# 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]

## Works

• 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.

## References

1. ^ a b c d Vucinich, Alexander (1963). Science in Russian Culture, A History to 1860. Stanford, CA: Stanford University Press
2. ^ a b c "Bonfils, Emmanuel Ben Jacob". JewishEncyclopedia.com. Retrieved 2015-02-20. CS1 maint: discouraged parameter (link)
3. ^ Dimont, Max I. (2004). Jews, God, and History. Signet Classics
4. ^ Shatzmiller, Joseph (2013). Cultural Exchange; Jews, Christians, and Art in the Medieval Marketplace. Princeton, NJ: Princeton University Press
5. ^ a b Blech, Benjamin (2004). The Complete Idiot's Guide to Jewish History and Culture. Indianapolis, IN: Alpha Books
6. ^ a b Suzuki, Jeff (2009). Mathematics in Historical Context. Washington, DC: The Mathematical Association of America
7. ^ Ben-Menahem, Ari (2009). Historical Encyclopedia of Natural and Mathematical Sciences. Springer Verlag
8. ^ Solon, Peter (1971). "The Six Wings of Immanuel Bonfils and Michael Chrysokokkes". Centaurus. 15: 1–20. Bibcode:1971Cent...15....1S. doi:10.1111/j.1600-0498.1971.tb00147.x.
9. ^ Ragep, F. Jamil and Sally P. Ragep (1996). Tradition, Transmission, Transformation. Netherlands: Brill Academic Pub
• 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