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From the Introductory. EUCLID, famed founder of the Alexandrian School of Mathematics, was the author of not less than nine works. Approximately complete texts, all carefully edited, of four of these, (1) the Elements, (2) the Data, (3) the Optics, (4) the Phenomena, are now our possession. In the case of (5) the Pseudaria, (6) the Surface-Loci, (7) the Conics, our fragmentary knowledge, derived wholly from Greek sources, makes conjecture as to their content of the vaguest nature. On (8) the Porisms, Pappus gives extended comment. As to (9), the book On Divisions (of figures), Proclus alone among Greeks makes explanatory reference. But in an Arabian MS., translated by Woepcke into French over sixty years ago, we have not only the enunciations of all of the propositions but also the proofs of four of them. Whilst elaborate restorations of the Porisms by Simson and Chasles have been published, no previous attempt has been made (the pamphlet of Ofterdinger is not forgotten) to restore the proofs of the book On Divisions (of figures) . And, except for a short sketch in Heath's monumental edition of Euclid's Elements, nothing but passing mention of Euclid's book On Divisions has appeared in English. In this little volume I have attempted: (1) to give, with necessary commentary, a restoration of Euclid's work based on the Woepcke text and on a thirteenth century geometry of Leonardo Pisano. (2) to take due account of the various questions which arise in connection with (a) certain MSS. of Muhammed Bagdedinus, (b) the Dee-Commandinus book on divisions of figures. (3) to indicate the writers prior to 1500 who have dealt with propositions of Euclid's work. (4) to make a selection from the very extensive bibliography of the subject during the past 400 years....

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9781976543371

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