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Commentariolus
Original: lost. Copies: Aberdeen, University Library, King's College, 521 Cop 2 (2), fol. r-v, 85bis r-v, 100bis r, 148bis r-v, 160 bis v, 168ter r-v (Duncan Liddel's copy dated 1585); Stockholm, Kunglige Svenska Vetenskapsakademiens Bibliotek, fol. 1-16 (in Johann Hewelke's exemplar of "De Revolutionibus", Basileae 1566); Wien, Österreichische Nationalbibliothek, Sammlung von Handschriften und alten Drucken, Cod. 10530, fol. 34-43 (Christian Sorensen Longberg's Copy, after 1589).
The earth is a planet in: motion. This basic truth was proclaimed and rationally elaborated, for the first time in mankind's long history, by the little treatise commonly called Copernicus' Commentariolus. That title was not bestowed on it by him. In fact, he did not give it any title. Nor did he attach his name to it. He had good reason to conceal his authorship. Since the earth is a planet, it is in heaven along with the other planets. Since the earth is in heaven, the old distinction between earth and heaven is dissolved. Nobody on earth has to wait for death in order to go to heaven. Every human being is already in heaven at the instant of birth. The familiar exhortation to lead a moral life in order to ascend to heaven is bound to sound silly to anyone who understands the theological implications of the Copernican astronomy and wants to lead a moral life for secular reasons.
As a canon of Varmia, as a Roman Catholic ecclesiastic, Copernicus had no desire to weaken belief in the cosmological underpinnings of his own religion. On the other hand, as an innovative astronomer, he was profoundly convinced that the traditional view of the earth as stationary was wrong. Living in an age of savage sectarian strife, he knew only too well what fate awaited those accused of spreading disbelief in hallowed dogma. Yet his momentous discovery, or re-discovery, would not remain quietly locked up in his own brain. He therefore committed it to paper. And what then? It is not true that he "concealed his theories" throughout "the entire period that had elapsed since his first discovery of the heliocentric theory"1. He neither "concealed his theories" nor did he have them printed. Instead, he chose a middle course. Avoiding complete silence on one side, and unrestricted publication on the other side, he distributed handwritten copies to a few trusted professional friends.
He had as friends ... Cracow astronomers, formerly his fellow-students, with whom he corresponded about eclipses and observations of eclipses according to his earliest well-informed biographer2.
One of these handwritten copies found its way into the possession of a professor at the University of Cracow, Matthew of Miechów (1457-1523), who completed the inventory of his library on 1 May 1514. An entry in that inventory reads as follows:
A manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still3.
This description unmistakably fits Copernicus' Commentariolus with respect to both its length and its essential contents. The entry also shows that the manuscript circulated without the author's name and without any title. Matthew of Miech6w's last will and testament disposed of the wooden box containing his copy of Commentariolus. With this clue as a guide, the writer of the recent study of Matthew's library searched long and hard and unsuccessfully for the present whereabouts of Matthew's copy of Commentariolus, which he concluded no longer exists4.
By the same token no trace has ever been found of Copernicus' original draft of Commentariolus. Nevertheless it is possible to form a reasonable conjecture concerning its fate. Toward the end of his life Copernicus acquired his only disciple, George Joachim Rheticus (1514-1574). Arriving in Frombork with an armful of valuable books for his new master, Rheticus undoubtedly received gifts in exchange. These apparently included Commentariolus as written by Copernicus' own hand. Whereas Rheticus bequeathed his unfinished trigonometrical works and Copernicus' autograph manuscript of Revolutions to his younger collaborator, he left the remainder of his library to a fellow-physician, Thaddeus Hajek (1525-1600). The following year, on l. November 1575, at the ceremonies celebrating the crowning of the king of the Romans Rudolph II at Regensburg, Hajek, who was the emperor's personal physician, met the illustrious Danish astronomer Tycho Brahe (1546-1601). A book about the nova of 1572, a subject dear to the heart of Brahe, had just been published by Hajek. While talking to Brahe, Hajek found out that he had a high regard for Copernicus, and therefore gave him Copernicus' draft of Commentariolus, which had formed part of Rheticus' legacy to Hajek. The latter could not have chosen a more suitable person to whom to transmit this precious document. For, as Brahe related in a published work, a certain little treatise (tractatulus) by Copernicus, concerning the hypotheses which he formulated, was presented to me in handwritten form some time ago at Regensburg by that most distinguished man Thaddeus Hajek, who has long been my friend. Subsequently, I sent the treatise to certain other astronomers in Germany. I mention this fact to enable the persons into whose hands the manuscript comes to know its provenience5.
