In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented later.
See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , be a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289-290.
Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: "Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet's orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ).
In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented later.
See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , be a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289-290.
Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: "Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet's orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ).
Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), p. 189. From the bottom of p. 189: "Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, … ")
An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
Johannes Kepler, Astronomia nova … (1609), p. 5 of the Introductio in hoc opus (Introduction to this work). From page 5:"Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam, … Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem, … " (The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone, … However the moon flies swiftly across the zenith; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west, … )
In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented later.
See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , be a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289-290.
Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: "Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet's orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ).
In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented later.
See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , be a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289-290.
Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: "Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet's orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ).
Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), p. 189. From the bottom of p. 189: "Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, … ")
An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
