## The Harmony of the WorldJohanne 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." |

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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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Apotome arithmetic aspects Axiom Bodin body Book Chapter comma congruence consonances construction cube decagon Definition degree diameter diapason diapente diatessaron diesis dissonant distances divided division dodecagon dodecahedron Earth eccentric Elasson equal Euclid trans Expressible extreme motions fact faculty fifth figures follows four right angles fourth geometrical greater harmonic proportions Harmonice mundi harmonies Heath heptagon hexagon icosahedron Jupiter Kepler kind knowability latter major tone Mars mathematical mean Medial melodic intervals melody Mercury mind minor sixth minor third minor tone Mizon motion at aphelion motion at perihelion motion of Saturn musical nature number of sides octagon octahedron octave pairs pentagon perfect perihelion planetary planets Plato polygons position Proclus Proposition Ptolemy Ptolemy's Pythagoreans quantity ratio reason rectangle Saturn semitone sensible sixth soft solid soul spheres square star string tetrachords tetragon tetragon angle tetrahedron things third tion triangle trigon angles Venus zodiac

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

Page 413 - 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 268 - 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 392 - 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 499 - as long as I shall live. For from Him and through Him and in Him are all things,

Page 302 - (He is not far from every one of us; in Him we live, move and have our being.)