Did Tycho Eliminate the Celestial Spheres before 1586?

See Kuhn Thomas S. , The Copernican Revolution: Planetary astronomy in the development of Western thought (Cambridge, MA, 1957), 205f. Curiously, Christianson John R. adopts the same terminology in his discussion of the ‘crystalline’ spheres in his valuable study, On Tycho's island: Tycho Brahe and his assistants, 1570–1601 (Cambridge 2000), 64.

Kepler Johannes , Epitome astronomiae copernicanae , in Caspar M. (eds), Gesammelte Werke (Munich, 1937–), vii, 260f: “Solidos orbes … refellit Tycho Braheus.”.

Rosen Edward , “The dissolution of the celestial spheres”, Journal for the history of ideas , xlvi (1985), 13–31.

Ibid. 31. Rosen owed his information on Rothmann to Moran Bruce T. , “Christoph Rothmann, the Copernican theory, and institutional and technical influences on the criticism of Aristotelian cosmology”, Sixteenth century journal , iii (1982), 85–108, p. 108.

Lerner Michel-Pierre , “Le problème de la matière céleste après 1550: Aspects de la bataille des cieux fluids”, Revue d'histoire des sciences , xlii (1989), 255–80, p. 265. Lerner assumed here several results published by Edward Grant in a noteworthy article of 1987, which we cite below (ref. 12). Lerner offers further explication on the subject in his valuable monograph, Le monde des sphères (2 vols, Paris, 1996).

Lerner , “Le problème de la matière céleste après 1550” (ref. 5), 277.

Ibid. 277f.

Ibid. 279.

Goldstein B. R. Barker Peter , “The role of Rothmann in the dissolution of the celestial spheres”, The British journal for the history of science , xxviii (1995), 385–403, p. 387.

Ibid. 401. Cf. p. 385: “… he [Rosen] errs in giving Rothmann priority for views that Pena had already held.”.

Barker Peter , “Jean Pena (1528–58) and Stoic physics in the sixteenth century”, The Southern journal of philosophy , xxiii (1985), Supplement, 93–107. He had been preceded, however, by Jardine Nicholas , who in 1984 Called attention to Pena as “the first to challenge solid spheres on empirical grounds”; see Jardine N. , The birth of history and philosophy of science: Kepler's A defence of Tycho against Ursus with essays on its provenance and significance (Cambridge, 1984), 230. In subsequent publications Barker and his collaborators have continued to affirm Tycho's indebtedness to Rothmann, that is, that Tycho began to contemplate the inexistence of the celestial spheres only after reading Rothmann's treatise of 1586. See Barker Peter Goldstein Bernard R. , “Theological foundations of Kepler's astronomy”, in Brooke J. H. Osler M. J. van der Meer J. (eds), Science in theistic contexts: Cognitive dimensions (Osiris , 2nd ser., xvi (2001)), 88–113, p. 94Immediately after receiving this book [i.e., Rothmann's treatise on the comet of 1585], Tycho adopted the view that the substance of the heavens was a continuous fluid, solving the problem posed by the intersections of the orbs of Mars and the Sun.”.

Grant Edward , “Celestial orbs in the Middle Ages”, Isis , lxxviii (1987), 153–73. Grant has since published a vast historical reconstruction of the problem in its entirety. See Grant Edward , Planets, stars and orbs: The medieval cosmos, 1200–1687 (Cambridge 1994).

Grant , “Celestial orbs in the Middle Ages” (ref. 12), 153–5.

Ibid. 154.

Ibid. 154.

Ibid. , 156–9; our citation on p. 159.

Ibid. 172.

See Swerdlow Noel , “Pseudodoxia Copernicana: Or, enquiries into very many received tenets and commonly presumed truths, mostly concerning spheres”, Archives internationales d'histoire des sciences , xxvi (1976), 108–58; Jardine Nicholas , “The significance of the Copernican orbs”, Journal for the history of astronomy , xiii (1982), 168–94.

