Euclid's Book on Divisions of Figures by Raymond Clare Archibald

By Raymond Clare Archibald

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Kastner, Gottingen, 1793. 68 J. A. Editio nova. Volumen quartum, Hamburgi, MDCCLXXXV, p. 81. 09 J. C. Lipsiae, MDCCXLII, p. 438, 163-4. 70 J. F. 6d. nouv. Tome 1, An v n , p. 216. 71 H . H A N K E L , Zur Geschichte der Math, in Alterthum u. Mittelalter, Leipzig, 1874, p. 234. 72 J. A. G R U N E R T , Math. von G. S. Kliigel, fortgesetzt von C. B. Mollweide und beendigt von J. A. , fiinfter Theil, erster Band, Leipzig, 1831, p. 76. 73 74 (Abh. F A V A R O , pp. 141-144. H. SUTER, " D i e Mathematiker und Astronomen der Araber und ihre W e r k e " z.

Join zh. Through i draw ik parallel to hz, and meeting ab in k. ]. ~] PROPOSITION 9. 30. " [Leonardo 30, 3197, p. 133, 11. ] I shall interpret "longer side" as in Proposition 8, and lead up to the consideration of any given point on bg after discussing the cases of points on the shorter side ad. ) Suppose it be required to divide the trapezium in the ratio ez: zi98. Divide ad, bg in the points /, k, respectively, such that at: td= ez : zi = bk : kg. g. ' number ez : number zi, not ez : zi. Euclidean MSS.

X. Heft, Leipzig, 1900), p. 202, No. 517. 19] ARABIAN WRITERS ON DIVISIONS OF FIGURES 25 of the Dee book On Divisions was Muh. b. Muh. el-Bagdadi who wrote at Cairo a table of sines for every minute. A little later75, however, Suter discovered facts which led him to believe that the true author was Abu Muhammed b. 'Abdelbaqi el-Bagdadi (d. 1141 at the age of over 70 years) to whom an excellent commentary on Book x of the Elements has been ascribed. Of a MS. by this author Gherard of Cremona (1114-1187) may well have been a translator.

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