Mishnat ha-Middot

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The Mishnat ha-Middot (Hebrew: מִשְׁנַת הַמִּדּוֹת‎; "treatise of measures") is considered the earliest known Hebrew treatise on geometry. The treatise was discovered in the Munich Library by Moritz Steinschneider, who dated it between 800 and 1200 C.E. Hermann Schapira argued the treatise dates from an earlier period and Solomon Gandz conjectured Rabbi Nehemiah (c. 150 C.E.) to be the author. The content resembles both the work of Hero of Alexandria (c. 100 C.E.) and that of al-Khwārizmī (c. 800 C.E.) and the proponents of the earlier dating therefore see it linking Greek and Islamic mathematics.

The Mishnat ha-Middot argues against the common belief that the Bible defines the geometric ratio π (pi) as being exactly equal to 3 and defines it as 3 1/7 instead.[citation needed]

See also[edit]


  • Gandz, Solomon (ed.), 1932. “The Mishnat ha Middot, the First Hebrew Geometry of about 150 C.E., and the Geometry of Muhammad ibn Mūsā al-Khowarizmi, the First Arabic Geometry <c. 820>, Representing the Arabic Version of the Mishnat ha Middot. A New Edition of the Hebrew and Arabic Texts with Introduction, Translation and Notes”. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen 2.
  • Gandz, Solomon (ed.) (1958). Mishnat ha-Middot (English translation, 1932); Ẓarefati, in: Leshonenu, 23 (1958/59), pp. 156–71; 24 (1959/60), pp. 73–94.