Sefer Uklidus Ha-Hakham
Sefer Uklidus ha-Hakham is a Hebrew translation manuscript of Euclid’s Elements. It was written by a Jewish scribe in Italy and completed in the year 1704. The name of the scribe is not recorded anywhere in the book, nor is there any publishing or copyright information. The manuscript is now held in the University of Pennsylvania’s Kislak Center for Special Collections by way of purchase from a Sotheby’s auction in 2015.
Historical Context
Hebrew Translations of Elements
Although there have been several attempts to translate Elements into Hebrew, three particular translations are among the most well-known. Two of the three were translated by members of the ibn Tibbon family from the Provence region of France. The first was by Moses ibn Tibbon, completed in in 1270, and the second was by his nephew, Jacob ben Makhir ibn Tibbon, completed in 1289. The ben Makhir translation is regarded to be more accurate and more succinct than his uncle’s translation.[1] The copy of the Elements in Hebrew held in the Kislak Center is an early eighteenth-century transcription of the Jacob ben Makhir ibn Tibbon translation.
The other well-known Hebrew translation of Elements was completed by Rabbi Baruch Schick of Shklov in 1780. This translation is famous for being commissioned by Rabbi Eliyahu ben Shlomo Zalman, commonly known as the Vilna Gaon, one of the foremost Torah scholars of eighteenth-century Europe who is revered to this day. He encouraged the publication of a Hebrew translation of the famous mathematical text at a time when secular studies were unpopular in the Orthodox Jewish sphere.[2]
The Apocryphal Books
One of the clues that this particular copy is a transcription of the Jacob ben Makhir ibn Tibbon translation is the fact that it includes the apocryphal fourteenth and fifteenth books of Elements. The fourteenth "book" or chapter, has been attributed by scholars to Hypsicles. Somewhere in its transmission from the Library of Alexandria through the late modern era, Hypsicles' treatise became a part of Euclid's Elements.[3] The fifteenth chapter is similarly believed to be apocryphal, but scholars do not agree on who authored it.[4]
Material Analysis
Substrate
The book is made from laid paper as evidenced by the appearance of wire and chain lines. In order to keep the lines of text straight and justified, given the handwritten nature of the text, the scribe scored each line and pricked the ends of each line before writing the words. The front and back covers of the book are made of stacked layers of wastepaper that create a thick cardboard-like texture. On the back cover, some of the layers of scrap paper have mathematical calculations written on them, suggesting that the book was self-bound by the mathematically proficient scribe himself with his own leftover papers.
Format
The book is of a codex format, and the writing proceeds from right to left since it is Hebrew. The size indicates a folio format, however this is complicated by the fact that the chain lines are horizontal instead of vertical. Each gathering is labeled with a Hebrew letter denoting its order in the book. This further suggests that the Jewish scribe did not write in a generic blank notebook, but rather assembled the codex himself for the sake of writing the specific text.
Overview
The book opens to an architectural title page featuring an archway and the proclamation “Zeh Sefer Shel Uklidus haHakham” (זה ספר של אקלידס החכם) which translates to “This is the book of Euclid the Wise.” The next page with writing consists of a list of definitions of important geometrical terms such as “point,” “line,” and “plane.” The rest of the book consists of alternating propositions and their coordinating proofs. These are separated into fifteen “books” or chapters, and each proposition-proof pair is numbered within its chapter. Throughout the text block, rectangular spaces are intentionally left blank for diagrams to be filled in.
Paratexts
Aside from the artistic title page in the beginning, the book contains paratexts following the conclusion of each chapter that pronounce the respective chapter to be finished. Some of these texts include the date in which the given section was completed by the scribe and some even include overtly religious wording and sentiments.
