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 only in 1621.
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, ... is a perfect ellipse: ... ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289–290.
Kepler stated that every planet travels 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), book 5, chapter 3, 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.
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 only in 1621.
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, ... is a perfect ellipse: ... ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289–290.
Kepler stated that every planet travels 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), book 5, chapter 3, 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.
Mercator, Nic. (1670년 3월 25일). “Some considerations of Mr. Nic. Mercator, concerning the geometrick and direct method of signior Cassini for finding the apogees, excentricities, and anomalies of the planets; ...” (라틴어). 《Philosophical Transactions of the Royal Society of London》 5 (57): 1168–1175. doi:10.1098/rstl.1670.0018. Mercator criticized Cassini's method of finding, from three observations, an orbit's line of apsides. Cassini had assumed (wrongly) that planets move uniformly along their elliptical orbits. From p. 1174: "Sed cum id Observationibus nequaquam congruere animadverteret, mutavit sententiam, & lineam veri motus Planetæ æqualibus temporibus æquales areas Ellipticas verrere professus est: ... " (But when he noticed that it didn't agree at all with observations, he changed his thinking, and he declared that a line [from the Sun to a planet, denoting] a planet's true motion, sweeps out equal areas of an ellipse in equal periods of time: ... [which is the "area" form of Kepler's second law])
Mercator, Nic. (1670년 3월 25일). “Some considerations of Mr. Nic. Mercator, concerning the geometrick and direct method of signior Cassini for finding the apogees, excentricities, and anomalies of the planets; ...” (라틴어). 《Philosophical Transactions of the Royal Society of London》 5 (57): 1168–1175. doi:10.1098/rstl.1670.0018. Mercator criticized Cassini's method of finding, from three observations, an orbit's line of apsides. Cassini had assumed (wrongly) that planets move uniformly along their elliptical orbits. From p. 1174: "Sed cum id Observationibus nequaquam congruere animadverteret, mutavit sententiam, & lineam veri motus Planetæ æqualibus temporibus æquales areas Ellipticas verrere professus est: ... " (But when he noticed that it didn't agree at all with observations, he changed his thinking, and he declared that a line [from the Sun to a planet, denoting] a planet's true motion, sweeps out equal areas of an ellipse in equal periods of time: ... [which is the "area" form of Kepler's second law])
