Research for this article was supportd by a grant from the American Philosophical Society. The Institute for the History of Science and Technology of what was then the Leningrad Branch of the Academy of Science of the USSR, the Archives of the Leningrad Branch, and Dr Nina Ivanovna Nevskaya in particular, responded to my enquiries with extraordinary hospitality. The generous assistance of Dr Volker Bialas of the Kepler Kommission of the Bayerische Akademie der Wissenschaften in correcting transcripts of some of the passages from the manuscripts is gratefully acknowledged.

¹ Copernicus, , De revolutionibus, Nuremberg 1543, 1, 10, fols. 9^r and 10^rGoogle Scholar; Kepler, , Mysterium cosmographicum, Tübingen, 1596, ch. 1, pp. 15–16Google Scholar, in Johannes Kepler Gesammelte Werke (KGW), i, pp. 18–19Google Scholar, translated as The Secret of the Universe by Duncan, A. M., New York, 1981, 80–1Google Scholar (hereafter cited as Secret…).

² Kepler, to Maestlin, , 14 09 1595Google Scholar, letter 22 in KGW, xiii, 33.Google Scholar

³ Astronomia nova αιτιολογητος, the title Kepler gave to his great work on Mars.

⁴ Kepler, to Maestlin, , 14 09 1595Google Scholar, letter 22 in KGW, xiii, 33.Google Scholar

⁵ Kepler, to Maestlin, , 3 10 1595Google Scholar, letter 23 in KGW, xiii, 33.Google Scholar

⁶ Mysterium cosmographicum, Tübingen, 1596, 69–74Google Scholar, in KGW, i, 68–72Google Scholar, Secret…, 196–203.Google Scholar

⁷ The ‘whole eccentricity’ is the eccentricity of the equant. Kepler actually wrote ‘the third part of the whole eccentricity’ here, because the eccentricity of the Copernican eccentric is half again as great as that of the Ptolemaic eccentric. This is a result of Copernicus's substitution of a small epicycle for Ptolemy's equant. Kepler discusses the partial equivalence of this substitution in chapter 4 of the Astronomia nova (KGW, iii, 73–7).Google Scholar

⁸ Mysterium cosmographicum, ch. 22, 78–9Google Scholar, KGW, i, 76–7Google Scholar, Secret…, 216–19. The present translation is mine, and differs significantly from Duncan's in certain places.

⁹ Although there are numerous examples of pre-Keplerian systems that attempt to relate speed to distance from some centre or other (such as those of Telesio, Patrizi, Campanella and Lydiat, as well as Aristotle and other ancients), none that I am aware of (other than the Ptolemaic equant, which applies only to planets singly) was used to generate testable results. Even the Cartesian vortices, which were conceived as providing a mechanism that could produce the results already noted and quantified by Kepler, failed to give an adequate simultaneous account of Kepler's three planetary laws. See Aiton, E. J., The Vortex Theory of Planetary Motion, New York, 1972.Google Scholar

¹⁰ ‘Dupl. (a:b)’ stands for ‘The duplicate ratio of a to b’. Euclid states, ‘When three magnitudes are proportional, the first is said to have to the third the duplicate ratio of that which it has to the second’ (Elements, Book v, Definition 9).

¹¹ Kepler manuscripts, vol. 14, fols. 307^r–310^v.Google Scholar

¹² Fol. 276 of the manuscripts, vol. 14, contains the date 23 November 1601. Since the pages were numbered by Kepler and their contents are almost entirely sequential, the ‘Consideratio’ appears to have been written in December 1601 or January 1602. On the dating of the manuscripts, see Gingerich, Owen, ‘Kepler's treatment of redundant observations’, Internationales Kepler-Symposium Weil der Stadt 1971 (ed. Krafft, F., Meyer, Karl and Sticker, Bernhard), Hildesheim 1973, 307–14Google Scholar. Gingerich states (p. 313) that ‘the end of the notebook seems to come late in 1601 or at the beginning of 1602’. However, Gingerich missed the sections on the oval (fols. 356–8 and elsewhere), as well as the Easter date on fol. 351^v. These require that the end of the notebook be dated no earlier than the beginning of April 1602. See also Donahue, W. H., ‘Kepler's first thoughts on the oval’, Journal for the History of Astronomy (1993), 75, 71–100.CrossRefGoogle Scholar

¹³ For example, vol. 14, fols. 356^v–8^vGoogle Scholar, where Kepler considers the evidence and comes to accept the idea of an oval orbit.

¹⁴ The passage appears in Frisch, Christian, Joannis Kepleri astronomi opera omnia, 8 vols., Frankfurt 1858–1870, viii, 229–34Google Scholar (cited as Opera omnia).

¹⁵ Manuscripts, vol. 14, fol. 307^rGoogle Scholar, in Opera omnia, viii, 229Google Scholar: ‘Deinde planetam pro accessu vel recessu a Sole tarde vel velociter incedere, id physicum est. Confirmant id planetae secum bini comparati. Cujus enim est longior radius, longior etiam est in aequali spatio mora. Porro differentia haec est, quod in binis et binis non est omnino proportionalis tarditas ambitui…sed est consilio accommodata ad harmonicas rationes, in uno vero et eodem tarditas vel mora omnino proportionalis est distantiae. Nam quae alia esset ratio accommodationis eccentricitatis aequantis ad eccentricitatem eccentrici?’

¹⁶ These results were later to appear in Astronomia nova, chs. 19 and 16, respectively.

¹⁷ Manuscripts, vol. 14, fol. 308^vGoogle Scholar, in Opera omnia, viii, 229–30Google Scholar: ‘Hinc mihi nata est nova speculatio, eccentricitatem aequantis non manere per totum circuitum eandem, eam causam esse, cur major eccentrici altitudo prodeat ex observationes ακρονυχιοις, cum aequantis eccentricitas assumta sit manere eadem in omnibus 4 sitibus ακρονυχιοις’.

