A history of Greek mathematics - Wilbourhall.org

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224 SUCCESSORS OF THE GREAT GEOMETERS
to have been a sort of encyclopaedia of the subject. The
quotations of Proclus from Geminus's work do not stand
alone; we have other collections of extracts, some more and
some less extensive, and showing varieties of tradition according
to the channel through which they came down. The
scholia to Euclid's Elements, Book I, contain a considerable
part of the commentary on the Definitions of Book I, and are
valuable in that they give Geminus pure and simple, whereas
Proclus includes extracts from other authors. Extracts from
Geminus of considerable length are included in the Arabic
commentary by an-Nairizi (about A.D. 900) who got them
through the medium of Greek commentaries on Euclid,
especially that of Simplicius. It does not appear to be
doubted any longer that Aganis ' ' in an-Nairizi is really
Geminus ; this is inferred from the close agreement between
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an-Nairizi's quotations from Aganis ' and the corresponding
passages in Proclus ; the difficulty caused by the fact
that Simplicius calls Aganis ' socius noster ' is met by the
suggestion that the particular word socius is either the
result of the double translation from the Greek or means
nothing more, in the mouth of Simplicius, than ' colleague
in the sense of a worker in the same field, or authority ' \
A few extracts again are included in the Anonymi variae
collectiones in Hultsch's Heron, Nos. 5-14 give definitions of
geometry, logistic,
geodesy and their subject-matter, remarks
on bodies as continuous magnitudes, the three dimensions as
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principles ' of geometry, the purpose of geometry, and lastly
on optics, with its subdivisions, optics proper, Gatoptriea and
o-KT}uoypa(f>LKrj, scene-painting (a sort of perspective), with some
fundamental principles of optics, e.g. that all light travels
along straight lines (which are broken in the cases of reflection
and refraction), and the division between optics and natural
philosophy (the theory of light), it
being the province of the
latter to investigate (what is a matter of indifference to optics)
whether (1) visual rays issue from the eye, (2) images proceed
from the object and impinge on the eye, or (3) the intervening
air is aligned or compacted with the beam-like breath or
emanation from the eye.
Nos. 80-6 again in the same collection give the Peripatetic
explanation of the name mathematics, adding that the term