The Hebrew Geometrical Compendium.

The Hebrew Geometrical Compendium (HGC) is one of the most complete encyclopedic presentations of geometry from the Middle Ages extant today. The compendium presents mainly works by Euclid, Archimedes, Hypsicles, Theodosius, Menelaus, but relies also on Thābit Ibn Qurra, and on some additional materials from Greek and Arabic geometry. The text was first noticed by Tzvi Langermann, who commented that the compilation could have originally been written in either Greek, Arabic, or Hebrew. The present study confirms that it was written in Hebrew and was addressed to a Jewish audience. With the exception of some unidentified additions at the end of HGC V, all the texts included in the compilation were available in Hebrew translations by Moses Ibn Tibbon, Jacob ben Makhir, and Qalonimos ben Qalonimos. The compiler relied on these translations. It is likely that he could read some Arabic and/or Latin, but definite proof of this ability has not been found. Three preliminary studies of HGC are included in this paper. The first introduces this interesting text, its context, structure, sources, genre and editorial strategies. The second offers a synopsis of the books that deal with plane geometry, namely HGC I-III and V, which cover Elements I--IV and VI. More than half of HGC V is imported from other -- some known, some unknown -- sources. There is no way to know if these additions include original contributions. The third study focuses on a particularly interesting part of HGC: the presentation of the first book of Archimedes' Sphere and Cylinder. With considerable rearrangements, exporting and importing of propositions, a few deletions, and several additions, presumably his own ideas, the compiler of HGC offers a bold and original interpretation of Archimedes' canonical text. [ABSTRACT FROM AUTHOR]