Mathematics occupies a central place in the traditional liberal arts.
The four mathematical disciplines of the quadrivium-arithmetic,
geometry, music, and astronomy-reveal their enduring significance in
this work, which offers the first unified, textbook treatment of these
four subjects. Drawing on fundamental sources including Euclid,
Boethius, and Ptolemy, this presentation respects the proper character
of each discipline while revealing the relations among these liberal
arts, as well as their connections to later mathematical and scientific
developments.
This book makes the quadrivium newly accessible in a number of ways.
First, the careful choice of material from ancient sources means that
students receive a faithful, integral impression of the classical
quadrivium without being burdened or confused by an unwieldy mass of
scattered results. Second, the terminology and symbols that are used
convey the real insights of older mathematical approaches without
introducing needless archaism. Finally, and perhaps most importantly,
the book is filled with hundreds of exercises. Mathematics must be
learned actively, and the exercises structured to complement the text,
and proportioned to the powers of a learner to offer a clear path by
which students make quadrivial knowledge their own.
Many readers can profit from this introduction to the quadrivium.
Students in high school will acquire a sense of the nature of
mathematical proof and become confident in using mathematical language.
College students can discover that mathematics is more than procedure,
while also gaining insight into an intellectual current that influenced
authors they are already reading: authors such as Plato, Aristotle,
Augustine, Thomas Aquinas, and Dante. All will find a practical way to
grasp a body of knowledge that, if long neglected, is never out of date.
