Letter against Werner

Letter Copernicus’ against Werner, Frombork, 3 VI 1524

Original: lost. 16th century copies: Berlin, Staatsbibliothek Preussischer Kulturbesitz, Cod. Lat. Fol. 83, k. 8-10; Wien, Österreichische Nationalbibliothek, Sammlung von Handschriften und alten Drucken, Cod. 9737, fol. 1-9v; Oxford, Bodleian Library, Ms Saville 47, fol. 28-32v.; Uppsala, Astronomska Observatoriet, Coll. Hjörter, H III. 34; Schweinfurt, Stadtarchiv, Handschrift 1 Ha 14, fol. k. 9-13 v.

Copernicus’ Letter against Werner was provoked by Johann Werner's work "Motion of the Eighth Sphere," published in his second collection of essays (Nuremberg, 1522).

Johann Werner was a Nuremberg vicar of St. John's and famous mathematician known for his works in spherical trigonometry, conic sections, cartography, as well as the first regular observations of the weather conditions in Germany.

Werner's "Motion of the Eighth Sphere" came to the notice of Bernard Wapowski (c. 1475-1535), the founder of Polish scientific cartography and a secretary of the king of Poland. Nowadays a book like Werner's second collection of essays would be reviewed in appropriate scientific periodicals. But these had not yet come into existence. In their absence Wapowski sought the opinion of his old friend Copernicus, who had been his fellow-student at the University of Cracow.

Knowing that Copernicus in far-off Frombork was not in touch with foreign cultural centers and developments, as he himself was, Wapowski sent Copernicus a copy of Werner's "Motion of the Eighth Sphere," remarking that it was widely praised, and requesting the astronomer's judgment.

What Wapowski sent Copernicus was not a complete copy of Werner's 1522 collection of essays, but only "The Motion of the Eighth Sphere". For, the preceding essays dealt, not with any astronomical problem, but with three purely mathematical topics: conic sections, uplication of the cube, division of a sphere in a given ratio.

When did Werner's essay (or 1522 collection of essays) reach Wapowski in Cracow? When did the royal secretary send "The Motion of the Eighth Sphere" to Frombork? Our only clue is Copernicus' use of an imprecise word at the outset of his reply:

Some time ago (pridem), my dear Bernard, you sent me alittle treatise on "The Motion of the Eighth Sphere.

Evidently Copernicus did not dash off an instant reply. Instead, on 3 June 1524 he sent Wapowski a carefully considered report, which has come to be known in the literature as his Letter against Werner.

Cast in the form of a private letter to Wapowski, it was not intended for publication. Nevertheless it has been called by Leopold Prowe an "open letter", "intended for the public, as is shown by its content and form," with the author "permitting the recipient to give it wider distribution"¹. But nothing in the Letter against Werner authorizes further distribution. Nothing in its form shows that it was an open letter, intended for the public. Had that been Copernicus' purpose, he would surely have refrained from using such harsh language about Werner, whose work had been widely praised by others, as he was informed by Wapowski. Copernicus' Letter against Werner was a private communication to Wapowski, not intended for the general public.

For his part, Wapowski deemed the scientific content of the Letter against Werner to be too important to be shut up in his personal files. For in the first place, Copernicus' Letter against Werner made a notable contribution to the emerging discipline of chronology by correcting Werner's woeful error of eleven years in dating Ptolemy's catalog of fixed stars, a conspicuous landmark in the history of astronomy. Secondly, the Letter against Werner insisted on technical terms being defined and used with precision: in a recurring periodic nonuniform motion, the mean velocity cannot also be the slowest, although Werner would have it both ways. Lastly, the Letter against Werner maintained the primacy of fact over theory. Having constructed a theory in conflict with ancient observations, Werner concluded that the observations were wrong. On the contrary, Copernicus replied, the theory is wrong, being inconsistent with itself to boot. With regard to our attitude toward the ancient scientists, Copernicus writes that we must

hold fast to their observations, bequeathed like a legacy. But if anyone, holding fast to his own view, thinks that they are untrustworthy in this regard, surely the gates of this art are closed to him. Lying in front of the entrance, he will dream the dreams of the deranged about the motion of the eighth sphere, and receive what he deserves for supposing that he should support his own hallucination by defaming the ancients.

It has recently become somewhat fashionable to link Copernicus with Pythagoreanism, neo-Pythagoreanism, Neoplatonism, and hermeticism. The evidence adduced for such linkage would easily pass through the eye of a needle without noticeably deforming the needle. On the other hand, Copernicus' familiarity with the writings of Aristotle, that well-known critic of the Pythagoreans and Plato, is quite apparent in his Letter against Werner. Its opening paragraph quotes from the Metaphysics, mentioning Aristotle by name. Later on, it echoes a striking statement in Aristotle's Physics, without even alluding to that work or its author. Such familiarity with Aristotle's treatises does not of course make Copernicus an Aristotelian in the sense that he regarded the Stagirite as infallible. On the contrary, where he detected a flaw in Aristotle, as in the Stagirite's division of simple motion into three mutually exclusive types, he did not hesitate to correct it. But he did not undertake to overthrow Aristotelianism, as he did the Ptolemaic astronomy. On the other hand, what he believed was sound in both systems, he retained with gratitude and affection, an attitude which some of our contemporaries would do well to consider.

