Chapter XXVII: Introduction

In spite of the high development of geometry among the Greeks it never took root as a pure science in the western Roman world,[249] and neither the various practical applications of its principles nor its use as a disciplinary educational subject sufficed to fasten thoughtful attention upon it; in consequence, it lost almost its entire content. As it appears in the four writers who treat of it in later Roman and early medieval times, Martianus Capella, Boethius,[250] Cassiodorus, and Isidore, it furnishes a striking commentary upon the intellectual conservatism that could retain without a suspicion of criticism a subject that was no longer anything but empty form.

[249] Cantor, _Vorlesungen über Geschichte der Mathematik_, vol.
i, p. 521.

[250] The authenticity of the work on geometry that has been
handed down under Boethius’ name is questioned. (See Cantor,
_ibid._, pp. 536 _et seq._) It contains the complete proof
of only three of Euclid’s propositions. It also contains
calculations of areas of geometrical figures. See edition of
Friedlein (Leipzig, 1867).

The substance of Isidore’s _De Geometria_ comes with little change from Cassiodorus. It is noteworthy that these two writers have nothing that does not go with the subject according to the modern conception of it, and do not follow the example of their predecessor Martianus Capella,[251] in whose account of the seven liberal arts the void caused by the loss of the proper content of geometry is filled with geography.

[251] _Cf._ Martianus Capella’s definition: “Geometria vocor
quod permeatam crebro admensamque tellurem eiusque figuram,
magnitudinem, locum, partes et stadia possim cum suis rationibus
explicare neque ulla sit in totius terrae diversitate partitio
quam non memoris cursu descriptionis absolvam.” Eyssenhardt, 198,
30.

TRANSLATION[252]

[252] The whole of Isidore’s _De Geometria_ is here given,
with the exception of a few passages that are untranslatable.
It is given as a whole to enforce attention to the loss of the
traditional content, partial or complete, which was so striking
a feature of all the members of the quadrivium in early medieval
times.