I have written about Johannes’ Kepler’s studies of Platonic and Archimedean solids several times on this blog. In those write-ups, I would use publicly available reproductions of Kepler’s works. Recently I discovered that Kepler’s original editions reside in Southern California, within driving distance from my home. It turns out that the California Institute of Technology (Caltech) acquired these rare books in the 1950’s, and they are available to view by appointment with the Caltech Archives.
I jumped at the opportunity to view these books, graciously shown to me and several American Institute of Mathematics mathematicians by Caltech Archivist Peter Collopy. The experience was an unforgettable view into the world of science, art, and communication of the late 16th and early 17th century.
The first work shown to us was the original edition of Mysterium Cosmographicum, printed in 1596. This was Kepler’s treatise on the solar system. I have never been in the presence of a book this old that was not in a glass case. The pages were in excellent condition. Their longevity is due to the fact that paper in those days was made of linen fibers.
The most famous picture from Mysterium was this foldout:
The image shows Kepler’s concept of the Solar system. At the time, he thought that the proportions of the radii of orbits of various planets around the sun were the same as the proportions of radii of inscribed and circumscribed spheres of nested Platonic Solids. You can see these solids shown as frames, going outside to inside: cube, tetrahedron, dodecahedron, icosahedron, and octahedron. The octahedron is so small that it is difficult to see, and the sun inside it is even harder to see. Fortunately, we were able to take a close up view:
The sun has a face! I found this so delightful that I made a reel about it to the tune of an appropriately named Beatles song. The fine detail of the image was only possible if the image was engraved, as opposed to a woodcut. Just as in the present day we decide to allot more resolution to images based on their importance and level of detail, so too in Kepler’s time, only very fine images were deemed worthwhile to be engraved.
The next work we saw was the first printing of Harmonices Mundi, Harmonies of the World, from 1619. Some of the topics presented in the wide-ranging work are Kepler’s theory of how music was related to the movement of the planets in the solar system and his work on geometric solids. The title page had a beautiful woodcut decoration shown in detail below.
I was particularly thrilled to see the iconic prints of the Archimedean Solids, which Kepler had rediscovered.
There is also this famous page which I call “polyhedron salad”:
In the upper right are instructions for making Platonic solids, and in the middle right are the elements (air, fire, the zodiac, earth, water) associated to the Platonic Solids. I have written about these solids on this blog. The other solids on the page are ones that Kepler has discovered— the stellated ones in the lower left and the rhombic ones on the lower right. The only reason I can think of as to why so many important solids were put together on one page is that this entire page was engraved. I am imagining that it must have been easier to put them all on one page, rather than have an engraving each solid as part of a printed page.
Seeing these original editions was especially meaningful because, in their day, they were the state of the art way of communicating the beauty of polyhedra. These works continue to serve as inspiration for my work of conveying the beauty of math through Geometiles.