From Edward Rosen's Introduction published in: Nicholas Copernicus Minor Works (Warsaw-Cracow, 1985).

Some time ago, my dear Bernard, you sent me a little treatise on "The Motion of the Eighth Sphere," published by Johann Werner of Nuremberg. Your Reverence stated that the work was widely praised and asked me too to give you my opinion of it. I would surely have done so gladly to the extent that I too could have really commended it wholeheartedly. Yet I may laud the fellow's zeal and effort. Moreover, it was Aristotle's advice to be grateful not only to the philosophers who have spoken well but also to those who have spoken incorrectly because to those who wish to follow the right road, it is often no small advantage to have noted the blind alleys too. Besides, faultfinding is of little use and scant profit, for it is the very mark of a shameless mind to prefer the role of the censorious critic to that of the creative poet. Hence I even fear that I may arouse anger if I reprove another while I myself produce nothing better. Accordingly, I wanted to leave these matters, just as they are, to the attention of others, and I would have replied in such a way that your Reverence would learn my attitude expressed concisely. I am aware, however, that it is one thing to snap at a man and assail him, but another thing to set him right and redirect him when he strays, just as it is one thing to praise, and another to flatter and play the fawner. Hence I see no reason why I should not comply with your request or why I should appear to hamper the pursuit and cultivation of these studies, in which you have a conspicuous place. And therefore, lest I even seem to condemn the man gratuitously. I shall try to show as clearly as possible in what respects he erred regarding the motion of the sphere of the fixed stars and maintains an unsound position. This may perhaps even contribute not a little to the formation of a better understanding of this subject.

In the first place, then, he went wrong in his calculation of time. For he thought that the emperor Antoninus Pius' second year, when Claudius Ptolemy drew up the catalog of the fixed stars as observed by himself, was A.D. 150, when in fact it was A.D. 139. For in the Great Syntaxis, Book III, Chapter l, Ptolemy says that the autumnal equinox observed in the 463rd year after Alexander the Great's death fell in Antoninus' third year. But from Alexander's death to Christ's birth there are counted 323 uniform Egyptian years, 130 days, because from the beginning of Nabonassar's reign to Christ's birth 747 uniform years, 130 days, are reckoned. This is not questioned, I observe, certainly not by our author, as is evident in his Proposition 22, except that he adds one day, in accordance with the Alfonsine Tables. The reason for this [discrepancy of one day] is that Ptolemy takes noon of the first day of the first Egyptian month Thoth as the starting point of the years reckoned from Nabonassar and Alexander the Great, while Alfonso begins with noon of the last day of the preceding year, just as we compute the years of Christ from noon of the last day of the month December. Now from Nabonassar to Alexander the Great's death 424 uniform years are counted by Ptolemy, Book III, Ch. 8, with whom Censorinus, relying on Marcus Varro, agrees in his Natal Day, dedicated to Quintus Caerellius. [This interval of 424 years, when subtracted] from 747 years, 130 days, leaves a remainder of 323 years, 130 days, that is, from Alexander's death to Christ's birth. And from that time to the aforementioned observation of Ptolemy [there are] 139 uniform years, 303 days. Therefore, the autumnal equinox observed by Ptolemy, it is clear, occurred on the ninth day of the month Athyr, 140 uniform years after the birth of our Lord, but 139 Roman years, 25 September, Antoninus' third year.

Again, in his Great Syntaxis, Book V, Ch. 3, in his observation of the sun and moon in Antoninus' second year Ptolemy counts 885 years of Nabonassar, 203 days. From Christ's birth, therefore, 138 uniform years, 73 days, would have elapsed. The fourteenth day thereafter, that is, 9 Pharmuthi, when Ptolemy observed Regulus [in the constellation] of the Lion, was 22 February, in the 139th Roman year after Christ's birth. And this was Antoninus' second year, which our author thinks was 150 [A.D.]. Hence he went wrong by eleven years too much.

If, however, anyone is still in doubt and, not satisfied by the foregoing [criticism], wants to make a further test of this matter, he should remember that time is the number or measure of the motion in heaven considered as "before" and "after." For by this motion we determine our years, months, days, and hours. But the measure and the measured, being related, are mutually interchangeable. Besides, as far as Ptolemy's tables are concerned, since in addition they were built up on the basis of his own recent observations, it is unbelievable that they contain any deviation from the observations which is detectable by the senses, or any discrepancy that would make them inconsistent with the foundations on which they rest. Since this is so, if [our skeptic] consults Ptolemy's tables and computes the positions of the sun and moon with reference to Regulus as found by Ptolemy using the astrolabe in Antoninus' second year on the ninth day of the month Pharmuthi at 5 1/2 hours after noon, he will find these positions, not 149 years after Christ, but 138 years, 88 days, 5 1/2 hours, equal to 885 years after Nabonassar, 218 days, 5 1/2 hours. In this way the error is now exposed which frequently vitiated our author's investigation of the motion of the eighth sphere when he mentions time.

