By Marshall. Clagett
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Extra resources for Archimedes in the Middle Ages. I. The Arabo-Latin Tradition
His name appears on the pages o f the works of the great figures who fashioned the beginnings o f modern mechanics. For example, Galileo owed a not inconsiderable debt to Archi medes—both direct and indirect. Galileo mentions Archimedes by actual count over one hundred times1 and in almost Homeric hyperbole, using such expressions as suprahumanus Archimedes, inimitablilis Archimedes, divi nissimus Archimedes, and so on. Archimedes’ significance for these founders o f early modern science lay in the use of mathematics in the treatment of physical problems2 as well as in the originality and fertility o f his mathemat ical techniques.
For if the area of the circle is not equal to P D Fig. i it, then it will be either greater than or less than it. Flaving assumed first that it is greater, let the square A C be inscribed in the circle. Hence within the square there will be contained more than half of circle A B C D in which it is inscribed. Then we bisect arc A B at point R , and the other arcs at other points. After this, let us draw two other lines, A R and R B . Hence more than half of the [area of the] remaining segments of the circle will I !
It now seems quite unlikely that they had access to any manuscript as complete as Greek manuscript A —the basis o f most o f our modern texts o f Archimedes. The Arabic Archimedes contains the follow ing works:5 the On the Sphere and the Cylinder and at least a portion o f Eutocius’ commentary on it; (2) the Measurement of the Circle—with perhaps Eutocius’ commentary; (3) a fragment of the On Floating Bodies (consisting o f the enunciations without proofs o f seven o f the nine propositions o f the first book and the first proposition o f the second book—apparently the Arabs were not interested in the abstruse problems o f the stability of been found in any early medieval Latin ed by Heiberg.