R. Eliyahu Mizrahi · c. 1500
Read the translation (PDF) · Editorial footnotes (PDF)
Kitsur ha-Melakhat ha-Mispar (“Compendium of the Art of Number”) is a Hebrew arithmetic textbook by Rabbi Eliyahu Mizrahi (ca. 1455–1526), the chief rabbi of the Ottoman Empire and one of the foremost Jewish mathematicians of his age.
Drawing on the Greek and Arabic traditions, it lays out the practical art of calculation step by step. It opens on the kinds of numeration, then takes the operations in turn: gathering (addition), striking (multiplication) — including the methods for multiplying multi-digit numbers — subtraction, and division, each carried through worked examples. From there it proceeds to the kinds of fractions, and onward to ratios and proportions, progressions and roots, and the rules for solving the everyday problems of trade and measurement.
A feature worth noticing is how much attention goes to verification. Each operation is followed by its check — the scales or balance, the casting-out method — so the student learns not only how to compute but how to know whether the computation is right. That instinct runs through the Hebrew mathematical tradition in this corpus, from bar Ḥiyya’s gate on testing a molad onward.
Mizrahi wrote from Constantinople at the head of Ottoman Jewry, and this book became the standard introduction to arithmetic for Hebrew readers. It is lucid and systematic in a way textbooks of its period often are not, and it is the computational floor beneath the astronomy: the tables and reckonings elsewhere in this corpus assume exactly the skills taught here.
The translation is made from the Hebrew text as printed in the first edition (Basel, 1546), where the work was bound together with bar Ḥiyya’s astronomy — the same volume, with the same Münster apparatus, that supplied Sefer Tsurat ha-Arets. It opens with Münster’s address to the studious and fair-minded reader.