A second error, no less serious than the first, is involved in his hypothesis expressing his belief that in the 400 years before Ptolemy the fixed stars moved only with a uniform motion. For the purpose of further explaining and clarifying what will be said below, it should in my opinion be pointed out that the science of the stars belongs to the category of those [subjects] which we learn in an order contrary to nature. For example, first nature knows that the planets are nearer than the fixed stars to the earth, then as a consequence that the planets appear less radiant. We, on the other band, first see that the planets do not twinkle, and then we know that they are nearer to the earth. So, by the same token, first we perceive that the motions of the heavenly bodies seem nonuniform, then we conclude that there are epicycles, eccentrics, or other circles by which the bodies are carried in this way. And therefore I would like it to be said that, with the aid of instruments, the ancient scientists first had to mark the positions of the heavenly bodies together with the intervals of time, and with this [information] as a sort of guideline, they had to devise a precise theory of the heavenly motions, lest the investigation of these matters remain interminable. They appear to have found this theory when it matched, with a certain agreement, all the observed and noted positions of the heavenly bodies. Such is also the situation regarding the eighth sphere's motion, which the ancient astronomers could not pass on to us in its entirety on account of its extreme slowness. Those who wish to examine it must follow in their footsteps, however, and hold fast to their observations, bequeathed like a legacy. But if anyone, holding fast to his own view, thinks that they are untrustworthy in this regard, surely the gates of this art are closed to him. Lying in front of the entrance, he will dream the dreams of the deranged about the motion of the eighth sphere, and receive what he deserves for supposing that he should support his own hallucination by defaming the ancients. It is well known, however, that those who handed down to us many famous and praiseworthy discoveries made all these observations with the utmost care and expert skill. Consequently I cannot possibly be persuaded that in noting the positions of the heavenly bodies they erred by 1/4° or 1/5° or even 1/6°, as this author believes. [I shall say] more about this [subject] later on.

In addition, it must not be overlooked that in every heavenly motion involving an irregularity, what we want above all is the entire period during which the apparent motion is recognized as having passed through all its variations. For, an apparent irregularity in a motion is what makes it impossible for an entire revolution and uniformity of motion to be measured by their parts. But in their investigation of the moon's path Ptolemy, and before him Hipparchus of Rhodes, divined with keen insight that the revolution of a nonuniform [motion] must have four diametrically opposite points. These are the maximum swiftness and slowness, and the mean and uniform [motion] at both [ends of the diameter] intersecting at right angles [the diameter connecting] both maxima. The circle is [thereby] divided into four equal parts, with the result that in the first quadrant the swiftest motion diminishes; in the second [quadrant] the mean motion diminishes; on the other hand, in the third quadrant the slowest motion increases, [as does] the mean [motion] in the fourth [quadrant]. By this device they could infer from the moon's observed and examined motions in what part of the circle it was at any specified time. Accordingly, when a similar motion had recurred, they understood that a revolution of the nonuniformity had now been completed, as this was explained at considerable length by Ptolemy in his Great Syntaxis, Book IV. This [procedure] should have been adopted also in analyzing the eighth sphere's motion. As I said, however, its extreme slowness, on account of which the nonuniform motion quite clearly has not yet returned upon itself in thousands of years, does not permit an immediate solution of this [problem], because it transcends many generations of men. Nevertheless it is possible by a reasonable conjecture to attain a solution even now with the aid of some observations added since Ptolemy, observations which conform to the same pattern. For what is determinate cannot have innumerable explanations. For example, if a circumference is drawn through three points not located on a straight line, superimposition of another circumference greater or smaller than the one drawn previously is impossible. But in view of my discussion of these matters elsewhere, I may return to the point where I digressed.

Hence we must now see whether our author is correct in saying that in the 400 years before Ptolemy the fixed stars moved only with uniform motion. Besides, lest we be mistaken about the meaning of terms, by "uniform motion" I understand what we usually also call "mean" motion, which is halfway between the slowest and the swiftest. Let him not mislead us by his statement in Proposition 7, Corollary 1, that "the motion of the fixed stars is slower" where according to his own hypothesis he puts the uniform motion, the rest of it being swifter, just as if it would never be slower. In these respects I do not know whether he is consistent with himself when later on he adduces a much slower [motion]. He derives his measure of the mean motion, however, from the uniformity with which the fixed stars traversed equal distances from the earliest observers of the fixed stars, Aristyllus and Timocharis, to Ptolemy, and in equal periods of time, to wit, approximately 1° every one hundred years, as is quite clear in Ptolemy, cited by our author in his Proposition 6.

