Jacques Sesiano Livres

Focusing on the critical examination of Diophantus' Arithmetica, this edition presents Books IV to VII, available only through a newly discovered Arabic translation. The work stems from a doctoral dissertation and includes a thorough critical text alongside the English translation. Significant enhancements are made in the mathematical commentary and the Arabic index, with fresh discussions on Greek and Arabic interpolations. Additionally, it reconstructs the historical journey of the Arithmetica from Diophantine to Arabic contexts, reflecting the author's gratitude toward his adviser for their support.

The discovery of an Arabic translation of an ancient treatise sheds light on advanced methods for constructing magic squares, significantly enhancing our understanding of Greek mathematics. The early tenth-century translator salvaged two damaged manuscripts, allowing him to piece together the text. This translation initiated Arabic studies on magic squares, revealing that Greek scholarship on the topic was more advanced than previously thought. However, the lack of additional preserved texts leaves a gap in the understanding of the earlier history of this mathematical concept.

The development of magic squares in the Islamic world during the Middle Ages highlights a significant evolution in mathematical methods. This progress began with the ninth-century translation of a Greek text, which detailed advanced arrangements believed to be the peak of ancient studies. The book explores the various construction techniques that emerged, showcasing the blend of cultural and intellectual advancements that enriched the field of mathematics during this period.

Focusing on the mathematical heritage of 12th-century Islamic Spain, this work offers a translation and commentary on the Liber Mahameleth, a key source in the field. It delves into the various problems presented in the text, providing a thorough analysis and summary of the mathematical methods utilized. This exploration not only enhances understanding of historical mathematical practices but also highlights the significance of the period's contributions to the discipline.

This volume contains the texts and translations of two Arabic treatises on magic squares, which are undoubtedly the most important testimonies on the early history of that science. It is divided into the three parts: the first and most extensive is on tenth-century construction methods, the second is the translations of the texts, and the third contains the original Arabic texts, which date back to the tenth century.