Grant , “Celestial orbs in the Middle Ages” (ref. 12), 172f. Cf. also Grant, Planets, stars and orbs (ref. 12), 347ff, where it is said, rather surprisingly, that “the firm connection [between solid and hard] occurred after Tycho's publication of 1588 and because of it, not between the time of Copernicus and Tycho”.

Cf., for example, Lerner Michel-Pierre , “Le problème de la matière céleste après 1550” (ref. 5), 257, 265; Lerner , Le monde des sphères (ref. 5), i, 158f.; Goldstein Barker , “The role of Rothmann in the dissolution of the celestial spheres” (ref. 9), 387.

Lerner , Le monde des sphères (ref. 5), i, 159; Granada Miguel A. , “II problema astronomico-cosmologico e le Sacre Scritture dopo Copernico: Christoph Rothmann e la ‘teoria dell'accomodazione”’, Rivista di storia della filosofia , li (1996), 789–828, esp. p. 805, also in idem, Sfere solide e cielo fluido: Momenti del dibattito cosmologico nella seconda metà del cinquecento (Milan, 2002), 89.

See Marcellus Palingenius Stellatus, Zodiacus vitae (Rotterdam, 1722), Book XI, “Aquarius”, vv. 350–2: “Proinde est durissimus aether / Plus adamante, adeo ut ferrum contemnat et ignem, / Vimque omnem, praeter Domini, a quo conditus ipse est.” Pena himself, in his De usu optices praefatio of 1557, characterized the Peripatetic ether as “solidum et durum”. See the edition in Ramus Petrus and Talaeus Audomarus , Collectaneae praefationes, epistolae, orationes (Marburg, 1599), 142.

Swerdlow , “Pseudodoxia Copernicana” (ref. 18), 113. In this article, Swerdlow continued to credit Tycho with the elimination of the spheres because of his observation of the course of the comet of 1577. See ibid. 113, 130, 137.

For a more thorough exposition of Rothmann's argument, see Granada Miguel A. , “Eliminazione delle sfere celesti e ipotesi astronomiche in un inedito di Christoph Rothmann: L'influenza di Jean Pena e la polemica con Pietro Ramo”, Rivista di storia della filosofia , lii (1997), 785–821 (also appearing in idem, Sfere solide e cielo fluido (ref. 21), 115–36). In this article (see Section 3), we indicate various irrefutable points in the Scriptum evidencing Rothmann's indebtedness to Pena.

See Brahe Tycho , Opera omnia , ed. by Dreyer J. L. E. (Copenhagen, 1913–29 [in what follows we refer to this edition as TBOO followed by the number of the volume; line numbers are given after the page numbers]), vi, 88: “Nec enim ego, multis ab hinc annis, in ea fui sententia, orbes aliquos realiter in caelo existere, materiamque caeli duram et imperviam esse, Stellasque tantum ad motum orbium convolvi. Multa siquidem hinc sequuntur absurda, et si nihil aliud, sane tot Cometae in aethere cursum praecedentibus aliquot annis exercere a nobis animadversi, qui nullius orbis ductum concomitabantur, idipsum sufficienter refellunt” [transl. in Rosen , “The dissolution of the celestial spheres” (ref. 3), 29]. Later, in a letter to Rothmann of November 1589, Tycho would attempt to quash his correspondent, imposing by the authority of his own word the priority of having eliminated the celestial spheres himself: “… cumque scias me etiam longe antequam de his somniaris idipsum concessisse atque pronuntiasse … quam [the fluidity of the heavens] ego nunquam denegavi, sed primus forte omnium id ita se habere non saltem assseverare, sed e certissimis demonstrationibus probare elaboravi”, ibid. 186 [transl. in Rosen , “The dissolution of the celestial spheres” (ref. 3), 29].

Rosen , “The dissolution of the solid celestial spheres” (ref. 3), 29f; Lerner , “Le problème de la matière céleste après 1550” (ref. 5), 276.

See Lerner , Le monde des sphères (ref. 5), ii, 3–20.

See the excellent summary in Lerner , “Le problème de la matière céleste après 1550” (ref. 5), 266–9, which contains additional references.