But being a great astronomer, he is not aware that around the points of uniform motion, that is, the intersections of the circles (the tenth sphere's ecliptic with [the circles] of trepidation, as he calls them), the stars' motion cannot possibly appear more uniform than elsewhere. Indeed, the opposite conclusion must be drawn: at those times the motion appears to vary the most, but the least when the apparent motion is swiftest or slowest. He should have seen this even from his own hypothesis and system as well as from the tables based on them, especially the last table, which he drew up to exhibit the revolution of the entire nonuniformity or trepidation.

In this regard, according to an earlier computation, for 200 years before the birth of Christ the apparent motion is found to be only 49' of 1° in the first 100 years, and in the second century 57'. Then after Christ's birth in the first 100 years the stars would have moved about 1 1/10°, and in the second 100 years about 1 1/4°. Thus in equal periods of time the successive motions increase by a little less than 1/6°. But if you combine the motion of the two centuries in either era, the first period's [total] will fall short of 2° by more than 1/5°, while the second [period's total] will exceed [2°] by about 1/4°. Thus again in equal times the later motion will exceed the earlier motion by about 1/2° + 1/15°. Yet previously in reliance on Ptolemy our author had reported that the fixed stars passed through 1° every 100 years. By the very law of the circles which he assumed, however, the opposite happens in the eighth sphere's swiftest motion, when a variation of scarcely 1' in the apparent motion is found in 400 years, as may be seen for the years A.D. 600-1000 in the same table, and likewise in the slowest [motion] also, as for the 400 years after 2060.

Now the reason for the nonuniformity is, as was said above, that in one semicircle of the trepidation, namely, that which [extends] from the maximum slowness to the maximum swiftness, there is always some increase in the apparent motion. In the other semicircle, which [is reckoned] from the maximum swiftness to the maximum slowness, the motion which had previously increased decreases steadily. The greatest increase and decrease occur at the diametrically opposite points of uniform motion. In the apparent motion, consequently, equal motions are not to be found in two continuous equal periods of time. One [of the two motions] becomes greater or smaller than the other, except in the vicinity of the maximum swiftness or slowness. Only there do [the motions] on either side traverse equal arcs in equal times; starting or ceasing to increase or decrease, at those times they counterbalance each other. Consequently it is by no means correct that the motion in the 400 years before Ptolemy was the mean motion. On the contrary, it was rather the slowest motion. Indeed I see no reason why we should speculate about another slower motion concerning which we have heretofore been unable to obtain any hint. For, no observation of the fixed stars made before Timocharis has come down to us, nor did any come down to Ptolemy. Besides, since the swiftest motion has already passed, we are now as a consequence in the second, post-Ptolemaic, semicircle, in which the motion decreases, and no small part of it too bas passed.

Accordingly it should not seem surprising that with these assumptions of his our author could not approach more closely to what was reported by the ancients, and that in his opinion they erred by 1/4° or 1/5° or even 1/2° and more. Yet nowhere does Ptolemy seem to have exercised greater care than in striving to pass on to us the motion of the fixed stars free from error. For this [precision] would have been available to him only in that restricted portion of [precision] would have been available to him only in that restricted portion of the motion from which he undertook to devise that entire revolution. An error, however imperceptible when occurring in the restricted portion, could undoubtedly emerge as significant in that whole immense framework. Ptolemy seems to have linked Aristyllus with his contemporary Timocharis of Alexandria, and Agrippa of Bithynia with Menelaus of Rome, in order in this way to have absolutely certain and unchallenged evidence in the agreement of these [observers] from such widely separated places. Hence it is unbelievable that such great errors were made by them or by Ptolemy, men who were able to understand many other even more difficult matters down to the last detail, as the saying goes.

Finally, nowhere is our author more foolish than in Proposition 22 and especially its Corollary. Wishing to praise his own work, he censures Timocharis with regard to two stars, namely, Arista in the Virgin, and the most northerly of the three stars in the Scorpion's brow, by claiming that in the first case Timocharis' computation falls short, and is excessive in the second case. Here our author prattles in an exceedingly childish way. For with regard to both of the stars under consideration, the displacement between Timocharis and Ptolemy is the same, namely, 4 1/3° in almost exactly the same time interval, and the numerical result of that computation is therefore practically identical. Yet our author completely fails to notice that adding 4°7' to the place of the star found by Timocharis in 2° of Scorpion could not properly fill out the 6°20' of Scorpion where it is found by Ptolemy. Conversely, the subtraction of the same number from 26°40' for Arista according to Ptolemy could not restore 22 1/3°, as it should, but remained at 22°32'. Thus our author thought that in the first case the computation was deficient by as much as it was excessive in the second case, as though this disparity were inherent in the observations, or as if the road from Athens to Thebes were not the same as the road from Thebes to Athens. Besides, had he either added or subtracted the number in both cases, as parity of reasoning required, he would have found that both computations proceed in the same way.

