This article concerns the exact sciences in Byzantium, namely the four traditional sciences that were usually designated in the Middle Ages by the term quadrivium : arithmetic, astonomy, geometry and music. It offers a review of the Byzantine texts and documents preserved in these domains from the sixth century to the Fall of Constantinople. The article presents the leading trends : continuation of Hellenistic Greek science, Islamic Jewish or Latin influences, in practical or scholarly directions, as well as the great (...) historical changes that mark the stages of scientific knowledge. The ancillary sciences, geography, optics and mechanics, as well as astrology, are briefly sketched. (shrink)

This paper gives a critical edition of the Treatise on the Easter Computus of Barlaam of Seminara, with a French translation and commentary. Written around 1333 this treatise demonstrates systematically and scientifically why the Easter Canon used at that time by the Church is superseded. Nevertheless Barlaam advises that the usual Canon should not be changed. In spite of its objectivity, Barlaam's treatise must be seen in the context of his rivalry with Nicephorus Gregoras, who had already proposed to modify (...) the Canon. The paper analyses Gregoras' text and gives a comparison with Barlaam's treatise. At the scientific level, both scholars rely on Ptolemy for the date of the spring equinox and the length of the Solar year, but Barlaam introduces a supplementary argument, which is the inexactness of the 19 year cycle. (shrink)