Moritz Steinschneider dated the Mishnat ha-Middot to between 800 and 1200 CE.[1] 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.[2][3]
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.[4]Solomon Gandz conjectured that the text was compiled no later than 150 CE (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.[5] The content resembles both the work of Hero of Alexandria (c. 100 CE) and that of al-Khwārizmī (c. 800 CE) and the proponents of the earlier dating therefore see the Mishnat ha-Middot linking Greek and Islamic mathematics.[6]
Modern history
The Mishnat ha-Middot was discovered in MS 36 of the Munich Library by Moritz Steinschneider in 1862.[1] 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.[7] Steinschneider published the work in 1864, in honour of the seventieth birthday of Leopold Zunz.[8] The text was edited and published again by mathematician Hermann Schapira in 1880.[4]
Although primarily a practical work, the Mishnat ha-Middot attempts to define terms and explain both geometric application and theory.[9] 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.[10] The text concludes with a discussion of the proportions of the Tabernacle in Chapter VI.[11][12]
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 22⁄7 instead.[5] The book arrives at this approximation by calculating the area of a circle according to the formulae
^ abSteinschneider, Moritz, ed. (1864). Mischnat ha-Middot, die erste Geometrische Schrift in Hebräischer Sprache, nest Epilog der Geometrie des Abr. ben Chija (in Hebrew and German). Berlin.{{cite book}}: CS1 maint: location missing publisher (link)
^Sarfatti, Gad B. (1993). "Mishnat ha-Middot". In Ben-Shammai, H. (ed.). Ḥiqrei Ever ve-Arav [Festschrift Joshua Blau] (in Hebrew). Tel Aviv and Jerusalem. p. 463.{{cite book}}: CS1 maint: location missing publisher (link)
^Langermann, Y. Tzvi (2002). "On the Beginnings of Hebrew Scientific Literature and on Studying History through "Maqbiloṯ" (Parallels)". Aleph. 2 (2). Indiana University Press: 169–189. doi:10.2979/ALE.2002.-.2.169. JSTOR40385478. S2CID170928770.
^ abSchapira, Hermann, ed. (1880). "Mischnath Ha-Middoth". Zeitschrift für Mathematik und Physik (in Hebrew and German). Leipzig.
^Gandz, Solomon (1938–1939). "Studies in Hebrew Mathematics and Astronomy". Proceedings of the American Academy for Jewish Research. 9. American Academy for Jewish Research: 5–50. doi:10.2307/3622087. JSTOR3622087.
^Thomson, William (November 1933). "Review: The Mishnat ha-Middot by Solomon Gandz". Isis. 20 (1). University of Chicago Press: 274–280. doi:10.1086/346775. JSTOR224893.
^Sarfatti, Gad B. (1974). "Some remarks about the Prague manuscript of Mishnat ha-Middot". Hebrew Union College Annual. 45: 197–204. ISSN0360-9049. JSTOR23506855.
External links
MS Heb. c. 18, Catalogue of the Genizah Fragments in the Bodleian Libraries.