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About Mispar

Mispar is an open access MediaWiki research platform for the study of medieval Hebrew arithmetic. It provides annotated transcripts of almost all surviving Hebrew medieval arithmetic and algebraic treatises, as well as a few Hebrew geometric, Arabic and Judeo-Arabic treatises. The transcripts are organized into a peer-updatable database that includes English descriptions of the components of each treatise as well as search features that allow for comparing thematic components across all treatises.

The database offers the following pages:

  • Lexicon - a list of English mathematical terms, linking each term to examples of Hebrew equivalents in the database
  • Terms - a list of Hebrew mathematical terms, linking each term to examples in the database
  • Mathematical formulas - a list of modern mathematical expressions and formulas, linked to examples of equivalent expressions and formulas in the database
  • Word problems - a list of types of word problems (following Van Egmond's classification), linked to examples in the database

The Mispar database in still under construction. This means that some of the pages are undergoing editing, and that some of the information in the above pages is incomplete. The discussion page of each of the mathematical sources pages should specify the current editing stage of that source

The databases and search capacities are based on the tailor-made YATA semantic annotation system. Users with editing privileges can use it to perform their own searches. Please note: the "search mispar" field at the top right of each page is a default Wikimedia search feature. It should find all pages with the relevant search terms, but not all occurrences of those terms.

Mispar database is a service provided by ETH, Zürich. The initial version of the database is being prepared by Naomi Aradi.

Mispar is cooperating with the Peshat project (Premodern Philosophic and Scientific Hebrew Terminology) to complete the documentation of medieval Hebrew mathematical terms in the Peshat database and link them to examples in the Mispar database.

This project is supported by the René & Susanne Braginsky Stiftung, Gedenkstiftung Rapaport, Stiftung zur Förderung der Mathematischen Wissenschaft in der Schweiz and the ETH Zürich Foundation.

To contact us, please send an email.

Aims and Development

The primary aim of the project is to allow an integrative view of the entire medieval Hebrew mathematical culture (based on surviving texts) with advanced search capacities. The database will include about 40 different treatises (ca. 2000 manuscript pages), some of which exist in several manuscripts. The long-term objective is to create a model digital system for presenting and analyzing medium-size collections of thematically related manuscripts.

Current phase

Naomi Aradi is re-coding the transcripts of medieval arithmetic works on the Mispar platform. The manuscripts are presented together with the usual meta-data (author, time, place, etc.), as well as a detailed list of headings and subheadings in English, notes with modern transcriptions of mathematical operations, and partial English translations. A unique feature of this project is tagging each treatise by mathematical subjects and motifs arranged in a hierarchical tag tree Category Page. Subsequently, one can use these tags to search the texts. Our tagging system was especially developed by ETH Zürich to allow tagging a dynamic MediaWiki page. It is unique in that it allows for editing and reprocessing a page even after it is tagged. As a result, gradual crowd-sourced amendment and improvement of the page is still possible after the tagging.

The tagging allows, among other things, to compare all definitions of a certain English or Hebrew mathematical term across the corpus, all algorithms for specific arithmetical operations (such as root extraction), and all treatments of specific subjects across this entire corpus. It enables to track routes of transmissions of knowledge and the evolution of ideas within the scientific culture. It will also facilitate tracking down the influences of non-Hebrew sources through translation and adaptation.

Users now has the possibility to browse, search, and read this material. Editing the texts (and, in particular, creating tag-based searches) is not open for the general public at this point, but if you wish to collaborate on this project with us, please ask us for the necessary editorial privileges. Please note that at this stage many of the pages are still under construction and may contain errors. Suggestion, corrections and criticism, however, will be welcome.

The medium-term

In the near future, users will be allowed to add their own corrections, updates, and comments such as English translations, scholarly comments, etc. They will also be able to use the tags for searching the database.

We intend to add critical apparatuses to some of the texts, in order to update old existing editions and create a modern corpus edition of the arithmetical works.

The long-term

Mispar may be transformed to a platform for the study of medieval Hebrew mathematics by including Hebrew geometrical manuscripts. Ultimately it may even be extended to a multi-lingual database for medieval mathematics in general, by including relevant non-Hebrew manuscripts.


