## The Harmony of the World"Johannes Kepler published Harmonies of the World in 1619. This was the summation of his theories about celestial correspondences, and ties together the ratios of the planetary orbits, musical theory, and the Platonic solids. Kepler's speculations are long discredited. However, this work stands as a bridge between the Hermetic philosophy of the Renaissance, which sought systems of symbolic correspondences in the fabric of nature, and modern science. And today, we finally have heard the music of the spheres: data from outer system probes have been translated into acoustic form, and we can listen to strange clicks and moans from Jupiter's magnetosphere." -- Amazon.com viewed August 11, 2020. |

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I really appreciate the work of the authors, making this text accessible at no cost to modern English readers. It is slow reading for me, but really rewarding. One can understand Kepler's frame of mind and how he saw the world, and how this understanding provides the framework for his mathematical arguments.

I'm not a mathematician, but I do question whether all the illustrations are genuine or complete or correctly placed. I came across one or two sections where I had the feeling the diagrams weren't fully explained or supported by the text.

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according actual angles aphelion apparent aspects Axiom body Book called cause Chapter chord circle combined common compared complete congruence considered consonances construction continuous corresponding cube definition diameter diatessaron diesis dissonant distances divided division double Earth Elements equal Euclid Expressible extreme fact faculty fifth figures five follows former four fourth geometrical given gives greater half hand hard harmonies heptagon hexagon individual intervals Jupiter Kepler kind latter laws length less major Mars mean melody Mercury mind minor motions musical namely nature octave origin pairs pentagon perfect perihelion planets position proportion Proposition quantity ratio reason reference regular remaining result right angles Saturn scale semitone sense side single sixth smaller soft solid soul sounds spheres square star string taken things third tion tone triangle trigon true Venus whole

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Page xxxviii - write the book. Whether it is to be read by the people of the present or of the future makes no difference; let it await its reader for a hundred years, if God Himself has stood ready for six thousand years for one to study Him.""

Page 77 - the side of a regular hexagon inscribed in a circle is equal to the radius of the circle

Page 395 - distances of the Earth and Saturn from the Sun. For the cube root of 1 is 1, and the square of that is 1.

Page 58 - is the side of a square whose area is equal to that of a rectangle

Page 41 - add up to twice as many Right angles as the figure has sides, less four.

Page 254 - the archbishops of Mainz, Cologne, and Trier, the King of Bohemia, the Count Palatine and the Margrave of Brandenburg.

Page 57 - That is, the square of the side of the pentagon is equal to the sum of the squares of the sides of the

Page 374 - If you forgive me, I shall rejoice; if you are enraged with me, I shall bear it. See, I cast the die, and I write the book. Whether it is to be read by the people of the present or of the future makes no difference: let it await its reader for a hundred years, if God Himself has stood ready for six thousand years for one to study him.

Page 481 - as long as I shall live. For from Him and through Him and in Him are all things,

Page 284 - (He is not far from every one of us; in Him we live, move and have our being.)