The brilliant German mathematician Johannes Kepler (1571-1630), one of the founders of modern astronomy, revolutionized the Copernican heliocentric theory of the universe with his three laws of motion: that the planets move not in circular but elliptical orbits, that their speed is greatest when nearest the sun, and that the sun and planets form an integrated system. This volume contains two of his most important works: The Epitome of Copernican Astronomy (books 4 and 5 of which are translated here) is a textbook of Copernican science, remarkable for the prominence given to physical astronomy and for the extension to the Jovian system of the laws recently discovered to regulate the motions of the Planets. Harmonies of the World (book 5 of which is translated here) expounds an elaborate system of celestial harmonies depending on the varying velocities of the planets.

The History and Practice of Ancient Astronomy combines new scholarship with hands-on science to bring readers into direct contact with the work of ancient astronomers. While tracing ideas from ancient Babylon to sixteenth-century Europe, the book places its greatest emphasis on the Greek period, when astronomers developed the geometric and philosophical ideas that have determined the subsequent character of Western astronomy. The author approaches this history through the concrete details of ancient astronomical practice. Carefully organized and generously illustrated, the book can teach readers how to do real astronomy using the methods of ancient astronomers. For example, readers will learn to predict the next retrograde motion of Jupiter using either the arithmetical methods of the Babylonians or the geometric methods of Ptolemy. They will learn how to use an astrolabe and how to design sundials using Greek and Roman techniques. The book also contains supplementary exercises and patterns for making some working astronomical instruments, including an astrolabe and an equatorium. More than a presentation of astronomical methods, the book provides a critical look at the evidence used to reconstruct ancient astronomy. It includes extensive excerpts from ancient texts, meticulous documentation, and lively discussions of the role of astronomy in the various cultures. Accessible to a wide audience, this book will appeal to anyone interested in how our understanding of our place in the universe has changed and developed, from ancient times through the Renaissance.

In the disastrous years before and during the Second World War, when confidence in a harmonious future was as difficult as it was crucial for spiritual survival, two German artists in exile wrote what would become their late masterpieces. The composer Paul Hindemith conceived an opera on the famous astronomer Johannes Kepler's mature life and theories, The Harmony of the World; the poet and novelist Hermann Hesse wrote a complex literary collage, i>The Glass Bead Game. Both works address the topic of universal harmony in the fabric of creation and culture, as well as the urgent problem of how such harmony can heal the spiritual, mental, and emotional developments of individuals and of society at large. The two quests are mirrored into circumstances that are almost equidistant from the mid-20th-century period in which their stories are being told. Hindemith's opera centers on an outstanding intellectual in the late 16th and early 17th centuries, while Hesse's work focuses on this intellectual's counterpart projected into a fictional world of the early 23rd century. In both cases, the quest for harmony and truthful proportion manifests at all levels of the stories told and of the works telling them. Siglind Bruhn's thought-provoking interdisciplinary study is organized along the lines of the seven areas in which scholars of the Pythagorean tradition from Plato to Kepler and beyond found universal harmony paradigmatically realized music, arithmetic, geometry and astronomy (the quadrivium of the medieval liberal arts) complemented by metaphysics, psychology, and art.