R. Mordecai Comtino · 15th c. (composition; this is a later manuscript copy)
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An instructional treatise on arithmetic and practical geometry by Mordecai ben Eliezer Comtino (Constantinople, 15th c.), one of the leading Rabbanite scholars of Byzantine Jewry. It combines numerical method with practical geometry, and no English translation is known.
The work divides into two books. The first is arithmetic, proceeding part by part and chapter by chapter through addition, multiplication — including squaring — and division, each carried through worked numeric examples in the manuscript’s own hand. A dedicated section of problems (meqom ha-she’elot) follows, where the operations are put to use.
The second book is the science of measures — geometry. It works through mensuration systematically: the measurement of triangles, including finding the altitude and the segments of the base, then the measurement of quadrilaterals and onward. The text is accompanied by labeled construction diagrams, and the prose is written to be followed with the figure in view.
Comtino taught Karaite as well as Rabbanite students, which is unusual enough to say something about how mathematics functioned in fifteenth-century Constantinople: it was common ground between communities that disagreed sharply about much else. The same crossing appears elsewhere in this corpus — Delmedigo’s Sefer Elim is a reply to the Karaite Zerah ben Nathan — and suggests the sciences were where these conversations could happen.
The pairing of arithmetic with practical geometry in one volume is also characteristic: this is mathematics for people who needed to compute and measure, in the tradition that Mizrahi, Comtino’s near-contemporary in the same city, was writing in as well.
The translated witness is BnF Hébreu 1031, folios 26r–65r — the same anthology that preserves ibn al-Aḥdab’s Keli Ḥemda and ibn Tibbon’s Roba’ Yisrael.