COMMENTARY ABBREVIATIONS OF WORKS FREQUENTLY CITED A Astronomia instaurata (Amsterdam, 1617), the 3rd ed. of the RB'Oolutions B The 2nd ed. of the Reoolutions (Basel, 1566) GV Valla, Giorgio, De expetendis et fugiendis rebus (Venice, 1501) Me Menzzer, C. L., Uber die Kreisbewegungen der Weltkorper (Leipzig, 1939; reprint of Thom 1879 ed.) MK Birkenmajer, L.A., Mikolaj Kopernik (Cracow, 1900). An abridged English version was published by Xerox University Microfilms, Ann Arbor, Michigan, in 1976, too late for use herein. Mu Nikolaus Kopernikus Gesamtausgabe, vol. II (Munich, 1949) N Copernicus, De reoolutionibus orbium coelestium (Nuremberg, 1543) NCCW Nicholas Copernicus Complete Works: vol. I (London/Warsaw, 1972) p Prowe, Leopold, Nicolaus Coppernicus (Berlin, 1883-1884; reprinted, Osnabriick: Zeller, 1967): PI: vol. I, part I PI1: vol. I, part II PII: vol. II P-R Peurbach, George and Johannes Regiomontanus, Epitome (Venice, 1496) PS Ptolemy, Syntaxis PS 1515 Ptolemy, Syntaxis; Latin translation issued in Venice, 10 January 1515 SC Birkenmajer, L. A., Stromata Copernicana (Cracow, 1924) T Copernicus, De r8fJolutionibus orbium caelestium (Thom, 1873) 3CT Rosen, Edward, Three Copernican Treatises, 3rd ed. (New York: Octagon, 1971) W Copernicus, De reoolutionibus orbium coelestium (Warsaw, 1854) Z Zinner, Emst, Entstehung und Ausbreitung der coppernicanischen Lehre (Erlangen, 1943) ZGAE Zeitschrift jar die Geschichte und Altertumskunds Ermlands 332 NOTBS ON PP. VII-XV NOTES ON TilE FRONT MATTER P. VII-xn. No Table of Contents appears in Copernicus' autograph. What appears in N was prepared by the editors of N not by Copernicus. P. XV. This title page was designed in Nuremberg by the persons responsible for the first edition of the RBf!olutions (cited hereafter as N). They surely did not consult Copernicus, who was at that time gravely ill in distant Frombork. Whether he as the author had supplied his own formal title page cannot be determined from his autograph in its present condition. For at .some undetermined time (as was indicated in NCCW, I, 6, 11) the first leaf of the first quire was carefully cut away and the loose edge glued firmly in place to avoid damage to the rest of the autograph. On what is now the recto or upper side of the first folio, in the lower right comer, the letter a as the designation of the first quire was written by someone other than Copernicus, whereas he himself had written all the other quire designations. In the absence of folio 0 (zero, as the missing leaf has been labeled) nobody can say with any degree of certainty whether or not it was the title page as conceived by Copernicus, if indeed he did conceive one. A dark cloud therefore hangs over the title Six Books on the Revolutions of the Hetl'08nly Spheres (De r8'Do­ lutionibus orbium coslsstium libri VI). In particular, the words orbium coelestium were deleted in a number of copies of N. The unauthorized insertion therein of Andreas Osiander's Foreword was bitterly attacked by George Joachim Rheticus (1514-1574), Copernicus' only disciple and his loyal supporter. Rheticus' thoroughly justified protest against the interpolation of Osiander's Foreword may somehow have given rise to the notion that the Nuremberg preacher also without warrant tacked on the two words orbium coelestium (on the assumption that De rBflolutionibus, used by Copernicus for convenience as a short title, was likewise his choice for the full title). Yet in themselves these two words orbium coslsstium are completely unobjectionable. For (like Rheticus) Copernicus believed that the visible celestial bodies, that is, the stars and planets, were imbedded in invisible heavenly spheres ( orbes coslestss), which moved the visible bodies in accordance with the cosmological thinking accepted since Greek antiquity. Hence, although we cannot be absolutely sure what formal title, if any, Coper­ nicus had in mind for his masterpiece, on conceptual grounds no fault can be found with the title as printed in N. For at the head of Book I, Chapter 10, in the autograph Copernicus himself wrote "The Order of the Heavenly Spheres" (De ordine coelestium orbium; NCCW, I, fol. sr, line 1), and in the Preface he referred to the "revolution of the celestial spheres" (revolutions orbium coslestium). Thus, the two contested words not only expressed one of his basic ideas but also formed !p1 integral part of his working vocabulary. If the deletion of orbium coelestium occurred before these supposed celestial spheres were forever banished from the heavens by Tycho Brahe, that great admirer of Copernicus, then perhaps the opposition was based on our astronomer's choice of words in the opening sentence of his Preface. There he refers to the six books which he has written "about the revolutions of the spheres of the universe" (de revolutionibus sphaerarum mundi). Perhaps some poorly informed person may have failed to realize the semantic equivalence of the expressions sphaerarum mundi and orbium