The conclusion of the tenth chapter informs the reader that the scribe completed the chapter “on the thirty-third day of the omer of the year 5464.” This refers to the period in the Jewish calendar called the Omer in which Jews count the days between the second day of Passover and the holiday of Shavuot. The thirty-third day is very significant and is celebrated as a mini holiday within the counting period because it commemorates the cessation of a plague that affected the Jews during the period when they were under Roman rule. The year 5464 refers to the Hebrew year and corresponds with the Gregorian year 1704. Thus, it can be infered that the scribe completed writing the tenth chapter on May 22, 1704. After denoting the date, the scribe includes a praise to God that says, “Praise to God the Good, from whom all is good.” The inclusion of explicitly religious sentiment suggests that the scribe was a religiously devout Jew. Perhaps he saw his task of transcribing Euclid’s Elements as one that harmonized with his religious worldview. As in the case of Rabbi Baruch Schick of Shklov’s translation, the scribe may have felt that studying fundamental principles of philosophy such as geometry is essential to a comprehensive understanding of God.
Book Use and Readership
The book does not contain much in the way of navigation aids from the original scribe. There is no table of contents or index. The scribe did include a catchword at the end of the textblock on each page to make reading continuous, or perhaps even to mark their place during the scribing process. The scribe also makes sure to note the beginning and end of each chapter in a different script than is used for the main text. This can help the reader when flipping through the book to look for a given chapter.
Another navigation aid is the penciled foliation numbers on the upper left of each recto leaf. The Penn catalog entry says these are modern foliations, so they were probably written there by an archivist or cataloger long after the book was completed by the scribe and after it had been in circulation for a while.
Marginalia and Annotations
Various marginalia and annotations can be found throughout the book, although most are concentrated in the beginning and the first several chapters. On the definition page in the beginning, corresponding definitions in Italian are written in the right-hand margin next to the Hebrew. The left-hand margin on this page contains explanatory drawings. These marginalia seem to be written in a different ink than the main text, suggesting that they were made by a reader. In the first chapter, a reader added marginal headings to the right of the first word of each proposition and proof and numbered each one using Hebrew letters. Other marginalia seems to be explanations of the content in Hebrew.
The most prominent annotations are the geometrical diagrams that pepper the text. These are specifically not marginalia since the scribe left blank spaces for diagrams throughout the entire text. The diagrams are only filled in for the first several chapters. Some diagrams have been pasted in on a separate piece of paper as opposed to having been drawn straight on the page of text.
Other asemic markings can be found in the book such as crossed-out phrases and the “therefore” symbol of mathematical proof notation.
The annotation pattern of this copy of Euclid’s Elements suggests an interactive reader. The scribe provided the basic foundation of the Hebrew text and left spaces for diagrams, and the reader, perhaps multiple, interacted with this text as they read. The reader treated the book like a workbook as opposed to just a textbook and practiced the concepts within the pages themselves. Euclid’s principles came to life for the reader as they etched in the diagrams and followed the logic of the proofs not only mentally, but with their pen as well.
This material object, from the gatherings of paper, to the marginalia paint a picture of Italian Jewish craftsmen and intellectuals collaborating and passing material to each other for the sake of learning and perhaps growing connection to God.
References
- ↑ Elior, Ofer (2019-10-01). "The Hebrew Translations of Euclid's Elements By Moses IBN Tibbon and by Jacob Ben Makhir–A Study of Differences in Book I". Journal of Semitic Studies. 64 (2): 481–506. doi:10.1093/jss/fgz005. ISSN 0022-4480.
- ↑ Etkes, Immanuel. The Gaon of Vilna: the man and his image. Univ of California Press, 2002. pp. 37-72
- ↑ Wardhaugh, Benjamin. Encounters with Euclid: How an Ancient Greek Geometry Text Shaped the World, Princeton: Princeton University Press, 2021. pp. 26-30 https://doi-org.proxy.library.upenn.edu/10.1515/9780691219813
- ↑ Cameron, Alan. "Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts." Greek, Roman, and Byzantine Studies 31.1 (1990): 103-127.