¹⁸ Manuscripts, vol. 14, fol. 308^rGoogle Scholar, in Opera omnia, viii, 230Google Scholar: ‘Porro quamvis hoc quam proxime verum sit, eccentrici altitudinem aequantis esse dimidium, tamen neque Copernici, ut prius dictum, neque Ptolemaei hypothesis rei satisfacit, eo quod ex hisce principiis (cum motum proportionalem distantiis assumsimus), ut supra dictum, aequantis punctum idem non manet. Distantiae enim parum mutantur circa apsides, multum in longitudinibus mediis, eo quod illic in circumferentiam circuli lineae e Sole quasi perpendiculariter incidunt, quemadmodum η δια κεντρον, hic vero ut in obliquam’.

¹⁹ Kepler, , New Astronomy (tr. Donahue, W. H.), Cambridge, 1992, 467Google Scholar, note 6, and 589.

²⁰ Manuscripts, vol. 14, fol. 308^rGoogle Scholar, in Opera omnia, viii, 230Google Scholar: ‘Porro quaeritur, et quomodo invenienda sit ex hac hypothesi dimensio orbium, et quomodo calculanda aequationum tabula? De posteriori prius. ‘Cum in circulo sint infinita puncta, sat subtiliter egerimus, si circulum dicamus habere sexagies 360 puncta, totidem radios e centro et rursum totidem e Sole in eodem illo imaginemur. Tunc ergo ut summa omnium radiorum ad tempus periodicum planetae, ita summa aliquot ordine distantiarum in unam summam conjectarum ad tempus, quod labitur, dum omnes illas distantias planeta facit’.

²¹ In Definition 3 of Book v of the Elements, Euclid stipulates that ratios must be between magnitudes ‘of the same kind’. Thus no ratio could exist between a distance and a time.

²² Manuscripts, vol. 14, fol. 309^rGoogle Scholar, in Opera omnia, viii, 231Google Scholar: ‘Sane hoc verisimilitudinem facit, quod supra inter binos et binos planetas medium proportionale valuit, si hac speculatione potuissemus uti. Data ergo proportione temporis, quae est inter gradum unum apogaeum et medium, datur proportio radiorum, et data proportione temporis, quod est inter aliquot arcus apogaeos et medios, datur proportio summae radiorum mediocrium et apogaeorum. Haec quidem supra ταυτολογιαν nobis peperunt. Nam non ita scitur tempus mediorum arcuum, ut inter planetas’.

²³ Manuscripts, vol. 14, fol. 309^vGoogle Scholar, in Opera omnia, viii, 232Google Scholar: ‘Sed considera: ut mediocris distantia ad longam, sic mediocris arcus ad longum arcum, ut jam tempus sit arcus. Cum ergo haec distantia illum arcum moderetur et ponat, non est absurdum, et hujus distantiae arcum complecti illius arcus distantiam. An vero in eadem proportione, dubitatur’.

²⁴ ‘Investigatio methodi ad inveniendas eccentrictates’, in manuscripts, vol. 14, fol. 315^rGoogle Scholar. This passage does not appear in Frisch's edition, though he does include a section entitled ‘Methodus construendi aequationes et distantias’, which he describes as ‘the first rudiments of Kepler's attempts at establishing the laws of areas in the motions of the planets’. Here, as elsewhere, Frish does not name a source for his text.

²⁵ ‘Sint loca D.C.E. in Eccentrico. Et noti anguli EAC, CAD: Nota etiam tempora in EC, et CD. Ergo ut tempus EC ad totam revolutionem sic planum EAC ad planum circulj’.

²⁶ Archimedes, , Measurement of a CircleGoogle Scholar, Proposition 1, in The Works of Archimedes (ed. Heath, T. L.), Cambridge, 1897 etc., 91–3.Google Scholar

²⁷ That is, the sun. Since Kepler presents many of his arguments in Ptolemaic, Copernican and Tychonic forms, he used this phrase to avoid having to specify what was at the centre in the various systems.

²⁸ Astronomia nova, ch. 40, in KCW, iii, 264–5.Google Scholar

²⁹ Kepler himself remarks, a few pages later, that the area law is not exactly equivalent to the distance law, and throughout the Astronomia nova regards it as only a convenient means of computation. See Aiton, E. J., ‘Kepler's second law of planetary motion’, Isis (1969), 60, 75–90.CrossRefGoogle Scholar

³⁰ Kepler, manuscripts, vol. 14, fol. 358^vGoogle Scholar: ‘Tempus non numerat…Nisi forte sui corporis seu naturali contentione motus tempus ipse sibi facit aequalitatem motus spectans, tempus efficit’. For a complete transcription and further analysis of this page, see Donahue, , op cit. (12).Google Scholar

³¹ Kepler, manuscripts, vol. 14, fol. 358^vGoogle Scholar: ‘Non est bona definitio motus aequalis cuius partes tempori sint proportionales. Definitur enim sic ratione eius intellectus. Inest in ipsa motus esse alia causa aequalitatis, unde haec temporis aequalitis postmodum sequitur.’

³² Letter to Maestlin, Michael of 3 10 1595Google Scholar, no. 23 in KCW, xiii, 35.Google Scholar

³³ Aristotle, , Physics, IV, 11, 220 a 25.Google Scholar

³⁴ For Kepler's portrayal of himself as an Aristotelian, or of Aristotle as a Keplerian, see Epitome astronomiae Copernicanae, Linz, , 1618–1620, 421–5Google Scholar, in KGW, vii, 251–3.Google Scholar