See Telesio Bernardino , Varii de naturalibus rebus libelli (a modern critical edition of which has been published by Luigi De Franco (Florence, 1981)), pp. 464f of the modern edition.

Bruno Giordano , The Ash Wednesday supper , transl. by Gosselin E. A. Lerner L. S. (Hamden, CT, 1977), 90 [for the original see Bruno G. , La cena de le ceneri , in Giovanni Aquilecchia (ed.), Oeuvres complétes , ii (Paris, 1994), 47–49].

“Planetae per aerem quasi pisces per aquam velocissime cientur.” The observation that comets exhibited a smaller parallax than that of the Moon, along with the assertion that they moved through air, led Muñoz to consider comets to be celestial phenomena and the heavens to be made up of air. On Muñoz's brief essay, which has yet not been published and which merits far greater attention than it has received, see Victor Navarro Brotóns and Enrique Rodríguez Galdeano, Matemáticas, cosmología y humanismo en la España del siglo XVI: Los ‘Comentarios al segundo libro de la Historia Natural de Plinio'de Jerónimo Muñoz (Valencia, 1998), 94–96. In contrast with Bruno and Patrizi, who acknowledge a hardness to the supposed spheres, Muñoz never explicitly addresses the question of their solidity or fluidity, but rather that of their mere existence as a plurality of individual orbs.

Neander Michael , Elementa sphaericae doctrinae, seu De primo motu (Basel, 1561), 22f. Neander studied until 1543 at Wittenberg, where he was the student of Melanchthon and Reinhold. Cf. Elementa 147: “Erasmus Reinholdus, praeceptor meus.” Neander is considered one of the first authors to employ the expression ‘Systema mundanum’ ( ibid. 20), which became part of general parlance only during the 1570s, firmly establishing itself during the 1580s. See Michel-Pierre Lerner, “The origin and meaning of ‘World System'”, Journal for the history of astronomy , xxxvi (2005), 407–41.

Neither Lerner nor Grant mentions Neander in their respective studies. A brief reference can be found in Randles W. G. L. , The unmaking of the medieval Christian cosmos, 1500–1700: From solid heavens to boundless aether (Aldershot, 1999), 46.

Praetorius Johannes , De cometis, qui antea visi sunt, et de eo, qui novissime mense novembre apparuit, narratio (Nuremberg, 1578). For more on Praetorius, see Westman Robert S. , “Three responses to the Copernican theory: Johannes Praetorius, Tycho Brahe and Michael Maestlin”, in Westman Robert S. (ed.), The Copernican achievement (Berkeley, Los Angeles and London, 1975), 285–345, pp. 289–305.

Praetorius , De cometis , sig. B3r-v. As we shall see later in this section, Praetorius was echoing the common “Wittenberg interpretation” of the nova.

Ibid. , sig. Cr. The shortage of instruments, claimed Praetorius, had prevented him from establishing the position and parallax of the comet of 1577, although he conjectured that the parallax had been diminishing, which contributed to the possibility that the comet had been rising in the heavens (“sursum ipsum [cometam] promotum fuisse”, ibid.). Contrary to Caspar Peucer (cf. Tycho Brahe, Astronomiae instauratae progymnasmata, TBOO , iii, 122, 12–19), Praetorius was also inclined towards the theory of Peter Apian, according to whom comets were exhalations deriving their brilliant appearances from illumination rather than fire. On this theory, see Barker Peter , “The optical theory of comets from Apian to Kepler”, Physis , xxx (1993), 1–25.

Praetorius , De cometis , sig. B3v: “Mihi sane hoc Sidus corroborare uidetur Ioh. Penae opinionem, qui reiecta Regionum Aëris discrepantia, ignis quoque Sphaera sublata, arbitratur aërem continuum, absque ulla materiae diuersitate, a nostro uisu ad extremas usque Stellas extendi.” Very probably Caspar Peucer, Jr, intends Jean Pena among the French authors alluded to as hostile to the Aristotelian distinction between supralunary and elementary realm, whose works were circulating in Wittenberg. Cf. his Quaestio on the nova proposed in Wittenberg in March 1573, reproduced in full by Tycho in Astronomiae instauratae progymnasmata, TBOO , iii, 132–5: “Etsi autem de Aristotelica discriminatione talis orae AEtherae et Elementaris, ante hoc tempus, et superioribus annis, etiam ex Italiae et Galliae doctis, aliqui quaerere ceperunt, et rem in controversiam vocavere, quorum disputationes in medio sunt” (134, 18–21; our italics).

