The Essence of Mathematics, Al-‘Amili, Baha’ al-Din Muhammad ibn Husain, Istanbul 1687

Al-‘Amili, Baha’ al-Din Muhammad ibn Husain. Khulasat al-Hisab (The Essence of Mathematical Sciences). Manuscript. Arabic. H-1099 (1687), Istanbul-Turkey.

25 x 16 cm. [3], 113 leaves including tipped-in leaves. Bound in the original brown leather with a şemse-style motif. The binding shows signs of aging and wear over time. Features mathematical diagrams and illustrations, enriched with annotations (shukka) and commentaries. Written in black soot ink and red highlights, on polished aharlı and occasionally watermark-stamped European paper. The text is beautifully executed in nezih script. There are many mathematical diagrams throughout, some coloured and many tipped-in additional leaves and cut-out pieces,

The Essence of Mathematical Sciences

Khulasat al-Hisab, or “The Quintessence of Arithmetic,” is not merely a textbook but a masterwork that distills centuries of mathematical knowledge into an accessible and comprehensive guide. Authored by Bahā’ al-Dīn al-‘Āmilī (d. 1031 AH/1662 CE), a towering figure in Islamic mathematics, the work represents a synthesis of theoretical and applied mathematics. It covers arithmetic, algebra, and measurement, blending practical applications with profound theoretical insights.

This text served as the cornerstone of mathematical education in the Islamic world for centuries, replacing earlier works like Ali Kuşçu’s al-Risala al-Muhammadiyya fi’l-Hisab. Its adoption as a teaching manual across regions like Anatolia, the Balkans, Iran, and India underscores its pivotal role in shaping mathematical pedagogy.

A Masterpiece of Pedagogical Clarity

One of the key features of Khulasat al-Hisab is its clarity and conciseness, making complex mathematical concepts accessible while retaining intellectual rigor. Despite its compact and dense style, the work invites engagement through numerous examples and practical applications. It introduces innovative methods, such as numerical approximations for square roots and advanced discussions on rational and irrational numbers.

The book’s structure is meticulous, divided into a foreword (dibace), an introduction (mukaddime), ten chapters (bab), and a conclusion (hatime). Each section builds upon the previous, guiding readers from foundational arithmetic to advanced algebra and geometric problem-solving. Its final section, a collection of unsolved problems, reflects the intellectual curiosity of its author and his desire to inspire future scholars.

Applied and Theoretical Contributions

Beyond its theoretical depth, the manuscript includes practical applications for commerce, engineering, and surveying (misaha). The chapters on land measurement, canal construction, and the calculation of distances and heights reflect the integration of science and daily life. This dual focus on theory and practice makes the manuscript a rare bridge between abstract knowledge and real-world utility.

A Legacy of Influence

The widespread survival of Khulasat al-Hisab in over 100 manuscripts across Turkish libraries and the numerous commentaries it inspired are a testament to its enduring influence. It was not only a teaching tool but also a foundation for future advancements in mathematics, attracting attention from both Islamic and European scholars. Translations into German and French further extended its reach, solidifying its place as a global mathematical treasure.

A Rare and Enduring Manuscript

This manuscript, preserved in its original binding and enriched with mathematical diagrams and commentary, is a rare embodiment of the intellectual legacy of Islamic science. It represents the synthesis of centuries of knowledge, skillfully compiled into an educational and practical guide that remains relevant to this day. For collectors and scholars alike, Khulasat al-Hisab is an exceptional example of the Islamic mathematical tradition at its peak.

Al-‘Amili, Baha’ al-Din Muhammad ibn Husain (d. 1622) was a prominent Shia Islamic scholar, theologian, and jurist from the Safavid period. He is best known for his contributions to Islamic jurisprudence and theology, particularly in the Twelver Shia tradition. Among his notable works are “Al-Mahajjah al-Bayda” (The White Path), an influential commentary on various aspects of Islamic teachings, and “Sharh al-Maqasid,” which elaborates on principles of Shia jurisprudence.

Al-‘Amili also played a significant role in the intellectual and religious life of his time, being involved in the establishment of seminaries and promoting Shia scholarship. His influence extended beyond theology into philosophy and mysticism as well.