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By Wilbur Richard Knorr

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Extra resources for Ancient sources of the medieval tradition of mechanics: Greek, Arabic, and Latin studies of the balance

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We have already seen the marked superiority in precision of L. Kar. VII and VIII over its Arabic correlate. We shall see below the same attempt at clarity and conciseness separating L. Kar. VI from its Arabic form 16. Similarly, L. Kar. II, III and V supply proofs for what is incomplete or stated without proof in the Arabic. Finally, L. Kar. provides numerical examples of most of the theorems, a device entirely absent from the Arabic. These considerations are the basis of my acceptance of Gerard's Liber Karastonis as representative of Thabit's treatise in preference to the Arabic manuscripts which bear the title Kitab al-Qarastun and the attribution to Thabit.

Qar. ) If all of line GD is straight and without mass and there is suspended over one of its sections - namely, section AE - an extended weight - namely, the weight of section AGTS - and there is also suspended from the end of its shorter section - namely, the point D weight 0 , where beam ABGD is in equilibrium in parallel-ness with the horizon... Each can now invoke the replacement theorem, the Latin version by reference to L. Kar. VI (" as we have already proved "), the Arabic to the appropriate parts of K.

Can. We shall now search for signs that Thabit took advantage of that work in composing his Kitab al-Qarastun. The last proposition of K. Qar. invites comparison with L. Can. III, in that both express the solution in the form of a computational rule . In K. Qar. VIII, the counterweight W is worked out according to a series of multiplications and divisions ; these may be compiled as a formula W = (La-Lb) X (Wa + Wb) + (La + Lb) X (La + Lb)+2Lb, where the terms denote the lengths and weights of the segments A, B of the beam, as before.

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