We amend here our claim concerning the alleged meeting of Rothmann and Tycho with Praetorius in Wittenberg in 1575, as related in Granada Miguel A. , “Astronomy and cosmology in Kassel: The contributions of Christoph Rothmann and his relationship to Tycho Brahe and Jean Pena”, in Jitka Zamrzlová (ed.), Science in contact at the beginning of Scientific Revolution (Prague Studies in the History of Science and Technology, n.s., viii (Prague, 2004)), 237–48, pp. 244, 246. For Praetorius's life chronology, see Costil Pierre , André Dudith, humaniste hongrois, 1533–1589 (Paris, 1935), ad indicem. From March 1575 until late 1576 Praetorius resided in Cracow with Andreas Dudith.

See Rothmann Christoph , Scriptum de cometa , in Snell W. , Descriptio cometae, qui anno 1618 mense Novembri primum effulsit. Huc accessit Christophori Rothmanni… descriptio accurata cometae anni 1585 (Leiden, 1619), 137f: “Manifestum est, cometam nihil aliud esse quam globum in sublimi ex halitibus conflatum et a radiis solaribus illuminatum, qui pro sua raritate aut levitate vel caudam habeat, vel absque cauda appareat: Aut motu proprio instar reliquorum Planetarum … procedat, aut absque proprio motu semper in uno eodemque sphaerae stellarum fixarum loco immotus consistat”. Cf. ibid. 135, “Moveri etiam & circumduci [the comets] ut plurimum (quidam enim prorsus immoti consistunt) motu proprio” (our italics).

See TBOO , iv, 356–8.

See Astronomiae instauratae progymnasmata , in TBOO , iii, 153–7.

Ibid. 155f.: “Tamen, cum haec Stella aliquot centenis vicibus, molem, quam Terra et Maria componunt, exuperarit,… nullae sane exhalationes Terrae vel Maris, etiamsi Caelum subintrare possent (quod per se concedi nequit) ad tantum corpus conformandum sufficerent.”.

This quaestio was reproduced in its entirety by Tycho in Astronomiae instauratae progymnasmata , in TBOO , iii, 132–5.

Cf. Peucer, Jr, in Brahe Tycho , Astronomiae instauratae progymnasmata, TBOO , iii, 134, 32–36: “Cur [Aristoteles] perrumpere aliquid eo halituum aut anathumiáseon suarum non potest concedere? Nisi secundum Homerum [Ilias, 5, 504] prorsus aeneum Caelum introducamus, et ita compacta corpora orae Aethereae, ut poros nullos habeant. Sed hoc rursus alias habet enstáseis.”.

Also reproduced by Tycho in Astronomiae instauratae progymnasmata, TBOO , iii, 135–9.

See Schuler in Brahe Tycho , Progymnasmata, TBOO , iii, 138, 39–140, 2; 140, 14–30. For the conservation of the solid, impenetrable orbs, see ibid., 138, 39–48: “Institutus in Philosophia Aristotelica tot seculis approbata, et quae minus habet errorum, nequaquam concesserit exhalationes lentas et viscosas in generatione quidem Cometae ex Elementari regione ascendere in Aetheream, ibique accendi…. Hoc inquam, nequaquam concessero. Eo enim concesso, sequuntur plurima absurda. Conceditur penetratio dimensionum ut vulgo in scholiis appellatur, et effinguntur Orbibus Caelestibus meatus vel pori, sicut mixtis: Cum tamen sacra scriptura orbes expresse nominet Firmamentum et Graeci interpretes stereoma” (our italics). For lexical coincidences, in the opposite direction, between Schuler and Rothmann, see Rothmann's Scriptum de cometa (ref. 39), 117f, quoted below (ref. 52), with the allusion to the penetratio dimensionum.

