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Euclid's Fundamentals

Researchers examined the Hebrew translations of the "Elements" by Euclid and traced their origins

The cover of Euclid's book of fundamentals published in Holland in 1740.
The cover of Euclid's book of fundamentals published in Holland in 1740. From the HEBREWBOOKS website

"The Book of Elements" by Euclid, the Greek mathematician considered the father of geometry, was written in the third century BC in Alexandria. It is considered one of the canonical books of Western culture, a scientific achievement of the Greeks, and has been one of the main sources for learning mathematics almost to the present day. In the Middle Ages it was translated into Arabic, Hebrew and Latin.

The spread of Greek culture, and the Book of Elements in particular, was a lengthy process. In the seventh century, the Arabs conquered the Sasanian Empire (the pre-Islamic Persian Empire) and a large part of the Byzantine Empire (the Eastern Roman Empire), and reached the Iberian Peninsula in southwestern Europe through North Africa. From the eighth century (during the rule of the House of Abbas) the process of appropriating Greek culture began in the East; The Arabs began to translate Greek texts that dealt with mathematics, natural sciences, medicine and philosophy. The writings that were translated into Arabic were distributed in the East, in Muslim Spain, and over the years original additions and commentary books in Arabic were added to them. Thus, the Jews who lived in Spain and whose language was Arabic were also exposed to the treasure of Greek-Arabic knowledge.

How does scientific knowledge develop? And how is it transmitted over thousands of years?

In the 12th century (following the Reconquista, the re-conquest of the Iberian Peninsula by the Christians and the invasion of the Mujahideen - Muslim barbarian tribes - from North Africa), the social and cultural balance was broken and a massive migration of Jews from Spain to North Africa and Europe began. Many of them came to the south of France, home to many traditional Jewish communities. This is how these communities were exposed to the Greek-Arabic culture that the refugees brought with them, and a demand was created for translations from the West into Hebrew. At first, texts written by Jews were translated in Arabic (Rasg, Rambam, Yehuda Halevi, etc.), but gradually the translation work expanded and during the 13th and 14th centuries, many scientific texts were translated in fields such as mathematics, philosophy, astronomy and medicine. The translated texts also included the Sefer Yezotot.

The medieval Latin translations of the Book of Elements have been extensively studied and scholarly editions of them are available to scholars. Not so the Arabic and Hebrew translations. It used to be assumed that there were two Arabic translations, the first by Al-Hajj Ibn Yusuf Ibn Matar (786-833), and the second by Hanin Ibn Eshaq (809-873) edited by Thabat Ibn Qura (died 901). Very little is known about the first translation, and the surviving manuscripts are versions of the second translation. The second translation also does not yet have a scientific edition (except for two research works that deal with articles XNUMX and XNUMX-XNUMX). The Hebrew translations, in which the research of Prof. Ruth Glazner and Dr. Ofer Elior of the Faculty of Humanities at the Hebrew University of Jerusalem deals, have not yet been printed and are found only in manuscripts.

The main goal of Prof. Glazner and Dr. Elior was to make available to researchers in the field of mathematics, history, and the history of science the Hebrew translations of Sefer HaYedosot. Also, through the study of the Hebrew text, they seek to contribute to the accumulated knowledge of the history of the Book of Elements in all its incarnations.

The Hebrew translations are all in the Institute for Photographs of Manuscripts at the National Library in Jerusalem. The Latin translations are found in scientific editions. The Arabic manuscripts had to be collected from libraries and archives all over the world. "We wanted to know which texts the Hebrew translators used, what was on their table. Today, there are no complete answers - and often not unambiguous - to many questions concerning these translations, including: how many translations were created, when exactly, who were the translators, what translation methods they used, what their sources were and what they included in their translations," explains Dr. Elior. To this end, they compared several translations of the book into Hebrew and found two leading traditions: that of a scholar who identifies himself as Rabbi Jacob (perhaps Jacob Anatoli - a philosopher, biblical commentator and important translator of the 13th century) and of Moshe Ibn Tivon (a translator, physician and philosopher of the century the 13th). Artgate Fondazione Cariplo – Cifrondi Antonio, Euclide

Prof. Tony Levy from the CNRS (National Center for Scientific Research in Paris), showed a striking similarity between Rabbi Jacob's translation and the first Latin translation of the Book of Elements (by Adelard of Beth, who worked in the first half of the 12th century), and therefore the question arose whether the translation The Latin was a direct source for Rabbi Jacob's translation. Despite the similarity, Dr. Elior found many differences - in wording, nomenclature and drawings - between the Latin translation to me. Many of them stem from the fact that Rabbi Yaakov's translation was probably based on several sources.

The researchers also found that Ibn Tibbon's translation was clearly based on that of Hanin-Thabat, closely adhering to it and even preserving his mistakes. According to Dr. Elior, "Evan Tivon tried to translate the Arabic version of Hanin-Thabat word for word and preserve the structure of its sentences. The drawings he used are also identical to those that appear in Hanin-Thabet. This adherence created a translation that is not always easy to read. Its formulations and nomenclature are not uniform and errors were discovered in it. This may be what led to an improved version being proposed by Ibn Tibbon's brother, Jacob ben Machir. However, the original version of Ibn Tibbon was the one that was widespread and preserved by the majority

The manuscripts".

The edition edited by Dr. Elior as part of this research, which won a grant from the National Science Foundation, includes four columns. On the left page is the first Latin translation and next to it the Hebrew translation by Rabbi Jacob. On the right page is Ibn Tivon's Hebrew translation and next to it is an approximate Arabic version that was before him, compiled by Dr. Elior after a detailed comparison of the Arabic manuscripts he collected. The first volume of the edition (articles A-B accompanied by a very comprehensive introduction, appendix - notes, translations and explanations - and appendices that discuss the findings) was published by Brill Publishing in 2021. The second volume (articles 2023-XNUMX according to the same format) will be published by Brill Publishing in XNUMX.

Life itself:

Prof. Ruth Glazner was born in Jerusalem in 1944 and lives there until today. Studied mathematics, physics, computer science and philosophy at the Hebrew University, and currently focuses on the history of Hebrew science. Married + four children and seven grandchildren.

Dr. Ofer Elior, studied computer science, history and history and philosophy of science at the Hebrew University. He wrote his research paper on the book "Spirit of Grace" at Ben Gurion University. In addition, he published a scientific edition of the book "Wars of Hashem" in two volumes. 47 years old, married + two daughters, lives in Jerusalem. Lover of cinema and music.

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