Immanuel Bonfils

Immanuel ben Jacob Bonfils (c. 1300 – 1377) was a French-Jewish mathematician and astronomer in medieval times who flourished from 1340 to 1377, a rabbi who was a pioneer of exponential calculus and is credited with inventing the system of decimal fractions.^[1] He taught astronomy and mathematics in Orange and later lived in Tarascon, both towns in the Holy Roman Empire that are now part of modern-day France.^[2] Bonfils studied the works of Gersonides (Levi ben Gershom), the father of modern trigonometry^{[citation needed]}, and Al-Battani and even taught at the academy founded by Gersonides in Orange.^[3][4]

Bonfils preceded any attempt at a European decimal system by 150 years,^[5] publishing the treatise Method of Division by Rabbi Immanuel and Other Topics (Hebrew: דרך חילוק) on the general theory of decimal fractions around 1350. This was a forerunner to Simon Stevin, the first to widely distribute publications on this topic, and employed decimal notation for integers, fractions, and both positive and negative exponents.^[2][6][7]

While living in Tarascon in 1365, Bonfils published the work for which he would become best known, Sepher Shesh Kenaphayim (Book of Six Wings) (Hebrew: שש כנפים), a manuscript on eclipses that featured astronomical tables predicting future solar and lunar positions (divided into six parts).^[1][8] The book included data for every important date on the Jewish calendar and even correction factors necessary for those who lived as far away as Constantinople.^[6] Breaking the tables into six parts was an allusion to the six wings of the seraphim as mentioned in the Bible in Isaiah 6:2, earning Bonfils the nickname master of the wings.^[1]

For 300 years, Bonfils' calculations which were extensively used by sailors and explorers well into the 17th century.^[5] The book was translated from Hebrew into Latin in 1406 by Johannes Lucae e Camerino and into Greek in 1435 by Michael Chrysokokkes. The book inspired Chemist George Sarton to publish his own version of Six Wings nearly 600 years later.^[1] Bonfils translated a number of books from Latin to Hebrew. He also wrote a treatise on the relationship between the diameter and circumference of a circle and methods of calculating square roots.^[2]

• Bonfils, Immanuel (1365), The Wings of Eagles, Hebrew: שש כנפים, in six books. Other name: Book of Six Wings, Hebrew: שש כנפים. The main astronomical work of Bonfils.
• Bonfils, Immanuel (c. 1350), The Invention of the Decimal Fractions and the Application of the Exponential Calculus by Immanuel Bonfils of Tarascon^[9]
• Bonfils, Immanuel (c. 1350), Method of Division by Rabbi Immanuel and Other Topics, Hebrew: דרך חילוק, a course of decimal arithmetics, including decimal fractions.

• Gandz, S.: "The invention of the decimal fractions and the application of the exponential calculus by Immanuel Bonfils of Tarascon (c. 1350)", Isis 25 (1936), 16–45.
• P. Solon: The Six Wings of J. Bonfils and Michael Chrysokokkes, in: Centaurus, 15 (1970) 1–20

• BONFILS, IMMANUEL BEN JACOB in Jewish Encyclopedia.
• Six Wings.