For an exposition of this “Wittenberg Interpretation” of the nova in Cassiopeia see Weichenhan Michael , “Ergo perit coelum…”: Die Supernova des Jahres 1572 und die Überwindung der aristotelischen Kosmologie (Stuttgart, 2004), 472–88. Concerning Rothmann's anticipation by Hardeg see ibid. 476 and 486.

See Brahe Tycho , De stella nova , in TBOO , i, 27 f. For further explication of the contents of this work, see Dreyer J. L. E. , Tycho Brahe: A picture of scientific life and work in the sixteenth century (New York, 1963), 38–56; Thoren Victor E. , The Lord of Uraniborg: A biography of Tycho Brahe (Cambridge, 1990), 55–73; Weichenhan Michael , “Ergo perit coelum…” (ref. 47), 594–9.

We are grateful to Adam Mosley for the translation. The Latin reads: “Quod autem nec in orbe Saturni, nec Iovis, Martisve, aut aliorum Planetarum existat, hinc patet, quod elapso iam sex mensium spacio, nullo minuto ab eo loco, in quo primum eam conspeximus, motu proprio progressa est, quod fieri oportebat si in aliquo Planetarum orbe esset. Moveretur enim motu ipsius orbis peculiari, contra primi mobilis rationem…. Toti enim orbes propriis polis revoluti, sua circumducunt sidera, vel ab illis (ut Plinio et quibusdam aliis placere video) circumaguntur. Nisi quis receptam a Philosophis et Mathematicis sententiam negare velit, solasque stellas immotis orbibus convolvi (quod absurdum est) asserere. Unde si haec stella in aliquo orbium septem errantium siderum constitueretur, necesario cum ipso orbe, cui affixa esset, contra diurnam revolutionem circumduceretur. Atque hic motus etiam in lentissimo Saturni orbis progressu tanto temporis intervallo, etiam absque omni instrumento intuenti animadverteretur. Quapropter haec stella nova nec in Elementari infra Lunam, nec in orbibus septem errantium siderum, sed in octava sphaera inter reliquas fixas locum habet, quod erat demonstrandum”, TBOO , i, 27, 19–37 (our italics).

This objection was also stated later by Tycho against Caspar Peucer's location of the nova inside the spheres of Venus or Mercury by virtue of its presumed wide parallax of 19 minutes. See Brahe Tycho , Astronomiae instauratae progymnasmata, TBOO , iii, 125, 6–10: “At cum is [Peucer] tunc temporis Aristotelicis traditionibus nimium addictus, statuerit procul dubio Sphaeras Planetarum reales esse, quî quaeso fieri potuit, ut Stella haec, intra orbes Veneris sive Mercurii tanto tempore immobilis constaret, a nullo horum interea circumacta?” (our italics). As Maestlin did later on in the case of the comets of 1577 and 1580 (see below, ref. 69), neither Peucer nor the Landgrave Wilhelm IV (who conceded to the nova a parallax of 3 minutes and consequently located it in the sphere of Venus; see Brahe Tycho , Astronomiae instauratae progymnasmata 114, 128) felt obliged to attribute to the nova the motion of the planetary sphere in which it was placed.

Ibid. 28, 1–3.

Rothmann , Scriptum de cometa (ref. 39), 117f: “Ita iam patet, quomodo cometa in sphaera Saturni esse aut progredi potuerit…. ipse tamen cometarum motus firmissimo est argumento, sphaeras Planetarum corpora solida esse non posse. Fieri enim non potest quod corpus solidum admittat dimensionum penetrationem. Sic tu corpore tuo per parietem transire nequis. Non enim duo corpora simul in eodem loco Physico esse possunt. Ac toties iam a tot artificibus observatum est, firmissimeque ex Geometria demonstratum, cometas non tantum in regione Elementari, verumetiam supra Lunam in sphaeris Planetarum subsistere, longeque alium motum habere, quam habent Planetae ipsi, in quorum sphaeris subsistunt. Cum igitur nec penetratio dimensionum esse possit, nec unius sphaerae partes dispari ac dissimili motu moveri: Manifestum est Planetas in nullo alio corpore quam aere pendere, atque inibi tam constantissimo motu progredi.” We are grateful to Adam Mosley for the English translation.

