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quadrivium, the term he created to define the collection of the four-fold
path of learning in the mathematical sciences: arithmetic, music, geometry
and astronomy. He also followed in Symmachus's footsteps entering
public office to become the highest ranking official in the court of the
Ostrogothic king Theodoric the Great (c. 454-526), ruler of post-Roman
Italy, the man who would ultimately condemn him to death for the act of
treason [17].
Boëthius, along with Augustine and Aristotle, is considered to be a
fundamental philosophical author of late antiquity. His most famous work
De consolatione philosophiae
was written during his imprisonment in
Pavia before his execution there in 524 [18]. His treatises on arithmetic,
geometry, and music were not only essential contributions to the
quadrivium, but also contain a wealth of visualizations. The sources for his
works on arithmetic,
De institutione arithmetica
[19], and music,
De
institutione musica
, are believed to have been Pythagoras, Plato, Aristotle,
and, in particular, his direct translations from the Greek of Nicomachus of
Gerasa's (c. 60-c. 120) works,
Introduction to Arithmetic
[20] and
Manual
of Harmonics
[21].
Boëthius believed as Macrobius did that visual representation of
information was an important pedagogical tool for clarifying concepts. As
a result, his works on arithmetic and music are filled with illustrations.
Fig. 1.2 shows a diagram from Book 1 of
De institutione arithmetica
taken
from a mid-ninth century manuscript created in the region around Laon,
France (MS Cod. Sang. 248, fol. 10a, St. Gallen, Stiftsbibliothek) [22],
which he uses as part of a discussion of “the nature of the odd times the
even.” At the core of this diagram is a 4 x 4 square array consisting of
even numbers that are related through multiplication. Boethius takes a
cartographic approach to the table's design,
3
employing the terms
“latitude” and “longitude” to designate rows and columns, respectively,
and connecting these with arcs, each of which is labelled with a number
that is the product of two numbers anchoring each arc. For example, the
multiplication of the far left number 12 by the far right number 96 of the
top row produces 1152 (ƯcLii), the number viewed along the apical arc.
3. It is reasonable to assume that Boëthius's use of latitude and longitude was
influenced by his reading and translation of Ptolemy's works. Ptolemy (Claudius
Ptolemaeus, c. 90-c. 168 CE) has been credited with the invention of these terms,
and was the first individual to place a grid on a map [23, p. 3].
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