Mishnat ha-Middot
{{Short description|Hebrew work on geometry}}
The Mishnat ha-Middot ({{langx|he|מִשְׁנַת הַמִּדּוֹת}}, {{small|lit.}} 'Treatise of Measures') is the earliest known Hebrew treatise on geometry, composed of 49 mishnayot in six chapters. Scholars have dated the work to either the Mishnaic period or the early Islamic era.
History
=Date of composition=
Moritz Steinschneider dated the Mishnat ha-Middot to between 800 and 1200 CE.{{cite book|editor-first=Moritz|editor-last=Steinschneider|editor-link=Moritz Steinschneider|title=Mischnat ha-Middot, die erste Geometrische Schrift in Hebräischer Sprache, nest Epilog der Geometrie des Abr. ben Chija|location=Berlin|date=1864|language=Hebrew, German}} Sarfatti and Langermann have advanced Steinschneider's claim of Arabic influence on the work's terminology, and date the text to the early ninth century.{{cite book|first=Gad B.|last=Sarfatti|language=he|chapter=Mishnat ha-Middot|editor-first=H.|editor-last=Ben-Shammai|title=Ḥiqrei Ever ve-Arav [Festschrift Joshua Blau]|location=Tel Aviv and Jerusalem|date=1993|page=463}}{{cite journal|title=On the Beginnings of Hebrew Scientific Literature and on Studying History through "Maqbiloṯ" (Parallels)|first=Y. Tzvi|last=Langermann|journal=Aleph|volume=2|issue=2|year=2002|pages=169–189|publisher=Indiana University Press|jstor=40385478|doi=10.2979/ALE.2002.-.2.169|s2cid=170928770}}
On the other hand, Hermann Schapira argued that the treatise dates from an earlier era, most likely the Mishnaic period, as its mathematical terminology differs from that of the Hebrew mathematicians of the Arab period.{{r|schapira}} Solomon Gandz conjectured that the text was compiled no later than {{CE|150}} (possibly by Rabbi Nehemiah) and intended to be a part of the Mishnah, but was excluded from its final canonical edition because the work was regarded as too secular. The content resembles both the work of Hero of Alexandria (c. {{CE|100}}) and that of al-Khwārizmī (c. {{CE|800}}) and the proponents of the earlier dating therefore see the Mishnat ha-Middot linking Greek and Islamic mathematics.{{cite journal|title=Studies in Hebrew Mathematics and Astronomy|author-link=Solomon Gandz|first=Solomon|last=Gandz|journal=Proceedings of the American Academy for Jewish Research|volume=9|date=1938–1939|pages=5–50|publisher=American Academy for Jewish Research|jstor=3622087|doi=10.2307/3622087}}
=Modern history=
The Mishnat ha-Middot was discovered in MS 36 of the Munich Library by Moritz Steinschneider in 1862.{{r|steinschneider}} The manuscript, copied in Constantinople in 1480, goes as far as the end of Chapter V. According to the colophon, the copyist believed the text to be complete.{{cite journal|last=Scheiber|first=Sándor|author-link=Sándor Scheiber|issn=0360-9049|journal=Hebrew Union College Annual|pages=191–196|title=Prague manuscript of Mishnat ha-Middot|volume=45|jstor=23506854|year=1974}} Steinschneider published the work in 1864, in honour of the seventieth birthday of Leopold Zunz.{{r|thomson}} The text was edited and published again by mathematician Hermann Schapira in 1880.{{cite journal|editor-first=Hermann|editor-last=Schapira|editor-link=Hermann Schapira|title=Mischnath Ha-Middoth|location=Leipzig|year=1880|language=Hebrew, German|journal=Zeitschrift für Mathematik und Physik}}
After the discovery by Otto Neugebauer of a genizah-fragment in the Bodleian Library containing Chapter VI, Solomon Gandz published a complete version of the Mishnat ha-Middot in 1932, accompanied by a thorough philological analysis. A third manuscript of the work was found among uncatalogued material in the Archives of the Jewish Museum of Prague in 1965.{{r|scheiber}}
Contents
Although primarily a practical work, the Mishnat ha-Middot attempts to define terms and explain both geometric application and theory.{{cite journal|title=Solomon Gandz, 1884–1954|first=Martin|last=Levey|journal=Isis|volume=46|number=2|date=June 1955|pages=107–110|publisher=University of Chicago Press|jstor=227124|doi=10.1086/348405|s2cid=143232106}} The book begins with a discussion that defines "aspects" for the different kinds of plane figures (quadrilateral, triangle, circle, and segment of a circle) in Chapter I (§1–5), and with the basic principles of measurement of areas (§6–9). In Chapter II, the work introduces concise rules for the measurement of plane figures (§1–4), as well as a few problems in the calculation of volume (§5–12). In Chapters III–V, the Mishnat ha-Middot explains again in detail the measurement of the four types of plane figures, with reference to numerical examples.{{cite journal|title=Reflections on the Sources of Arabic Geometry|first=Erwin|last=Neuenschwander|journal=Sudhoffs Archiv|volume=72|issue=2|year=1988|pages=160–169|publisher=Franz Steiner Verlag|jstor=20777187}} The text concludes with a discussion of the proportions of the Tabernacle in Chapter VI.{{r|mishnathamiddot}}{{cite journal|last=Sarfatti|first=Gad B.|issn=0360-9049|journal=Hebrew Union College Annual|pages=197–204|title=Some remarks about the Prague manuscript of Mishnat ha-Middot|volume=45|year=1974|jstor=23506855}}
The treatise argues against the common belief that the Tanakh defines the geometric ratio π as being exactly equal to 3 and defines it as Approximations of π instead.{{cite journal|title=The Sources of Al-Khowārizmī's Algebra|first=Solomon|last=Gandz|author-link=Solomon Gandz|journal=Osiris|volume=1|date=January 1936|pages=263–277|publisher=University of Chicago Press|jstor=301610|doi=10.1086/368426|s2cid=60770737}} The book arrives at this approximation by calculating the area of a circle according to the formulae
: and .{{r|mishnathamiddot|page=II§3, V§3}}
See also
References
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External links
- [https://genizah.bodleian.ox.ac.uk/catalog/volume_29#MS_Heb_c_18-part10-item1 MS Heb. c. 18], Catalogue of the Genizah Fragments in the Bodleian Libraries.
{{Authority control}}
Category:15th-century manuscripts
Category:Bodleian Library collection
Category:Hebrew-language literature
Category:History of mathematics