This work was published for the first time in TBOO , iv, 381–96. An English translation with an excellent introductory study can be found in Christianson J. R. , “Tycho Brahe's German treatise on the comet of 1577: A study in science and politics”, Isis , lxx (1979), 110–40 (the treatise being located on pp. 132–41).

On these points see Christianson , “Tycho Brahe's German treatise on the comet of 1577” (ref. 53), 119f, 124–7, 130f; Thoren , The Lord of Uraniborg (ref. 48), 128–32.

TBOO , iv, 386–8; translation from Christianson (ref. 53), 135f.

TBOO , iv, 387; translation from Christianson (ref. 53), 135: “It thus follows through geometrical apportionment and reckoning, that this comet was at least 230 times the Earth's radius above the Earth.”.

Cf. van Helden Albert , Measuring the universe: Cosmic dimensions from Aristarchus to Halley (Chicago and London, 1985), 30, where an outline of the sizes and distances of planetary spheres according to Al-Farghani appears. The minimum and maximum distances for Venus are tabulated at 167 and 1120 terrestrial radii.

TBOO , iv, 387f; translation from Christianson (ref. 53), 136.

See Thoren , The Lord of Uraniborg (ref. 48), 239f.

TBOO , iv, 388; translation from Christianson (ref. 53), 136. For a reproduction of an original diagram of Tycho illustrating this Capellan disposition, see Christianson , 125. Rosen , “The dissolution of the solid celestial spheres” (ref. 3), 21, claimed, in our opinion erroneously, that “in Brahe's German treatise… he did not draw any cosmological conclusions”. Owen Gingerich, by contrast, saw the situation correctly according to our opinion; see his “Tycho Brahe and the great comet of 1577”, Sky and telescope , liv (1977), 452–8, pp. 456f, now in idem, The great Copernicus chase and other adventures in astronomical history (Cambridge, MA, 1992), 89–97. See also Gingerich Owen Westman Robert S. , The Wittich connection: Conflict and priority in late sixteenth-century cosmology (Transactions of the American Philosophical Society , lxxviii; Philadelphia, 1988), 47f. Incomprehensibly, Hellman Doris C. suggested in her influential study on the comet of 1577 ( The comet of 1577: Its place in the history of astronomy (New York, 1944), 122) that Tycho's 1578 piece “emphasizes the absence of parallax and consequently the untenability of the so-called Aristotelian concept of crystalline spheres”, an opinion recently echoed by Christianson (see ref. 1).

TBOO , iv, 385 f.; translation by Christianson (ref. 53), 134. As the diagram in Christianson , 125, shows, the comet's sphere was heliocentric (concentric to the spheres of Mercury and Venus around the Sun), and was included in the ‘carrier sphere’ of the Sun, by means of which, along with the inferior planets, it participated in the annual motion of the Sun in revolution around the central Earth.

TBOO , xiii, 305–25.

Ibid. 334f.

Ibid. 319: “… potes certior fieri, quod Cometa nullam habeat sensibilem parallaxin.”.

Maestlin Michael , Consideratio et observatio cometae aetherei astronomica, qui anno MDLXXX. mensibus Octobri, Novembri, et Decembri, in alto aethere apparuit (Heidelberg, 1581), p. xviii: “… manifestum est, Cometa[m] hunc nullam sensu perceptibilem parallaxin habuisse.”.

