Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

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.

Johanne Kepler's "Harmonice mundi" was planned in 1599 as a sequel to the "Mysterium cosmographicum." In 1618 Kepler discovered the third law of planetary motion relating to the periodic times of the planets to their mean distances from the sun - a crowning achievement that enabled him to bring the "Harmonice mundi" to completeion. The authors have presented and interpreted Kepler's Latin text to readers of English, by putting it into "the kind of clear but earnest language which we suppose Kepler would have used if he had been writing today."

Kepler's essay, On the Six-Cornered Snowflake, provides the first published evidence of the ideas of regular arrangements and close-packing which have proved fundamental to crystallography. In it, Kepler ponders on the problem of why snowflakes are hexagonal, two centuries before the first successful steps were taken towards its solution. The purpose of this volume is to display the historical, literary, scientific, and philosophical treasures of Kepler's essay. The book includes the modernized text of the 1611 Latin edition, with an English translation by Colin Hardie on the opposite pages. The text is accompanied by an introduction giving details of the history of the work, and two essays; Professor B. J. Mason's discussion of the scientific meaning and validity of Kepler's arguments and their relation to the history of crystallography and of space filling, and L. L. Whyte's examination of Kepler's facultas formatrix in relation to the history of philosophical and scientific ideas on the genesis of forms.

The Harmony of the World, by Johannes Kepler, is not only a seminal work in the history of astronomy, but a case study in the creative process of discovery. By rejecting empiricism and sense certainty, Kepler used his mental instruments, geometry and music, to investigate the harmony which orders all fundamental physical processes. The same mental processes which make humans unique must be coherent with the principles of creation and development of the universe as a whole. Kepler is remembered today chiefly for the 3 laws of planetary motion known after him. Rejecting the view of those who regarded astronomical hypotheses as mathematical fictions, Kepler sought to derive the true motions of the planets from physical causes. Yet he combined his search for physical causes with a vision of the world as a manifestation of divine harmony. Kepler's book contradicts Aristotle, who held science back for centuries because of his witting fraud upon the discoveries of Pythagoras, Thales, et al. Aristotle misrepresented the ideas concerning Music, Harmonics, Geometry as well as Astronomy, which Plato described in the Epinomis to be the fount of all knowledge. In this volume, Kepler proves that the pre-Aristotelean hypothesis of a helio-centric universe is correct, and provides the needed data to demonstrate that the planets arrange their orbits around the sun in the manner of a musical scale. Here one can understand the deeper meaning of Harmony, beyond what we hear in music. Kepler seeks out causes, in the musical domain, as well as in the astrophysical domain. Up to the time of this book, no one had solved the puzzle. Though written centuries ago, The Harmony of the World remains a work of genius.