Johannes Kepler

Harmonice Mundi


is a book written entirely in Latin, where Kepler discusses harmony & congruence in geometrical forms and physical phenomena.


There is the earliest mathematical understanding of two types of regular star polyhedra, commonly referred to as Kepler's solids or Kepler Polyhedra, viz:

⭐ the small stellated dodecahedron
⭐ the great stellated dodecahedron



The concept of musical harmonies intrinsically existing within the spacing of the planets existed in medieval philosophy prior to Kepler, i.e. Musica universalis

While medieval philosophers spoke metaphorically of the music of the spheres

Kepler discovered physical harmonies in planetary motion:

where the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion.

The final section of the work relates his discovery of
3^rd law of planetary motion


which shows a constant proportionality between the cube of the semi-major axis of a planet's orbit and the square of the time of its orbital period with relation to astronomical explanations.


The full title of the book is Harmonices mundi libri V
The Five Books of The Harmony of the World

which is commonly but ungrammatically shortened to Harmonices Mundi 1     2     3     4     K     V