Unknown · c. 150–850 CE
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The earliest known Hebrew treatise on geometry — a concise practical manual of mensuration covering the areas and perimeters of plane figures, the measurement of circles and segments, and an early value for π.
It is built from terse measurement rules, each tied to a labeled geometric figure and a worked numeric example. There is no demonstration in the Euclidean sense and no attempt at one: the reader is told how to measure a figure, shown the figure, and walked through a case with numbers. The work covers the plane figures and then the circle, including the segment — the hardest of the elementary mensuration problems, and the one where an approximation for π has to be committed to.
The printed edition closes with an epilogue of geometry, and opens with a dedicatory letter and the editor’s introduction.
Its importance is partly that it exists at all: a Hebrew geometry, in the practical Near Eastern tradition of measurement rules rather than the Greek tradition of proof, standing at the head of everything Hebrew mathematics later became.
Its date is the open question, and the range is extraordinary — scholars have placed the archaic core anywhere from the Mishnaic period to the Geonic era. The 1864 edition attributes it to R. Avraham bar Ḥiyya ha-Nasi, but the text plainly predates him; proposals have run from the Tanna R. Nehemiah around 150 CE to a ninth-century origin argued by Gandz. The corpus lists the author as Unknown for that reason. The stakes are not merely antiquarian: an early date would make this a bridge between rabbinic and Greek mathematics, and a late one makes it a product of the Arabic scientific world.
This volume presents Moritz Steinschneider’s critical edition (Berlin, 1864), where the work appears under the title Mischnat ha-Middot.