number of works on the balance and the qarastun, as well as on the principles of weight and centers of gravity 11.
2 (b) E Fig. 2: Lemma on the beam (a) K. Qar. Beirut Appendix (b) 1. Kar. VII. 1. Kar. 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.
Ancient sources of the medieval tradition of mechanics: Greek, Arabic, and Latin studies of the balance by Wilbur Richard Knorr