Moreover, between Timocharis and Ptolemy there were in fact not 443 years, but only 432, as I indicated in the beginning. Hence, the interval being shorter, the amount [of the precession] should be smaller, so that our author will deviate from the stars' observed motion not merely by 13' but by 1/3°. This is how he imputed his own error to Timocharis, while Ptolemy barely escaped. But while he thinks that their reports are untrustworthy, what else remains but to distrust his observations too?

So much for the eighth sphere's motion in longitude. From the foregoing [remarks] it can also be easily inferred what we should think about the motion in declination too. For our author complicates it with two trepidations, as he calls them, piling this second one on top of the first. But now that the underpinning itself has been destroyed, the superstructure must necessarily collapse, being weak and incohesive.

Lastly, what do I myself think about the motion of the sphere of the fixed stars? Since [my views] are to be stated elsewhere, I deemed it superfluous and improper to extend this communication further here. For it is enough if I satisfy your desire to have my opinion of this little work in compliance with your request. May your Reverence enjoy the best of health.

Nicholas Copernicus

Frombork, 3 June 1524

Translated by Edward Rosen

Frombork, 3 June 1524

Reuerendo domino Bernhardo Vapouski, Cantori et Canonico Ecclesiae Cracouiensis et S. R. Maiestatis Poloniae etc. Secretario, Domino et Fautori suo plurimum Obseruando, S. D. Nicolaus Copernicus Cum pridem ad me mitteres, optime Bernharde, Iohannis Werneri Nurembergensis editum De motu octauae sphaerae opusculum, quod a multis laudari dicebas, petijt ex me Venerabilitas tua, vt ei meam quoque sententiam de illo significarem. Quod certe tamo libentius fecissem, quanto honestius et re vera a me quoque commendari potuisset, nisi quod studium hominis et conatum laudem, et quod admonuit Aristoteles: "Non solum ijs, qui bene locuti sum, gratificandum esse philosophis, sed etiam non recte locutis". Quandoquidem non parum saepe contulit etiam deuia notassse viam rectam sequi volentibus. Caeterum ad modicum vtilis est reprehensio confertque parum, quin et impudentis ingenij est Momum potius agere velle quam poetam. Proinde etiam vereor, ne mihi succenseat aliquis, si alium reprehendam, quamdiu ipse non profero meliora. Itaque volebam illa, vt sum, dimittere curae aliorum, atque sic Venerabilitati tuae vt mentem meam acciperet, in summa responsum fuisse. Verum cum animaduertam aliud esse mordere et lacessere quemquam, aliud castigare et reuocare errantem, quemadmodum vicissim laudare aliud est quam adulari et agere parasitum, non inuenio, cur desiderio tuo obsequi non deberem, quod harum rerum studio et diligentia, qua praecipue polles, derogare viderer. Ac proinde, ne etiam emere videar reprehendere hominem, conabor quam apertissime ostendere, in quibus ille de motu sphaerae stellarum fixarum errauerit neque conueniat eius traditio. Quod forsitan ad certiorem eius rei capessendam rationem non parum etiam conducet.

Primum igitur fefellit illum supputatio temporum, quod existimauerit annum secundum Antonini Pij Augusti, quo Claudius Ptolemaeus obseruata a se fixa sydera in ordinem constituit, fuisse a natiuitate Christi anno CL cum fuerit secundum veritatem annus CXXXIX. Ptolemaeus enim libro tertio Magnae Constructionis, capite primo, obseruatum autumni aequinoctium ab Alexandri Magni morte anno CCCCLXIII ait fuisse Antonini anno tertio, a morte vero Alexandri ad Christi natiuitatem numerantur anni pariles Aegyptij CCCXXIII et CXXX dies. Nam a principio regni Nabonassaris ad Christi natiuitatem supputant annos pariles DCCXLVII et dies CXXX, de quo non video dubitari neque autorem hunc, vt apparet propositione XXII, nisi quod additur dies vnus secundum Canones Alphonsinos. Idque ideo, quod Ptolemaeus incipit a meridie primi diei primi mensis Thot bo apud Aegyptios annos Nabonassarios et Alexandri Magni, Alphonsus autem a meridie vltimi diei anni praecedentis, quemadmodum nos a meridie vltimi diei mensis Decembris annos Christi supputamus. A Nabonassare autem ad excessum Alexandri Magni Ptolemaeus eodem libro capite octauo numerat bt annos CCCCXXIIII pariles. Cui adstipulatur Censorinus De die natali ad Quintum Cerelium scribens, autoritate Marci Varronis. Relinquuntur ergo ex annis DCCXLVII et CXXX diebus CCCXXIII anni et CCXXX dies, videlicet ab Alexandri morte ad Christi natiuitatem. Atque hinc ad Ptolemaei obseruationem iam dictam anni pariles CXXXIX et dies CCCIII. Ergo obseruatum a Ptolemaeo aequinoctium hoc autumni constat fuisse a natiuitate Christi annorum parilium CXL, nona die mensis Athyr, Romanorum vero annorum CXXXIX, die XXV Septembris, Antonini tertio.

