Kepler Harmonices Mundi

J. Kepler, Harmonices Mundi (The Harmonies of the World) , Plank, Linz, 1619. 

Johannes Kepler, Harmonices mundi libri V (Linz, 1619). Robert Burton, The Anatomy of Melancholy Oxioid, 1621). Livius Galante, Christianae Theologiae cum platonica... 

Figure 1 A depiction of the five elements shown here as the five Platonic soiids. From Johann Kepler s hook Harmonices Mundi of 1619...

FIGURE 4. Polyhedra in Johannes Kepler s Harmonices Mundi (Linz, 1619). Note the five Platonic solids on the middle right of this figure representing the four earthly elements Air, Fire, Water, and Earth as well as the fifth (heavenly) element Ether (courtesy of Division of Rare and Manuscript Collection, Carl A. Kroch Library, Cornell University). 

Kepler s polyhedral model is beautifully illustrated and described on page 95 of the book by 1st-van and Magdolna Hargittai, Symmetry—Unifying Concept, Shelter, Bolinas, CA, 1994. This book also inspired my use of the polyhedra in Kepler s Harmonices Mundi. 

Before joining Brahe, Kepler had published a book in which he proposed that the structure of the planetary system was based on the five regular polyhedra, an idea clearly derived from the Pythagoreans. Using Brahe s observations Kepler formulated his first two laws of planetary motion. These state that the planets move in elliptical orbits with the sun at one focus, and that a line from the sun to a planet sweeps out equal areas in equal times. These ideas were published in Astronomia Nova in 1609. Kepler s third major work, Harmonice Mundi, was published in 1619. As well as containing his third law (the square of the planetary period of revolution is proportional to the cube of the mean distance of the planet... 

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