Jacob ben Machir ibn Tibbon

Born: 1236 in Marseilles, Spain (now France)
Died: 1305 in Montpellier, France

Jacob ben Tibbon is also known by the Latin version of his name, Prophatius Judaeus, and in Provence he is known by the name Don Pro Fiat. The ibn Tibbon family were famed over several generations so we begin by looking at the ancestors of the subject of this biography. We begin with Judah ben Saul ibn Tibbon (1120-1190) who was the great-grandfather of Jacob ben Tibbon. He lived for the first 30 years of his life in Granada which at this time was a Muslim country. There was a thriving community of Jews in this part of Spain from around the year 1000, many of whom made major contributions to the study of languages. The Almohads expelled the Jews from Muslim Spain in 1148, and Judah ben Saul ibn Tibbon together with many other learned refugees, went to the south of France. He settled in Lunel where he translated philosophical works from Arabic into Hebrew. His son, Samuel ben Judah ibn Tibbon, was born in Lunel and continued his father's work of translating although he, like his father, was a medical doctor.

Samuel ben Judah ibn Tibbon's son, Moses ben Samuel ibn Tibbon, was born in Marseilles. He again was a medical doctor who was famed as a translator from Arabic into Hebrew. He also translated Arabic-language works by Jews and Arabs dealing with philosophy, mathematics, astronomy, and medicine. One of the mathematical works he translated was Euclid's Elements. Jacob ben Machir ibn Tibbon, the subject of this biography, was the son of Machir ben Judah ibn Tibbon, Samuel ben Judah ibn Tibbon's brother. He, like his father, was born in Marseilles and he continued the family tradition of being a distinguished member of the medical profession while at the same time making important contributions through translating.

Jacob was educated in Lunel and then studied medicine in the medical faculty of the University of Montpellier. Certainly by 1266 he was in Gerona in the northeast of Spain just to the south of the Pyrenees. He lived there for at least a year but he then returned to Lunel, where he had family connections, and he also lived for long periods in Montpellier.

Jacob ben Tibbon is himself known as a translator as well as a mathematician and an astronomer. He translated into Hebrew many Arabic versions of Greek mathematical and astronomical works, including Euclid's Elements, Euclid's Data, Euclid's Optics, Menelaus's Spherics, Autolycus of Pitane's On the Moving Sphere, Ptolemy's Almagest as well as certain Arabic works such as al-Haytham's Configuration of the World (intended for the layman), and works by al-Ghazali, al-Zarqali, and others. He also translated many works on philosophy and zoology. It is interesting to read a comment Tibbon makes in the Preface of his translation of Euclid's Elements:-

And here is geometry, the basis for all mathematical sciences, and this book is the basis, the root and the beginning for all later books on this science. I, Jakob ben Makir, have undertaken to translate it into our language ... in order to avoid the mockery of the Christians, who say that we lack to all sciences.
Now Tibbon was much more than a translator, for he was a fine mathematician and astronomer writing original works in addition to the translations. For example, he wrote Jacob's Quadrant in which he describes a quadrant of his own invention. This work contains a table of 11 fixed stars which are to be used in the construction of the instrument which was later called the quadrans novus (new quadrant) to differentiate it from the traditional quadrant or quadrans vetus (old quadrant). Vernet writes in [1]:-
Examples of the quadrans novus have been preserved, and it apparently was much used in its time. It consists of a simplification of the face of the astrolabe by means of two successive rebates that have their axes the north-south and east-west lines. Whatever connections may exist between this apparatus and similar instruments used by the Arabs have not been clearly established.
Jacob ben Tibbon also wrote Luhot (Tables) a book of astronomical tables giving ascensions of certain stars at Paris. These tables are mentioned in Dante's Divine Comedy. The Italian astronomer Andalo di Negro wrote Canones Super Almanach Profatii in 1323 which dealt with Jacob ben Tibbon's tables in Luhot .

Another work by Jacob ben Tibbon was Almanach Perpetuum which, as the title indicates, was a work on the almanac. It was written for users in Montpellier, indicating that he was living and working there at the time, and the calculations begin with data for 1 March 1300. There has been a considerable debate among historians as to the basis for the tables. At the time Tibbon wrote the work both the Toledan Tables of Arzachel and the newer Alfonsine Tables created for King Alfonso X of Castile were in use. Tibbon appears to state that he used the Toledan Tables but Pierre Duhem criticised him for using 'old' tables instead of the latest available to him. Thorndike, in [6], defends Tibbon with a number of points, but also suggests that Tibbon may have meant the Alfonsine Tables rather than the Toledan Tables. Harper's analysis in [4] suggested that Tibbon's Almanach was based on original work but Toomer in [8] demonstrates errors in Harper's calculations. Toomer concludes:-

... in the introduction to the Latin version of the Almanach [it is written] that the author had based his work on the Toledan tables. Since all mention of the Toledan tables is absent from the Hebrew version, I had previously supposed that this was a mistaken interpolation by the person responsible for the Latin version. I now believe that it stems from Prophatius [Tibbon] himself, and that he did indeed use the Toledan tables as the basis for his Almanach.
Tibbon's work was used by Copernicus in forming his theories.

Article by: J J O'Connor and E F Robertson

July 2007
MacTutor History of Mathematics