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 All will find a practical way to grasp a body of knowledge that, if long neglected, is never out of date.
"Peter Ulrickson’s book is a marvelously lucid and engaging summa of the quadrivial arts of geometry, arithmetic, music, and astronomy. The book breathes new life into these arts and presents them with just the right amount of detail and in a spirit of fitting wonder. It contains a wealth of well-chosen examples and practical exercises that are both instructive and fun. This is the definitive text on the quadrivium. It is perfect for use in the classroom and for those who wish to know, through first-hand experience, why the arts of number and measure—together with the trivial arts of grammar, logic, and rhetoric—were long recognized as providing the foundation of a liberally educated human being."~Peter Kalkavage, St. John's College