Hebrew Texts
Mishnat ha-Middot (Treatise of Measures) משנת המדות
Hebrew translation of the Elements by Euclid ספר היסודות לאקלידס
Yesodei ha-Tevunah u-Migdal ha-Emunah (The Foundations of Understanding and Tower of Faith)
by Abraham bar Ḥiyya (1065-1136/1145)
ספר יסודי התבונה ומגדל האמונה / אברהם בר חייא
Sefer ha-Mispar (The Book of Number)
by Abraham ben Meir Ibn ‛Ezra (1089-1167)
ספר המספר / אברהם אבן עזרא
Abū Bakr al-Haṣṣār: Kitāb al-Bayān
tr. Moses Ibn Tibbon (1240-1283)
ספר החשבון לאל-חצאר / משה אבן תיבון
Nicomachus of Gerasa: Introduction to Arithmetic
tr. Qalonymos ben Qalonymos (1286/7-after 1329)
האריתמטיקה של ניקומכוס / קלונימוס בן קלונימוס
Sefer ha-Melaḵim (The Book of the Kings)
by Qalonymos ben Qalonymos (1286/7-after 1329)
ספר המלכים / קלונימוס בן קלונימוס
Sefer Ma‛ase Hoshev (Work of Calculation)
by Gersonides (1288-1344)
ספר מעשה חושב / לוי בן גרשום
Excerpts Attributed to Immanuel Bonfils (1340-1377) קטעים המיוחסים לעמנואל בונפיס
‛Ir Siḥon
by Joseph Ben Moses Ṣarfati (before 1384)
עיר סיחון / יוסף בן משה צרפתי
Igeret ha-Mispar (The Epistle of the Number)
by Isaac Ben Solomon Ben Al-Aḥdab (1350-1429/1433)
אגרת המספר / יצחק בן שלמה בן אלאחדב
The Encyclopedia of Abū al-Ṣalt
by Don Benveniste b. Lavi (1395/1435)
האנציקלופדיה של אבו אלצלת / דון בנבשת בן לביא
Bar Noten Ta‛am (An Expert Gives a Reason)
by Jacob Canpanṭon (ca. 1430)
בר נותן טעם / יעקב קנפנטון
Qiṣṣur ha-Mispar (Compendium on Number)
by Judah Ibn Verga (c. 1450)
קצור המספר / יהודה בן וירגא
‘Iyyun ha-‘Iqqarim
by Shalom Ben Josepp ‘Anavi (1450-1460)
ספר עיון העקרים לחשבון ההנדיים / שלום בן יוסף ענבי
Meleket ha-Mispar (The Art of Number)
by Isaac Ben Moses ‘Eli (15th century)
מלאכת המספר / יצחק בן משה עלי
Sefer ha-Ḥeshbon we ha-Middot (The Book of Calculation and Measurement)
by Mordecai ben Eliezer Comṭino (1402-1482)
ספר החשבון והמדות / מרדכי בן אליעזר כומטינו
Sefer Diney Mamonot (Laws of Properties)
by Gad Astruk (1503)
ספר דיני ממונות / גד אשתרוק
Collection from Fra Luca
by Gad Astruk? (1503)
לקוטים מספר פראלוקא / גד אשתרוק
Sefer ha-Mispar (The Book of Number)
by Elijah Mizraḥi (1450-1526)
ספר המספר / אליהו מזרחי
"To Calculate a Number" - an anonymous textbook לחשב מספר / אנונימי
JTS 2634/6 textbook from Latin ניו יורק 2634/6 - ספר חשבון מלאטינית
Arithmetic Textbook by R. Aharon ben Isaac כללי המספר ורוב פרטיו / אהרון בן יצחק
Arithmetic Textbook by Meir Shapira ביאור דרכי חשבון / מאיר שפירא
Sefer ha-Kelalim ba-Mispar (The Book on the Rules of Number) ספר הכללים במספר
Anonymous Hebrew-Italian Textbook ספר חשבון עברי-איטלקי אנונימי
Sefer Agris ספר אגריס
Ḥeshbon shel Shevarim (Calculation of Fractions) חשבון של שברים
Sefer Ṣifra ספר ציפרא
Ḥeshbon ze ha-Niqra Ṣifor (Calculation called Ṣifor) חשבון הנקרא ציפור
Qeṣat mi-ʽInyanei Ḥoḵmat ha-Mispar (Some Issues of Arithmetic) קצת מענייני חכמת המספר
Abū Kāmil Shujāʽ: Kitāb fī al-Jābr wa'l-Muqābala (the first section, first Hebrew version)
tr. Mordecai Finzi
חשבון השטחים / מרדכי פינצי
Abū Kāmil Shujāʽ: Kitāb fī al-Jābr wa'l-Muqābala (the first section, second Hebrew version)
tr. Mordecai Finzi
תחבולות המספר / מרדכי פינצי
Abū Kāmil Shujāʽ: The second section: on pentagons and decagons
tr. Mordecai Finzi
המחומשים והמעושרים / מרדכי פינצי
Abū Kāmil Shujāʽ: Kitāb Masā’il allatī hiya ghair Maḥdūda (The third section on indeterminate equations)
tr. Mordecai Finzi
השאלות החרשות/האלמות/ מרדכי פינצי
Maestro Dardi: Aliabraa Argibra
tr. Mordecai Finzi
ספר ג'יבלי אלמוקבאלא / מרדכי פינצי
Ḥeshbon ha-Alzibra (Calculation of Algebra)
by Simon Moṭoṭ
ספר האלזיברא / שמעון מוטוט
Arabic in Hebrew Characters
כתאב אקלידס פי אלאצול - Arabic in Hebrew Characters
Al-HAṢṢĀR - Arabic in Hebrew Characters
Kitāb al-Kāfī fī Mukhtaṣar al-Hind - Arabic in Hebrew Characters
Takmila fi al-Hisāb - Arabic in Hebrew Characters
אלתסהילאת פי פך אלמגהולאת - Arabic in Hebrew Characters
Arabic Texts
كتاب اوقْلِيدس في الأُصول
Commentary of al-Nayrīzī on Euclid’s Elements


The Hebrew text (right column) should reflect the text as appears in the manuscript:

  • No additional punctuation marks are inserted, but line breaks are used to separate sentences.
  • Text in superscript represents additions above the manuscript lines
  • Struck-through text represents text in the manuscript with deletion marks
  • Corrections, additions and comments in the margins of manuscripts are marked by references, preceded by the abbreviation: "marg."

The translation and commentary (left column) include interpretive elements:

  • Headings reflect the content of the text, even if they are not stated by the author.
  • Mathematical formalization should reflect the procedure described in the text while avoiding anachronism as much as possible (although some anachronism is inevitable). The general procedures are in black, the demonstrations in blue and errors are marked in red. The translation is not always complete, literal or up to contemporary standards of translations of scientific sources.

If the text has survived in a single manuscript, the numbers of the pages are noted in the text.

The metadata includes the following details (where available): date of birth and place of birth of author, date of death and place of death of the author, the date and place of composition.

The list of bibliographical items includes only the items that specifically deal with the text. If the text is a translation or a commentary, there is no need to include the items that concern the original.

Where available, we include links to manuscript sources. However, these may change, resulting in broken links.