# Mathematician:Levi ben Gershon

## Mathematician

French Jewish philosopher, Talmudist, mathematician, physician and astronomer/astrologer.

Notable for publishing an early proof using the principle of mathematical induction.

Anticipated Galileo's error theory.

One of the first astronomers to estimate the distance of the fixed stars to a reasonable degree of accuracy (of the order of $100$ light years).

Refuted Claudius Ptolemy's model of astronomy by direct observation, paving the way for the new model of Nicolaus Copernicus more than $2$ centuries later.

Was involved in a lively debate about Euclid's $5$th postulate, and whether it could be derived from the other $4$.

## Nationality

French

## History

- Born: 1288 in Bagnols now Bagnols sur Cèze, Provence, France
- Died: 20 April 1344 in Avignon, France

## Theorems and Definitions

- Inventor of Jacob's Staff

## Publications

- 1317 -- 1329:
*Sefer Milhamot Ha-Shem*("The Wars of the Lord")

- 1321:
*Maaseh Hoshev*("Work of Calculation", "Art of Calculation" or "Art of the Computer", or, by means of a Hebrew pun: "Clever Work") on mathematics

- (often confused with
*Sefer Hamispar*("The Book of Number"), by Abraham ibn Ezra)

- (often confused with

- 1342: A portion of
*Sefer Milhamot Ha-Shem*containing a survey of astronomy translated into Latin

- 1342:
*De sinibus, chordiis et arcubus*("On Sines, Chords and Arcs"), on trigonometry - 1343:
*De numeris harmonicis*("The Harmony of Numbers") (contains a proof of Consecutive Integers which are Powers of 2 or 3)

- Two geometry books:
- A commentary and introduction to the first five books of Euclid, but not presented axiomatically
*Science of Geometry*of which only a fragment has survived

- A number of non-mathematical works

## Also known as

Some sources give his name as **Levi ben Gerson**, and others as **Levi ben Gershom**.

Better known by:

- the Greek form of his name:
**Gersonides** - his Latinized name
**(Magister) Leo Hebraeus** - in Hebrew as
**RaLBaG**(by the abbreviation of first letters of**Rabbi Levi Ben Gershon**with vowels added for ease of pronunciation)

Less commonly he can be seen referred to as **Gersoni**, **Leo de Bagnols**, **Leo de Balneolis** or **Leo Judaeus**.

It could be complicated identifying someone specifically before the invention of surnames.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Levi ben Gershon": MacTutor History of Mathematics archive

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Levi ben Gerson**(1288-1344)