The manuscript owes not only its distribution to Brahe but also the title it now bears. For when Hajek turned it over to Brahe, telling him that its author was Copernicus (as he had learned from Rheticus), the work still lacked a title. This deficiency was made good by Brahe when he had his staff prepare copies to be sent to other astronomers. Those copies displayed the following heading:
Nicolai Copernici de hypothesibus motuum caelestium a se constitutis commentariolus Nicholas Copernicus' little treatise on the hypotheses formulated by himself for the heavenly motions.
Copernicus wrote Commentariolus before 1 May 1514. How long before that date? Not during his student years after 1491 at the University of Cracow, whose professors showed not the slightest interest in geokineticism. Nor about 1500, when Copernicus in Rome "lectured on astronomy before a large audience of students and a throng of great men and experts in this branch of knowledge6 ", whose silence about what Copernicus said proves that he did not mention geokineticism, then a highly controversial idea which would surely have provoked a host of heated reactions from so articulate an audience. Nor before the middle of 1508, when Corvinus referred to the "alternating movements7" of Copernicus' sun, which became motionless in Commentariolus. Hence we may safely conclude that Copernicus wrote Commentariolus at some time between the latter half of 1508 and early 1514. Late in 1510 he finally decided not to try to succeed his uncle as bishop of Varmia, and instead to devote his best energies to astronomy. For he had caught a glimpse of his new geokinetic, heliostatic universe, the glimpse that found its first expression in Commentariolus.
As a general rule, Commentariolus does not indicate from what sources it drew its information. Ptolemy, the greatest ancient astronomer, was not yet directly available, since the Greek text of Syntaxis was first published in 1538, and the earliest printing of a Latin translation was completed on 10 January 1515. Epitome, however, was published in Venice in 1496, the year of Copernicus' arrival in Italy;
Commentariolus' use of Epitome, 111,2, and V, 22, is evident. So is Commentariolus' use of Giorgio Valla's Seek and Avoid as well as of Pliny's Natural History. What other sources were tapped by Commentariolus will have to be determined by further research.
Copernicus sent out a few copies of Commentariolus, as we saw above. Perhaps an unpleasant rebuff made him decide against disclosing Revolutions, which he was already planning while he was writing Commentariolus. In later years, while working on Revolutions, he said nothing about Commentariolus, since it expressed views which were contradicted or abandoned in Revolutions. For all that Copernicus did about it, the world would never have known about the existence of Commentariolus. The same may be said about Rheticus (who presumably received Copernicus' original draft) and Hajek, who acquired it from Rheticus and passed it on to Brahe. Thanks to Brahe, however, Commentariolus survived, since all three of our manuseripts are descended in one way or another from the Copernicus-Rheticus-Hajek-Brahe manuscript. Brahe's enthusiastic diffusion of Commentariolus evoked only two responses, Liddel's and Longberg's. Thereafter a curtain of silence descended for two and three-quarter centuries until one of the copies was found in the Austrian National Library in Vienna by Maximilian
Curtze, who published it in 1878 and revived interest in Commentariolus, an interest that has continued unabated until the present day.
From Edward Rosen's Introduction published in: Nicholas Copernicus Minor Works (Warsaw-Cracow, 1985).
