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Download Archimedes in the Middle Ages. I. The Arabo-Latin Tradition by Marshall. Clagett PDF

By Marshall. Clagett

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Extra resources for Archimedes in the Middle Ages. I. The Arabo-Latin Tradition

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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.

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