R. Avraham bar Ḥiyya ha-Nasi · c. 1136
Read the translation (PDF) · Editorial footnotes (PDF)
A medieval Hebrew treatise on mathematical astronomy and the computation of the Jewish calendar. It sets out the structure of the heavens and the courses of the sun, moon, and planets, then applies them to the molad (conjunction), the tekufot (seasonal points), the nineteen-year cycle, and the rules of intercalation.
The work is organized into twenty gates, and it begins further back than its title suggests: the first gate teaches arithmetic itself — subtracting one number from another, multiplying degrees and fractions, dividing them, extracting roots. Bar Ḥiyya assumes a reader who wants the astronomy but may not yet have the computation, and supplies both.
The second gate turns to arcs and their chords, the trigonometric foundation of everything that follows, and the next gates work through the geometry of the sphere: the arc between the surfaces, the ascensions of the zodiacal signs on the equator and on the dividing circle, the latitudes of places north of the equator.
The later gates are where the book’s cosmopolitanism shows. Alongside the length of the solar and lunar years, bar Ḥiyya gives procedures for converting Hebrew years to the Egyptian reckoning, sets out the basis of the reckoning of the Arabs, converts between Anno Mundi and Hijra years in both directions, finds the weekday on which a Hijra year begins, computes planetary motions from Hijra years, and gives the root of the reckoning of the Greeks and Romans by the Sun.
Bar Ḥiyya stands at the head of the Hebrew tradition of computational astronomy that later authors such as Gersonides would extend — he is writing this material in Hebrew, with its vocabulary, more or less for the first time. The era-conversion gates capture his position precisely: a scholar in twelfth-century Barcelona, known in Latin as Savasorda, moving between Jewish, Muslim and classical reckonings because his world contained all three.
The translated volume reproduces a 1960 printing of the text.