coelestium. As a perceptive stylist, Copernicus studiously avoided the excessive repetition of the same locution. When sphaerarum mundi and orbium coelestium flowed from his pen, they were entirely interchangeable and the occurrence of the first expression in the Preface guarantees the validity of the second expression in the title. Although sphaera and orbis in this cosmographical context are in general synonymous, as precise mathematical terms they refer to two quite different bodies: a solid sphere, by contrast with a hollow spherical shell or ring. This distinction between sphaera and orbis was set forth with complete clarity by the celebrated philologist, astronomer, and geographer, Sebastian Miinster (1488-1552), in his textbook of elementary mathematics, Rudi­ menta mathematica (Basel, 1551), p. 60: 333 NOTBS ON PP. XV-XVI Among solid figures, the most important is the sphere, [which is] the most regular of all. It is a regular solid body, bounded by a single surface ... We conceive the sphere to be generated by the complete rotation of a semicircle: while the diameter of the semicircle remains fixed, the plane sur­ face of that circle is rotated ... An orb (orbis) is also a solid figure. It is bounded, however, by two round spherical surfaces, namely, an interior [surface], which is called concave, and an exterior [surface], which is labeled convex. If these surfaces have the same center, the orb will be uniform, that is, of equal thickness throughout. But if the surfaces have different centers, these will make the orb's thickness nonuniform and irregular. This is the kind which the heavens of all the planets have. Copernicus' conceptions of sphaera and orbis agree with those of his somewhat younger contemporary, Mtinster. The blurb on the tide page was obviously not composed by Copernicus. As a piece of advertising copy, it was evidendy contributed by the printer-publisher himself, for Johannes Petreius (Hans Peter) was an author in his own right. Two years later, in 1545, when he issued Girolamo Cardano's Ars magna (translated into English by T. Richard Witmer as The Great Art or the Rules of Algebra, Cambridge, Mass., 1968), Petreius placed a sim­ ilar blurb on the tide page of that foundation of the theory of equations. Then, when he published Cardano's De subtilitate in 1550, Petreius attributed the blurb to himself. By the same token, when Petreius published Algorithmus demonstratus in 1534, his blurb ended: Quare eme, lege, & iwaberis (Therefore buy, read, and enjoy yourself). Nine years later, his blurb for Copernicus closed with the same sentiment in slighdy different language: Igitur eme, lege, jruere. All four of these promotional passages unmistakably emanate from the same hand. The warning on the tide page to nonmathematical readers to stay away from the R800lutions (Copernicus' short tide is equally serviceable in English) in all likelihood was due to Osiander, who edited for Petreius not only Copernicus' R~olutions but also Cardano's Ars magna. Although Osiander became famous for his militant theological views and stirring sermons, his favorite hobby was the mathematical sciences. He left the warning to nonmathematicians on the tide page of the R800lutions in Greek. This warning was then commonly believed to have been inscribed over the entrance to Plato's Academy. As long as this famous school existed, nobody made any reference to any such inscription. But after the emperor Justinian ordered all pagan schools, includ­ ing Plato's Academy, to be closed in 529, the first reference to this supposed inscription was written by Joannes Philoponus in his Commentary on Aristotle's Soul (Commentaria in Aristotelem graeca, XV (Berlin, 1897), p. 117, lines 26-27). When Fran~is Viete (1540-1603) savagely attacked Copernicus as incompetent, the French math­ ematician turned this very warning against Copernicus himself. In denouncing Copernicus' ''ungeometrical procedure," Viete, although writing in Latin, used a Greek word (ageometresia) related to the first word in the warning, evidendy on the (mistaken) assumption that it was Copernicus who had been responsible for placing it on the tide page. That mistake did not die with Viete. In his Astronomical R~olution (Paris, 1973), p. 73, § 9, Alexandre Koyre said: "no doubt with the approval of his master [Copernicus], he [Rheticus] put on the tide page of De Revolutionibus the famous adage which, [at least] according to tradition, was placed above the portals of the [Platonic] Academy." The printing of the R~olutions was finished a few days before 21 March 1543, when Sebastian Kurz, an employee of the Fugger banking firm, sent a copy from Nuremberg to Emperor Charles V. On the other hand, Copernicus in Frombork did not receive a copy until 24 May 1543, the day he died. See Marcel Bataillon, "Charles-Quintet Copemic: documents inedits," Bulletin hispanigue, 1923,25:256-258, or La R~ de Pologne, 1923, 2nd series, 1: 131-134, and AtJant, awe, apris Copernic (Paris, 1975), p.