Rursus idem Ptolemaeus libro quinto Magnae Constructionis, capite tertio, in obseruatione Solis et Lunae anno secundo Antonini supputat annos Nabonassarios DCCCLXXXV et CCCIII dies. Fuissent ergo a Christi natiuitate anni transacti pariles CXXXVIII et LXXIII dies. Exinde post dies XIV, nempe Pharmuti nono, quo Ptolemaeus Leonis Basiliscum obseruauit, erat a natiuitate Christi Romanorum annus CXXXIX, XXII dies Februarij. Atque hic Antonini annus secundus, quem putat autor iste CL fuisse. Fefellit igitur se ipsum supra annos XI.

Adhuc autem si quis dubitet et his non contentus cupiat etiam huius rei capere experimentum, meminisse debet tempus esse numerum siue mensuram motus coeli secundum prius et posterius. Hinc enim anni, menses, dies et horae nobis constant. Mensura autem et mensum vicissim se habent, relatiua sunt enim. Porro Canones Ptolemaei cum essent adhuc ex recenter a se obseruatis conditi, credibile non est errorem aliquem ab his sensu perceptibilem vel discrepantiam continere, quominus suis principijs, quibus incumbunt, non congruerent. Quae cum ita sint, si loca Solis et Lunae circa Basiliscum organis astrolabicis inuenta a Ptolemaeo anno secundo Antonini, nouem diebus Pharmuti mensis quinque horis et dimidia a meridie transactis per tabulas ipsius inquirendo numeret, non inueniet ea post annos Christi CXLIX, sed post CXXXVIII annos, LXXXVIII dies et horas quinque et dimidiam. Qui sunt Nabonassaris DCCCLXXXV anni, dies CCXVIII et horae quinque et dimidia. Ita iam error iste manifestus est, qui illius inquisitionem de motu octauae sphaerae plerumque infecit ubi temporum facit mentionem.

Alius error est non minor praecedenti in ipsa eius hypothesi, in qua existimat CCCC annis ante Ptolemaeum aequali tantummodo motu non errantia sydera mutata fuisse. Quae vt apertius (quae inferius) dicentur, magisque perspicua fiant, animaduertendum puto scientiam stellarum eorum esse, quaecunque praepostere cognoscuntur a nobis, quam secundum naturam. Quemadmodum, verbi gratia, prius natura nouit viciniores esse Terrae planetas quam fixa sydera: deinde quod sequitur, vt minus vibrantes appareant. Nobis e contrario antea visi sunt planetae non scintillare et exinde cognitum propinquiores esse Terrae. Ita pariformiter prius deprehensum est anobis inaequales videri stellarum motus. Postea epicyclia esse, eccentros aliosue circulos, quibus ita ferantur, ratiocinamur. Atque ideo dictum id esse velim, quod oportuerit priscos illos philosophos primum loca stellarum instrumentorum artificio notare, tum temporum interuallis et ea tamquam manuductione quadam, (ne infinita quaestio de motu caeli remaneret) rationem aliquam de eis certam percunctari, quam tunc visi sunt inuenisse, quando consideratis visisque stellarum locis adstipulatione quadam omnibus conueniret. Ita etiam de motu octauae sphaerae se habet, quem prisci mathematici ob nimiam eius tarditatem nobis ad plenum tradere non potuerunt. Sed vestigia eorum sequenda sunt inuestigare eum volentibus et eorum considerationibus tanquam testamento relictis inhaerendum. Quod si quis suo sensui inhaerens putauerit illis non concedendum in hoc, certe huic clausa est ianua huius artis et ante ostium recubans aegrotantium somnia de motu octauae sphaerae somniabit. Et merito, vtputa qui per illorum calumniam existimauerit suae hallucinationi subueniendum. Constat autem illos summa diligentia et solerti ingenio omnia obseruasse, qui multa et praeclara inuenta et admiratione digna nobis reliquerunt. Quamobrem persuadere mihi haudquaquam possum in accipiendis stellarum locis eos errasse vel in quarta vel quinta siue etiam sexta parte vnius gradus, vt hic autor existimat, de quo postea latius.

