Skip to main content

1990 | Buch

Apollonius: Conics Books V to VII

The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā

herausgegeben von: Gerald J. Toomer

Verlag: Springer New York

Buchreihe : Sources in the History of Mathematics and Physical Sciences

insite
SUCHEN

Über dieses Buch

With the publication of this book I discharge a debt which our era has long owed to the memory of a great mathematician of antiquity: to pub­ lish the /llost books" of the Conics of Apollonius in the form which is the closest we have to the original, the Arabic version of the Banu Musil. Un­ til now this has been accessible only in Halley's Latin translation of 1710 (and translations into other languages entirely dependent on that). While I yield to none in my admiration for Halley's edition of the Conics, it is far from satisfying the requirements of modern scholarship. In particular, it does not contain the Arabic text. I hope that the present edition will not only remedy those deficiencies, but will also serve as a foundation for the study of the influence of the Conics in the medieval Islamic world. I acknowledge with gratitude the help of a number of institutions and people. The John Simon Guggenheim Memorial Foundation, by the award of one of its Fellowships for 1985-86, enabled me to devote an unbroken year to this project, and to consult essential material in the Bodleian Li­ brary, Oxford, and the Bibliotheque Nationale, Paris. Corpus Christi Col­ lege, Cambridge, appointed me to a Visiting Fellowship in Trinity Term, 1988, which allowed me to make good use of the rich resources of both the University Library, Cambridge, and the Bodleian Library.

Inhaltsverzeichnis

Frontmatter

Conics: Text and Translation

Frontmatter
The Fifth Book
Abstract
From Apollonius to Attalus, peace be on you. In this fifth book I have composed propositions1 on the maximum and minimum lines. You should realize that our predecessors and contemporaries paid (a little) attention only to the minimum [lines]: they proved thereby which straight lines are tangent to the sections and also the reverse, i.e. what properties are possessed by the tangents to the sections such that when those properties are possessed by lines they are tangents. But as for us, we have proven those things in Book 1 without making use, in our proof of that, of the topic of minimum lines; for we wanted to make the place where those [things] were put near to our discussion of the derivation of the three sections, in order to show in this way that in each of the sections there may occur an infinite number of properties and necessities of these things, as is the case with the original diameters.2
Gerald J. Toomer
The Sixth Book
Abstract
From Apollonius to Attalus: peace be on you. I have sent you the sixth book of the Conics. My aim in it is to report on conic sections which are equal to each other and those unequal to each other, and on those similar to each other and dissimilar to each other, and on segments of conic sections. In this we have enunciated more than what was composed by others among our predecessors. In this Book there is also how to find a section in a given right cone equal to a given section, and how to find a right cone, containing a given conic section, similar to a given cone. What we have stated on this [subject] is fuller and clearer than the statements of our predecessors. Farewell.
Gerald J. Toomer
The Seventh Book
Abstract
From Apollonius to Attalus. Peace be on you. I have sent to you with this letter of mine the seventh book of the treatise on Conics. In this book are many wonderful and beautiful things on the topic of diameters and the figures constructed on them, set out in detail. All of this is of great use in many types of problems,1 and there is much need for it in the kind of problems which occur in conic sections which we mentioned,2 among those which will be discussed and proven in the eighth book of this treatise (which is the last book in its. I shall strive to send that to you speedily. Farewell.
Gerald J. Toomer

Notes on the Text and Translation

Frontmatter
Notes on Book V
Gerald J. Toomer
Notes on Book VI
Gerald J. Toomer
Notes on Book VII
Gerald J. Toomer

Appendices

Appendix A: Preface to the Conics of the Banū Mūsā
Gerald J. Toomer
Appendix B: Premisses of the Banū Mūsā
Gerald J. Toomer
Appendix C: Premisses to Book VII of Abū ’l-Husayn ’Abd al-Malik b. Muḥammad al-Shīrāzī
Gerald J. Toomer
Appendix D: Huygens’ solution of the problem of Pappus, Book IV Prop. 30
Gerald J. Toomer

Figures

Frontmatter
Figures to the Introduction
Gerald J. Toomer
Figures to Book V
Gerald J. Toomer
Figures to Book VI
Gerald J. Toomer
Figures to Book VII
Gerald J. Toomer
Figures to the Appendices
Gerald J. Toomer
Backmatter
Metadaten
Titel
Apollonius: Conics Books V to VII
herausgegeben von
Gerald J. Toomer
Copyright-Jahr
1990
Verlag
Springer New York
Electronic ISBN
978-1-4613-8985-9
Print ISBN
978-1-4613-8987-3
DOI
https://doi.org/10.1007/978-1-4613-8985-9