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Über dieses Buch

This book provides a critical edition, translation, and study of the version of Euclid’s treatise made by Thābit ibn Qurra, which is the earliest Arabic version that we have in its entirety. This monograph study examines the conceptual differences between the Greek and Arabic versions of the treatise, beginning with a discussion of the concept of "given" as it was developed by Greek mathematicians. This is followed by a short account of the various medieval versions of the text and a discussion of the manuscripts used in this volume. Finally, the Arabic text and an English translation are provided, followed by a critical commentary.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
Already by the Roman Imperial period (1st–3rd century), the Data had begun to lead a double life. Originally composed, or arranged, by Euclid (early-3rd century BCE) as a purely geometrical text for use in geometrical analysis, in the late Hellenistic (3rd– 1st centuries) and early Imperial periods, mathematicians began to repurpose this work, and by the time of Heron (probably mid-1st century CE) and Ptolemy (mid-2nd century CE), it appears to have been used as a means to justify computational procedures. By the Late-ancient period (3rd–6th century), it was used as a foundational text in both of these, rather different, areas by scholars and teachers such as Pappus (early-4th century CE) and Theon of Alexandria (late-4th century CE).
Nathan Sidoli, Yoichi Isahaya

2. Text and Translation

Abstract
Surfaces, angles, and lines that are called known in magnitude are those of which we are able to find quantities equal to them; [D.2] and those that are called known in ratio are those of which we are able to find magnitudes in their ratio.
Nathan Sidoli, Yoichi Isahaya

3. Commentary

Abstract
In the commentary, we first discuss general differences between the Restoration and the Greek text as edited by Menge (1896), with an emphasis on the use of structure in Thabit’s text. This is followed by a detailed commentary of the text, proposition-byproposition, that provides a new interpretation of the concepts and methods of the Greek text as well as comparing the Restoration with the Greek text and al-Ṭusi’s Revision.
Nathan Sidoli, Yoichi Isahaya

4. Concordance of Proposition Numbers

Abstract
Here we provide a table of concordance for the proposition numbers in our two manuscripts (A, K) as compared with the Hyderabad (1939/40) printing of al-Ṭusi’s Arabic revision (T) and the critical Greek edition (G) prepared by Menge (1896). This table should be compared with that provided by Thaer (1942, 202–203).
Nathan Sidoli, Yoichi Isahaya

5. Critical Glossary

Abstract
This glossary is not exhaustive. We omit a number of words that are used frequently and are not subject to any interpretation—such as مثلث. The goal is to help the reader to understand our translation choices and to find examples in the text. Hence, in most cases, we give the occurrences of an entry by page and line number (p.l), but in the case that the word occurs on every page, we simply state that it is “ubiquitous,” and in the case that it can be found, on average, on a majority of pages, we state that it is “common.” The glossary has three sections: cojunctions used to control logical and temporal succession, expressions used to denote operations on ratios and proportions, and a general glossary of individual words and expressions organized in alphabetical order, often under the heading of a root.
Nathan Sidoli, Yoichi Isahaya

Backmatter

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