Illud quoque praetereundum non est in omni motu sydereo cui diuersitas inest, totam reuolutionem ante omnia desiderari, in qua intelligatur omnes motus apparentes differentias pertransiuisse. Diuersitas enim apparens in motu est, quae impedit, vt per partes tota reuolutio et aequalitas motus mensurari non possit. Sed sicut in inquisitione cursus Lunaris Ptolemaeus et ante eum Hipparchus Rhodius magna ingenij sagacitate considerauerunt, oportet esse quatuor momenta in reuolutione diuersitatis opposita sibi inuicem per diametros, vtputa extremae velocitatis et tarditatis, ac vtrobique per transuersum ambarum aequalitatum mediantium quadrifariam secantia circulum, fitque, vt in primo quadrante velocissimus decrescat motus, in altero diminuatur medius, et rursus crescat tardissimus in tertio quadrante, aequalis in quarto. Qua industria scire potuerunt ex obseruatis inspectisque Lunae motibus, in qua circuli portione quolibet tempore verteretur. Ac proinde, cum similis motus redijsset, intellexerunt iam factam inaequalitatis circuitio- nem lh . Quemadmodum hoc latius Magnae Constructionis libro quarto Ptolemaeus explicauit.

Quod etiam in inquisitione motus octauae sphaerae erat obseruandum. Sed nimia eius, vt dixi, tarditas (qua in annorum milibus nondum in sese reuersus inaequalitatis motus satis constat) non sinit id statim absoluere, quia multas hominum aetates excedit. Possibile tamen est coniectura rationabili ad id perueniri posse adiutos etiamnum aliquibus obseruationibus post Ptolemaeum adauctis, quae in eandem congruerint rationem. Nam quae determinata sunt, infinitam rationem habere non possunt. Quemadmodum, si per tria puncta non secundum rectam lineam posita circumferentia ducatur, non licet aliam superinducere, quae maior vel minor fuerit prius transmissae. Sed de his alias, vt reuertar ad id, vnde digressus sum.

Videndum igitur nobis nunc est, an recte se habeat quod dicit non errantia sydera CCCC ante Ptolemaeum annis aequali solummodo motu fuisse mutata. Porro, ne verborum significatione fallamur, aequalem accipio motum, quem et mediocrem dicere solemus, qui sit inter tardissimum et concitatissimum medius. Ne circumueniat nos, quod in corollario primo septimae propositionis dicit "tardiorem esse motum fixorum syderum", vbi penes suam hypothesin aequalem ponit, caeterum velociorem: perinde ac si nunquam futurus sit tardior. In quibus haud scio, an sibi ipsi constet, multo tardiorem postea adducens. Asseruit autem aequalitatis argumentum ex vniformitate, qua fixa sydera tantisper a primis stellarum fixarum obseruatoribus, Aristarcho et Timochare, vsque ad Ptolemaeum, ac per aequalia temporum interualla, vtputa per singulos annorum centenarios, singulos proxime gradus pertransiuerint. Vt apud Ptolemaeum satis apparet repetitum ab autore propositione septima.

Sed hic tantus mathematicus existens non aduertit, quod nullatenus esse potest, vt circa momenta aequalitatis, hoc est sectiones circulorum eclipticae decimae sphaerae et trepidationis, vt ille vocat, vniformior appareat stellarum motus quam alibi, quando contrarium eius sequi necesse sit, vt tunc maxime varius appareat, minime vero, quando velocissimus vel tardissimus est motus apparens. Quod vel e sua ipsius hypothesi et constructione debebat animaduertere et tabulis inde contextis, praesertim vltimo Canone, quem ad reuolutionem totius inaequalitatis siue trepidationis exemplificauit. Vbi a CC annis ante natiuitatem Christi secundum praecedentem supputationem in primo annorum centenario reperitur motus apparens scrupulorum primorum XLIX duntaxat vnius gradus; in altero centenario scrupulorum primorum LVII. Deinde ab ipsa natiuitate Christi per primum annorum centenarium transmutatae fuissent stellae gradu vno et decima fere parte vnius; in secundoi gradu vno et quarta fere, vt paulo minus sextante vnius gradus se inuicem excedant motus sub aequalibus temporum spacijs. Quod si coniungas CC annorum vtrobique motum, deficiet in primo interuallo a duobus gradibus plus quam quinta pars vnius. In secundo autem superaddet prope vnius quadrantem, sicque rursus sub aequalibus temporibus excedet motus sequens praecedentem in dimidio gradu et parte quintadecima fere, cum antea centesimo quoque anno singulos pertransisse im gradus stellas fixas Ptolemaeo credens detulisset. E contrario vero eadem lege assumptorum a se circulorum in velocissimo motu octauae sphaerae contingit, vt in CCCC annis vix vnius scrupuli differentia in motu apparente reperiatur. Quemadmodum videre licet ab annis Christi DC vsque ad M in eodem Canone. Similiter et in tardissimo, vt a MMLX annis in subsequentes CCCC. Et ratio diuersitatis est, quia, vt dictum est superius, in vno hemicyclio trepidationis (a summa videlicet tarditate ad summam velocitatem) accrescit semper aliquid motui apparenti ac in altero semicirculo (qui a summa velocitate ad tarditatem) continuo decrescit motus, qui antea creuerat, fitque summa augmentatio et diminutio in punctis aequalitatis e diametro oppositis. Adeo vt in motu apparente non sit reperirei motus aequales in duobus continuis temporum spacijsi, qui alter altero maior fiat aut minor, nisi circa velocitatis aut tarditatis extremitates, vbi duntaxat vltro citroque aequales circumferentiae pertranseunt temporis aequalitate atque incipientes vel desinentes augeri vel minui mutua tunc sese compensatione coaequant.