Further reading:
- Kopernik Mikołaj, Pisma pomniejsze, Warszawa 2007.
1 Noel M. Swerdlow, The Holograph of the Revolutions and the Chronology of its Composition, Journal for the History of Astronomy, 1974, 5, p. 191..
2 Simon Starowolski, Hekatontas (Venice, 1627), p. 161.
3 Leszek Hajdukiewicz, Biblioteka Macieja z Miechowa (Wrocław, 1960), p. 218, no. 189.
4 Ibid., p. 99.
5 Tycho Brahe, Astronomiae instauratae progymnasmata, part 2, see: Tychonis Brahe dani opera omnia (Copenhagen, 1913-1929), vol. II, 428/34-40.
6 Edward Rosen, Three Copernican Treatises, (New York, 1971), p. III.
7 See Corvinus' introduction to Copernicus' translation of: Theophilacti Scolastici Simocati, Epistolae morales, rurales et amatoriae, interpretatione latina, [Cracoviae, J. Haller, 1509], section V, last paragraph.
Our predecessors assumed, I observe, a large number of celestial spheres mainly for the purpose of explaining the planets' apparent motion by the principle of uniformity. For they thought it altogether absurd that a heavenly body, which is perfectly spherical, should not always move uniformly. By connecting and combining uniform motions in various ways, they had seen, they could make any body appear to move to any position.
Callippus and Eudoxus, who tried to achieve this result by means of concentric circles, could not thereby account for all the planetary movements, not merely the apparent revolutions of those bodies but also their ascent, as it seems to us, at some times and descent at others, [a pattern] entirely incompatible with [the principle of] concentricity. Therefore for this purpose it seemed better to employ eccentrics and epicycles, [a system] which most scholars finally accepted.
Yet the widespread [planetary theories], advanced by Ptolemy and most other [astronomers], although consistent with the numerical [data], seemed likewise to present no small difficulty. For these theories were not adequate unless they also conceived certain equalizing circles, which made the planet appear to move at all times with uniform velocity neither on its deferent sphere nor about its own [epicycle's] center. Hence this sort of notion seemed neither sufficiently absolute nor sufficiently pleasing to the mind.
Therefore, having become aware of these [defects], I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion. After I had attacked this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much more suitable constructions than were formerly put forward, if some postulates (which are called axioms) were granted me. They follow in this order.
POSTULATES
- There is no one center of all the celestial orbs or spheres.
- The center of the earth is the center, not of the universe, but only of gravity and of the lunar sphere.
- All the spheres encircle the sun, which is as it were in the middle of them all, so that the center of the universe is near the sun.
- The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance between the earth and the sun is imperceptible in comparison with the loftiness of the firmament.
- Whatever motion appears in the firmament is due, not to it, but to the earth. Accordingly, the earth together with the circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
- What appear to us as motions of the sun are due, not to its motion, but to the motion of the earth and our sphere, with which we revolve about the sun as [we would with] any other planet. The earth has, then, more than one motion.
- What appears in the planets as [the alternation of] retrograde and direct motion is due, not to their motion, but to the earth's. The motion of the earth alone, therefore, suffices [to explain] so many apparent irregularities in the heaven.
Having thus propounded the foregoing postulates, I shall endeavor briefly to show to what extent the uniformity of the motions can be saved in a systematic way. Here, however, the mathematical demonstrations intended for my larger work should be omitted for brevity's sake, in my judgment. Nevertheless, in the explanation of the circles themselves I shall set down here the lengths of the spheres' radii. From these anybody familiar with mathematics will readily perceive how excellently this arrangement of circles agrees with the numerical data and observations.
Accordingly, lest anybody suppose that, with the Pythagoreans, I have asserted the earth's motion gratuitously, he will find strong evidence here too in my exposition of the circles. For, the principal arguments by which the natural philosophers attempt to establish the immobility of the earth rest for the most part on appearances. All these arguments are the first to collapse here, since I undermine the earth's immobility as likewise due to an appearance.
