A history of Greek mathematics - Wilbourhall.org

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PEDIASIMUS. BARLAAM. ARGYRUS 555
ordinary fractions and sexagesimal fractions (printed at
Strassburg in 1592 and at Paris in 1600). Barlaam, as we
have seen, knew the Heronian formulae for finding successive
approximations to square roots, and was aware that they could
be indefinitely continued.
Isaac Argyrus, a monk, who lived before 1368, was one of
a number of Byzantine translators of Persian astronomical
works. In mathematics he wrote a Geodaesia and scholia to
the first six Books of Euclid's Elements. The former is contained
in the Paris MS. 2428 and is called 'a method of
geodesy or the measurement of surfaces, exact and shortened '
the introductory letter addressed to one Colybos is followed
by a compilation of extracts from the Geometrica and Stereometrica
of Heron. He is apparently the author of some
further additions to Rhabdas's revision of the Manual of
Planudes contained in the same manuscript. A short tract
of his On f the discovery of the square roots of non-rational
square numbers ' is mentioned as contained in two other manuscripts
at Venice and Rome respectively (Codd. Marcianus Gr.
333 and Vaticanus Gr. 1058), where it is followed by a table
of the square roots of all numbers from 1 to 102 in sexagesimal
fractions (e.g.