Nulla ergo ratione conuenit medium fuisse motum eum, qui in CCCC annis ante Ptolemaeum, sed tardissimum potius. Cum etiam non videam, cur alium diuinemur tardiorem, de quo nullam coniecturam hactenus habere potuimus, cum ante Timocharem nulIa stellarum fixarum annotatio facta sit, quae ad nos vsque peruenisset, sed neque ad Ptolemaeum. Cumque velocissimus etiam motus iam praeterierit, consequens est in altero a Ptolemaeo semicirculo iam nos esse, in quo diminuitur motus, cuius etiam non modica pars praeterierit.

Itaque mirum videri non debet, quod non potuerit hisce suis assumptionibus propius accedere ad ea, quae sunt ab antiquis annotata, putaueritque illos aberrasse in quarta vel quinta parte vnius gradus, siue etiamnum dimidia et amplius: cum tamen in nulIa parte Ptolemaeus maiorem videatur adhibuisse diligentiam, quam vt nobis non errantium stellarum motum sine vitio traderet, attendens, quod non nisi in modica eius particula id sibi fuisset concessum, qua in vniuersum illum circuitum coniecturus esset. Vbi error quantumlibet insensibilis interueniens in tota illa vastitate insignis nimirum poterat euenire. Ideoque Timochari Alexandrino Aristarchum adiunxisse videtur coaetaneum et Menelao Romano Agrippam Bythinium, vt sic etiam in tanta locorum distantia illis consentientibus verissima haberet et indubitata testimonia, quominus credibile sit eos vel Ptolemaeum in tanto errasse, qui multa alia etiam it difficiliora ad extremum, vt aiunt, vnguem deprehendere potuerunt.

NulIo demum loco ineptior est quam in XXII propositione et praesertim corollario eiusdem, dum opus hoc suum commendare volens taxat Timocharem circa duas stellas , vtputa Aristam Virginis et eam, quae ex tribus in fronte Scorpij borealior est, quod supputatio eius in illa deficiat, in hac autem abunder: vbi nimis pueriliter hallucinatur. Cum enim sit eadem vtriusque stellae distantia inter Timocharem et Ptolemaeum consideratarum, nempe gradus IV et tertia pars sub aequali fere temporis differentia, atque numerus supputationis illius perinde idem proxime, nihilo tamen magis aduertit, quod gradus IV, scrupula VII addita loco stellae, quam reperit Timochares in secundo gradu Scorpij, merito non possent supplere VI gradus et scrupula XX Scorpij, vbi Ptolemaeus ipsam inuenit. Et e conuerso idem numerus eleuatus ex XXVI gradibus et XL scrupulis Aristae secundum Ptolemaeum vsque ad gradum XXII et tertiam partem redire, vt par est, non potuit, sed residebat in XXII gradibus et scrupulis XXXII. Ita existimabat illic defecisse calculum, quanto hic abundasset, tanquam in obseruationibus haec incidisset diuersitas, vel quasi ex Athenis in Thebas et e Thebis in Athenas eadem via non sit. Alioqui si vtrobique vel addidisset numerum vel subduxisser, vt paritas rationis postulabat, inuenisset vtrumque eodem modo sese habere.

Adde etiam, quod reuera non erant inter Timocharem et Ptolemaeum anni CCCCXLIII, sed CCCCXXXII solum, vt a principio declaraui. Proinde breuiori tempore minorem esse numerum oportet, vt non solum in scrupulis XIII, sed in triente vnius gradus ab obseruato stellarum motu dissidebat. Ita errorem hunc suum imposuit Timochari vix euadente Ptolemaeo. At dum existimat illorum annotationibus non fidendum, quid aliud restat, quam vt suis quoque obseruationibus minus credatur?

Et haec de in longitudinem motu octauae sphaerae. E quibus etiam facile potest intelligi, quid de motu quoque declinationis existimandum sit. Inuoluit enim ipsam duabus, vt ait, trepidationibus inserendo secundam hanc supra primam. Sed dissipato ipso iam fundamento necesse est, vt superaedificata corruant infirmaque sint, ac minus sibi inuicem cohaerentis. Quid demum ipse de motu non errantium stellarum sphaerae semiam, quoniam alio loco destimata sum, superfluum putaui et impertinens hic amplius immorari, cum satis sit, si modo desiderio tuo satisfecerim, vt meam, quod a me exigebas, de isto opusculo habeas sententiam. Valeat Venerabilitas tua quam faustissime.

Ex Varmia 3 Iunij Anno MDXXIV

Nicolaus Copernicus