astronomy

Immanuel Bonfils

Immanuel Bonfils is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Immanuel Bonfils rather than just read about it. In short: 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. 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.

Key takeaways

Immanuel Bonfils belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Immanuel Bonfils to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Immanuel Bonfils from memory before moving on to harder problems.

Reference excerpt

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. 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. Bonfils studied the works of Gersonides (Levi ben Gershom), the father of modern trigonometry, and Al-Battani and even taught at the academy founded by Gersonides in Orange. Bonfils preceded any attempt at a European decimal system by 150 years, 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. 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). 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. 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. For 300 years, Bonfils' calculations which were extensively used by sailors and explorers well into the 17th century. 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. 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.

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 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

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

External links BONFILS, IMMANUEL BEN JACOB in Jewish Encyclopedia. Six Wings.

Worked examples

Example 1 — a first encounter with Immanuel Bonfils

Start with the simplest possible case. Write down what Immanuel Bonfils claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Immanuel Bonfils before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Immanuel Bonfils ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Immanuel Bonfils

In research: Immanuel Bonfils appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Immanuel Bonfils in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Immanuel Bonfils is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1300s births, 1377 deaths, 14th-century French Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Immanuel Bonfils outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Immanuel Bonfils in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Immanuel Bonfils means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Immanuel Bonfils out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Immanuel Bonfils in simple terms?

Why does Immanuel Bonfils matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Immanuel Bonfils?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Immanuel Bonfils.