By Roshdi Rashed
Mit dem funften Buch der Kegelschnitte erreicht die antike Mathematik einen Hohepunkt. Apollonius fuhrt darin die erste bekannte Theorie der Maxima- und Minima-Linien aus, die von den Mathematikern zu Beginn des 10. und vor allem des 17. Jahrhunderts wieder aufgegriffen wurde. Ebenso wie die folgenden beiden Bucher VI und VII ist dieses Buch, dessen griechische Original-Fassung verloren ist, nur in der arabischen Ubersetzung erhalten, die im nine. Jahrhundert in Bagdad erstellt wurde.
Der Leser findet in diesem Band eine im wahrsten Wortsinn kritische variation des funften Buches der Kegelschnitte von Apollonius, eine strenge und wortgetreue Ubersetzung, sowie eine so vielseitige und ausfuhrliche historische und mathematische Kommentierung, wie sie die Erschlieung eines solch gewichtigen Zeugnisses erfordert.
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Extra resources for Apollonius de Perge: Coniques, Tome 3: Livre V. Commentaire historique et mathématique, édition et traduction du texte arabe
B (= Codex Parisinus 2360, olim Mediceus). C (= Codex Parisinus 2361, Fonteblandensis). Of these it is certain that B was copied from the Yalla MS. This is proved by a note on the copy itself, which states that the archetype formerly belonged to George Valla and afterwards to Albertus Pius. From this it may also be inferred that B was written before the death of Albertus in 1531; for, if at the date of B the Valla MS. had passed to Rodolphus Pius, the name of the latter would presumably have been mentioned.
At the latest. d. only three were generally known, viz. On the Sphere and Cylinder, the Measurement of a circle, and On the equilibrium of planes. Thus Eutocius of Ascalon who wrote commentaries on these works only knew the Quadrature of the Parabola by name and had never seen it nor the book On Spirals. Where passages might have been elucidated by references to the former book, Eutocius gives explanations derived from Apollonius and other sources, and he speaks vaguely of the discovery of a straight line equal to the circumference of a given circle “by means of certain spirals,” whereas, if he had known the treatise On Spirals, he would have quoted Prop.
Archimedes wrote in the Doric dialect*, but in the best known books (On the Sphere and Cylinder and the Measurement of a circle) practically all traces of that dialect have disappeared, while a partial loss of Doric forms has taken place in other books, of which however the Sand-reckoner has suffered least. Moreover in all the books, except the Sand-reckoner, alterations and additions were first of all made by an interpolator who was acquainted with the Doric dialect, and then, at a date subsequent to that of Eutocius, the book On the Sphere and Cylinder and the Measurement of a circle were completely recast.