Ibid. , p. xxxiiii: “Verum ex qua sphaera trium superiorum, Saturni, ne Iovis an Martis (nam ex his tribus unum, hospicio hunc cometam recepisse, ex motus analogia colligi potest) terram horribili isto fulgori pulsarit, quamve spherae partem, sive orbem particularem inhabitaverit, ego iam… certo asserere non possum,… depraehendi posse puto, cometam hunc certi cuiusdam orbis ductum non minus secutum fuisse, quam de superiore Cometa demonstravi. Veruntamen crediderim motum eius ad Saturni sphaerae conversiones magis esse regularem, quam ad Iovis vel Martis sphaerae orbes, cuius etiam colorem tetrum magis quam caeterorum retulit.” It seems that Maestlin believed the comet could occupy a partial orb within the interior of the total sphere of the host planet.

As Dreyer reports in Tycho Brahe (ref. 48), note on p. 161, the orbit of the comet of 1580 was calculated in 1854 by Schjellerup H. C. F. in accordance with Tycho's observations. So far we have been unable to access Schjellerup's work.

TBOO , vii, 208, 21–25: “… quemadmodum in eo ipso Cometa, de quo nunc agimus [the comet of 1580; cf. in the same letter 204, 20f], affatim a me demonstratum est, is enim circa Solem instar Veneris et Mercurio obambulans neque etiam tam magnum designavit ambitum, ut Terram et Lunam simul includeret, et digresiones accessionesque ad Solem instar eorundem Planetarum oculis exhibuit.”.

In contrast with Tycho, Maestlin does not appear to have had any objection to locating the comets of 1577 and 1580 each in its own planetary sphere. Cf. Westman Robert S. , “The comet and the cosmos: Kepler, Mästlin and the Copernican hypothesis”, in Dobrzycki J. (ed.), The reception of Copernicus' heliocentric theory (Dordrecht, 1973), 7–30, p. 25.

“The comet's parallax nowhere can be discovered easily from these observations”, TBOO , xiii, 335. Cf. the letter to Hagecius T. of 23 September 1582 in TBOO , vii, 74, 18–19: “in tertio cometa [that from 1582] nondum feci periculum, nec adeo facile erit possible”; Apologetica responsio ad Craigum Scotum de cometis (written after May 1589), in TBOO , iv, 467: “… ut de eo [Cometa], qui anno 82 ob modicam durationem et supra horizontem boreum exiguam elevationem nunc nihil dicam [concerning parallax].” Later in 1597 Helisaeus Roeslin located it in the sphere of Venus. See Roeslin H. , Tractatus meteorastrologiphysicus (Strasbourg, 1597), 5v–6r.

TBOO , xiii, 315.

See Gingerich Westman , The Wittich connection (ref. 60), 48–50, 138–40.

“Each of the three epicycles for the major planets was a mirror of the orbis magnus of the Sun”, ibid. 49. See also Thoren , The Lord of Uraniborg (ref. 48), 243f.

TBOO , vi, 70, 29–42 (English translation in Gingerich and Westman, The Wittich connection (ref. 60), 70f). The claim here remains considerably ambiguous and appears rather to sketch out a line of research than to confirm an already acquired result. In any case, it is interesting to note that on the same page (lines 27–29) Tycho recalls the development in 1583 of a programme intended for the establishment of the various parallaxes of Venus and, as a consequence, the planet's circumsolar trajectory: “ipsius Veneris parallaxes pervestigare eodem anno non dubitabam, ut, an circa, vel infra Solem convolveretur, certius pateret.”.

TBOO , vii, 129, letter to Peucer C. of 13 September.

TBOO , vi, 86, letter of 20 1587; 179, letter of 21 1589.

See Gingerich Owen Voelkel James R. , “Tycho Brahe's Copernican campaign”, Journal for the history of astronomy , xxix (1998), 1–34, esp. pp. 5–9.

TBOO , vii, 80, 8–20.

TBOO , iv, 399–414.

TBOO , vi, 41–48, 65, 85f.

TBOO , iv, 399: “… circa Solis oppositum, toto durationis tempore versaretur.”.

