Kepler

Book V of Kepler's The Harmony of the World

Book 5. Astronomical, on the causes of the periodic motions

Synopsis

Prooemium (Preface) Kepler exults over his third law (see Ch.3 below) found 15 may 1618 Ch.1. Regular polyhedra Orders them as: primary (cube, tetrahedron, dodecahedron) and secondary (octahedron, icosahedron) Tetrahedron = unmarried cubic marriage = octa inside cube dodecahedric marriage = icosa inside dodeca Ch.2. Harmonic proportions Obtains sphere proportions as: tetra, 1:3 cubic marriage, 1:sqrt(3) dodecahedric marriage, "ineffable" [1:sqrt(15-6*sqrt(5)] Ch.3. Astronomical theory 13 propositions, including the three laws Ch.4. The proper and extreme harmonies Tries various parameters Settles on the apsidal angular velocities Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Kepler exults over his third law (see Ch.3 below); found 15 may 1618
Ch.1. Regular polyhedra Orders them as: primary (cube, tetrahedron, dodecahedron) and secondary (octahedron, icosahedron) Tetrahedron = unmarried cubic marriage = octa inside cube dodecahedric marriage = icosa inside dodeca Ch.2. Harmonic proportions Obtains sphere proportions as: tetra, 1:3 cubic marriage, 1:sqrt(3) dodecahedric marriage, "ineffable" [1:sqrt(15-6*sqrt(5)] Ch.3. Astronomical theory 13 propositions, including the three laws Ch.4. The proper and extreme harmonies Tries various parameters Settles on the apsidal angular velocities Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Orders them as: primary (cube, tetrahedron, dodecahedron) and secondary (octahedron, icosahedron); Tetrahedron = unmarried; cubic marriage = octa inside cube; dodecahedric marriage = icosa inside dodeca
Ch.2. Harmonic proportions Obtains sphere proportions as: tetra, 1:3 cubic marriage, 1:sqrt(3) dodecahedric marriage, "ineffable" [1:sqrt(15-6*sqrt(5)] Ch.3. Astronomical theory 13 propositions, including the three laws Ch.4. The proper and extreme harmonies Tries various parameters Settles on the apsidal angular velocities Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Obtains sphere proportions as: tetra, 1:3; cubic marriage, 1:sqrt(3); dodecahedric marriage, "ineffable" [1:sqrt(15-6*sqrt(5)]
Ch.3. Astronomical theory 13 propositions, including the three laws Ch.4. The proper and extreme harmonies Tries various parameters Settles on the apsidal angular velocities Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: 13 propositions, including the three laws
Ch.4. The proper and extreme harmonies Tries various parameters Settles on the apsidal angular velocities Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Tries various parameters; Settles on the apsidal angular velocities
Ch.5. The music of the planetary motions Transposes all planet ranges to Saturn's octave Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Transposes all planet ranges to Saturn's octave
Ch.6. Heavenly modes Staff notations for all six planetary ranges Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Staff notations for all six planetary ranges
Ch.7. Universal harmonies Six part polyphony, chords Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Six part polyphony, chords
Ch.8. The four voices of celestial harmony Assigns planets to four choruses Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Assigns planets to four choruses
Ch.9. The causes of the eccentricities Very long (almost half of Book V) 9 axioms, 39 propositions, and a summary establishes that the world harmony model is more accurate than the platonic solids model Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Very long (almost half of Book V); 9 axioms, 39 propositions, and a summary; establishes that the world harmony model; is more accurate than the platonic solids model
Ch.10. Inhabitants of the Sun Speculates on the angels in the sun who watch and hear the world harmony influenced by Proclus?: Speculates on the angels in the sun who; watch and hear the world harmony; influenced by Proclus?

Cf (Stephenson, 1994; ch 9).

Rev'd 14 apr 2003 by ralph abraham