By George Sarton
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Extra resources for Ancient Science and Modern Civilization
The table of chords is followed by a geometrical argument leading to the calculation of the relations of arcs of the equator, ecliptic, horizon and meridian, and tables ad hoc. The same kind of discussion is continued in Book to the length of the longest Book III deals day II with reference at a given latitude. ) Book IV. Length of the . month and theory of the Moon. This contained what is supposed to be one of his discoveries (as distinguished from those of Hipparchos), the second inequality of the it at Moon called evection.
Table to = = 45 ANCIENT SCIENCE AND MODERN CIVILIZATION theorem about quadrilaterals inscribed in a circle; that theorem enabled one to find the chord of a sum of angles. Opposite the value of each chord in the table is given 1/30 of the excess of that chord over the preceding one; this 1/30 is to Ptolemy's expressed in minutes, seconds and thirds; this would enable one to compute the chords for every minute of angle. Ptolemy understood the meaning of interpolations and approximations; his correct appreciation of them was one of the bases of applied mathematics.
25 However, the Latin climate was not so favorable The Arabic Abu 'Uthman was edited and Englished by Wilwith mathematical introduction by Gustav Junge (Harvard text of liam Thomson, Semitic Series 8, Cambridge, 1930; 26 to Isis 16, 132-36). The story is simplified for the sake of brevity; for details, see Marshall Clagett, "The medieval Latin translations from the Arabic of the Elements 34 EUCLID AND HIS TIME geometrical research in the twelfth century as the Arabic mate had proved to be from the ninth century on.