Ibid. 401:“… eas [Parallaxes] admodum fuisse exiguas vixque perceptibiles.” Cf. TBOO , vi, 46: “… pene insensibilem admisisse Parallaxin”; 65 (letter of 1587): “… et ego vel nullam, vel pene insensibilem [parallaxin]”; 86 (letter of 1587): “… ego vero unius circiter ab initio scrupuli, et postea saltem dimidii adinveni. Quamvis, ut verum fatear, et ipse eandem subinde plane nullam [parallaxin], ob tenuitatem illius tam exilem, discernere potuerim”. Rothmann , on the contrary, had not discerned any observable parallax.

TBOO , xiii, 357f; cf. ibid. 343: “infra sphaeram solarem.”.

TBOO , iv, 401.

TBOO , vi, 46. See the table with “Tycho Brahe's parallax reports for the 1585 comet” in Broecke Vanden Steven , “Teratology and the publication of Tycho Brahe's new world system (1588)”, Journal for the history of astronomy , xxxvii (2006), 1–17, p. 6.

TBOO , iv, 401; vi, 44.

After eliminating the spheres and assimilating Rothmann's Scriptum de cometa, Tycho accepted Rothmann's location of the comet high above the Sun, in the regions of Jupiter or rather Saturn. At the same time, most probably in 1587, he highlighted the different motion of the comet with respect to the superior planets. See De mundi aetherei recentioribus phaenomenis, TBOO , iv, 350, 35–38: “Nullatenus igitur iisdem motuum legibus obnoxius erat [the comet], quibus ullus ex his tribus planetis, quos superiores appellant, utut in rei veritate tantundem a Terra distiterit, quantum eorum aliquis; sed multo celeriori concitatione ab occasu in ortum ferebatur.”.

TBOO , vi, 55 for the notice of the sending of the Scriptum, which, despite being unfinished, did contain the crucial fifth chapter. Tycho received Rothmann's treatise at the latest in June 1586, given that on 1 July he wrote a letter to Hagecius in which he announced he was sending to him a copy of the treatise. See TBOO , vii, 108, 20–23.

See Tycho's allusions to this in his letter to Wilhelm IV of 18 January 1587 ( TBOO , vi, 70, 27–42; cf. ref. 74 above) and in his letter to Rothmann of 20 January the same year ( TBOO , vi, 86, 88, 103). In February–March 1587 he claimed to have found convincing evidence of the greater parallax of Mars; See Gingerich Voelkel , “Tycho Brahe's Copernican campaign” (ref. 77), 16–23.

TBOO , vi, 88, 10 (cit. supra, ref. 25).

Ibid. , lines 12–21. At this time, 1586, Tycho could (in the tenth chapter of his De mundi aetherei recentioribus phaenomenis, devoted to the criticism of the literature published on the comet of 1577) refuse both Helisaeus Roeslin's postulate of a new sphere for the comets and Maestlin's location of the comets of 1577 and 1580 in different planetary spheres. As for Roeslin (author of an interesting Theoria nova coelestium meteoron, published in Strasbourg in 1578) see TBOO , iv, 256, 2–7: “In tota enim Coeli vastitate ubique generantur Cometae, et cursum sortiuntur ab uno loco in alium, quemcunque libuerit… nec unius Cometae locus, qui aliquot annis praecessit, in sequentibus quidpiam Iuris, quo ad motum vel dispositionem attinet, sibi vendicat.” Concerning Maestlin, see ibid. 222f, where references to the comets of 1580 and 1585 (with explicit mention of the recently known results achieved by Rothmann ) are added as evidence against the comets' being affected by planetary motion and consequently against the existence of heavenly spheres.

See Maestlin , Observatio et demonstratio cometae aetherei, qui anno 1577. et 1578. constitutus in sphaera Veneris, apparuit (Tübingen, 1578), 52–53.

See Thoren Victor E. , “The comet of 1577 and Tycho Brahe's system of the world”, Archives internationales d'histoire des sciences , xxix (1979), 53–67, p. 61, repeated in his The Lord of Uraniborg (ref. 48), 257f.

TBOO , iv, 177–9. Cf. Broecke Vanden , “Teratology and the publication of Tycho Brahe's new world system” (ref. 85), 1–2, 4.