By O. Neugebauer
One of many most effective staff within the quarter of premodern technology offers the normal nontechnical insurance of Egyptian and Babylonian arithmetic and astronomy and their transmission into the Hellenistic international, including the particularly fascinating, remarkable sophistication of Babylonian arithmetic. fifty two figures.
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Additional info for The Exact Sciences in Antiquity
We call such fractions Usexagesimal fractions" and write numbers of this type in the following form: 0,31,25 1,2,50 1,34,15 2,5,40 We can say that these numbers show a constant difference 0,31,25. Later in our table the differences become smaller and smaller, but this is exactly what one should expect. If the first column indicates arcs increasing by i degree, as is indicated by the numbers already known, then we must expect that the chords do not grow simply proportionately with the arcs, though this might hold for very small angles at the beginning of the table.
W. E. van Wijk, Le nombre d'or. :Etude de chronologie technique suivie du texte de la Massa Compoti d'A1exandre de Villedieu. La Haye, Nijhoft', 1936. This work contains a valuable introduction to the medieval cyclic calendars in Europe. Cf. also Nils Lithberg, Computus, Stockholm 1953 (Swedish) = Nordiska Muscets Handlingar 29; very complete bibliography. ad 7. Jean-Gabriel Lemoine, Les anciens procedes de calcul sur les doigts en orient et en occident. Revue des etudes islamiques 6 (1932) p. 1-58 [with extensive critical bibliography].
Where we (and Ptolemy) would write for the integers 129, 259, and 28 respectively. The perfection to which Islamic scholars developed numerical methods has only recently become clear, especially through the work of P. Luckey on aI-Kishi, the astronomer royal of Ulugh Beg in Samarqand. AI-Kishi died in 1429; one of his last works is a treatise on the circumference of the circle in which he determines (correctly) 2n as 6;16,59,28,1,34,51,46,15,50. 2831853071795865. BIBLIOGRAPHY TO CHAPTER I The best existing book on numbers and number systems is Karl Menninger, Zahlwort und ZifTer.
The Exact Sciences in Antiquity by O. Neugebauer