Mishnat Ha-Middot

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MISHNAT HA-MIDDOT (Heb. מִשְׁנַת הַמִּדּוֹת; "treatise of measures"), considered the earliest Hebrew geometry. Mishnat ha-Middot comprises various methods for determining the dimensions of various plane and solid geometric figures. Its five chapters include, among other matters, a discussion of triangles, quadrilaterals, and frusta. The Heronic formula for the area of a triangle in terms of the lengths of the sides is given. For π the value of 31/7 is used and this divergence from the biblical 3 is homiletically justified. One of the extant manuscripts has a sixth chapter dealing with the Tabernacle which is similar to sections of the *Baraita de-Melekhet ha-Mishkan. In spite of the similar names, there seems to be no connection between this work and the Baraita de-49 Middot which is frequently cited by medieval commentators. This treatise is written in a distinctive Hebrew that combines mishnaic style with a technical terminology that has affinities with Arabic, although it stands apart from the Hebrew mathematical terminology of the Hispano-Arabic period. In content, the Mishnat ha-Middot belongs to the stream of Oriental mathematics represented, e.g., by Heron, Greek mathematician (c. 100 c.e.) in the Hellenistic period, and al-Khwarizmi (c. 825 c.e.) in the Arabic period, to both of whose works it offers striking parallels. Some attribute it to R. *Nehemiah (c. 150 c.e.), and see it as a link between the Hellenistic and Arabic texts, while others assign it to an unknown author of the Arabic period.


S. Gandz (ed.), Mishnat ha-Middot (Eng., trans. 1932); Ẓarefati, in: Leshonenu, 23 (1958/59), 156–71; 24 (1959/60), 73–94.

[Benjamin Weiss]