R. Avraham bar Ḥiyya ha-Nasi · c. 1122
Read the translation (PDF) · Editorial footnotes (PDF)
The earliest systematic Hebrew treatise on the science of the calendar, written in early-twelfth-century Barcelona. It sets out the astronomical and mathematical foundations of the Jewish calendar — the calculation of the new moon, the cycles that govern leap years, the reckoning of the seasons, and the interplay of lunar and solar time.
The work is built in discourses (ma’amarim), each divided into gates. The first discourse establishes the physical picture before the arithmetic: the form of the firmament, the motion of the sphere over the earth and how the constellations stand within it, and then the variation among places of habitation from north to south — the fact that makes calendar reckoning depend on where the observer is. Ten gates carry that argument through.
The second discourse turns to computation proper, and to the machinery a practitioner needs. Its later gates work through deriving the moladot from tables built for intercalation, supply the tables of the moladot in the simple and double cycles, and — characteristically — devote a part to checking a molad, to determine whether an error has crept into the reckoning. Bar Ḥiyya is as concerned with verifying a result as with obtaining it.
This is where the Hebrew science of the calendar becomes a systematic discipline rather than a body of inherited rules. Bar Ḥiyya writes it in Hebrew, supplies both the astronomy and the arithmetic, and organizes it so it can be taught — and later calendar scholars copied that organization for centuries. It is the foundation on which the rest of the Hebrew calendrical tradition in this corpus stands.
The printed volume carries an editor’s apparatus alongside the text: an introduction, a life of the author surveying his other works — Tsurat ha-Arets, Cheshbon Mahalechot ha-Kochavim, the Luchot ha-Nasi tables, Hegyon ha-Nefesh and Megillat ha-Megalleh — and explanatory notes, including the editor’s own attempt at a difficult dictum in the ninth gate of the second discourse, addressed to bar Ḥiyya directly.