THE ORDER OF THE SPHERES
The celestial spheres embrace one another in the following order. The highest is the immovable sphere of the fixed stars, which contains and gives position to all things. Beneath it is Saturn's, which Jupiter's follows, then Mars'. Below Mars' is the sphere on which we revolve; then Venus'; last is Mercury's. The lunar sphere, however, revolves around the center of the earth and moves with it like an epicycle. In the same order also, one sphere surpasses another in speed of revolution, according as they measure out greater or smaller expanses of circles. Thus Saturn's period end in the thirtieth year, Jupiter's in the twelfth, Mars' in the third, and the earth's with the annual revolution; Venus completes its revolution in the ninth month, Mercury in the third.
THE APPARENT MOTIONS OF THE SUN
The earth has three motions. First, it revolves annually in a Grand Orb about the sun in the order of the signs, always describing equal arcs in equal times. From the Grand Orb's center to the sun's center the distance is 1/25 of the Grand Orb's radius. This Orb's radius is assumed to have a length imperceptible in comparison with the height of the firmament. Consequently the sun appears to revolve with this motion, as if the earth lay in the center of the universe. This [appearance], however, is caused not by the sun's motion but rather by the earth's. Thus, for example, when the earth is in the Goat, the sun is seen diametrically opposite in the Crab, and so on. Moreover, on account of the aforementioned distance of the sun from the Orb's center, this apparent motion of the sun will be nonuniform, the maximum inequality being 2 1/6. The sun's direction with reference to the Orb's center is invariably toward a point of the firmament about 10° west of the more brilliant bright star in the head of the Twins. Therefore, when the earth is opposite this point, with the Orb's center lying between them, the sun is then seen at its greatest distance [from the earth]. By this Orb not only is the earth revolved, but also whatever else is associated with the lunar sphere.
The earth's second motion is the daily rotation. This is in the highest degree peculiar to the earth, which it turns on its poles in the order of the signs, that is, eastward. On account of this rotation the entire universe appears to revolve with enormous speed. Thus does the earth rotate together with its circumjacent waters and nearby air.
The third is the motion in declination. For, the axis of the daily rotation is not parallel to the Grand Orb's axis, but is inclined [to it at an angle that intercepts] a portion of a circumference, in our time about 23 1/2°. Therefore, while the earth's center always remains in the plane of the ecliptic, that is, in the circumference of a circle of the Grand Orb, the earth's poles rotate, both of them describing small circles about centers [lying on a line that moves] parallel to the Grand Orb's axis. The period of this motion also is a year, but not quite, being nearly equal to the Grand Orb's [revolution]. The Grand Orb's axis, however, being invariant with regard to the firmament, is directed toward what are called the poles of the ecliptic. The poles of the daily rotation would always be fixed in like manner at the same points of the heavens by the motion in declination combined with the Orb's motion, if their periods were exactly equal. Now with the long passage of time it has become clear that this alignment of the earth changes with regard to the configuration of the firmament. Hence it is the common opinion that the firmament itself has several motions. But even though the principle involved is not yet sufficiently understood, it is less surprising that all these phenomena can occur on account of the earth's motion. I am not prepared to state to what its poles are attached. I am of course aware that in more mundane matters a magnetized iron needle always points toward a single spot in the universe. It has nevertheless seemed a better view to ascribe the phenomena to a sphere, whose turning governs the movements of the poles. This sphere must doubtless be sublunar.
EQUAL MOTION SHOULD BE MEASURED NOT BY THE EQUINOXES BUT BY THE FIXED STARS
Accordingly, since the equinoxes and the other cardinal points of the universe shift considerably, whoever attempts to derive from them the equal length of the annual revolution necessarily falls into error. Besides, different determinations of this length were made in different ages on the basis of many observations. Hipparchus computed it as 365 1/4 days, and al-Battani the Chaldean as 365d 5h46m, that is, 13 3/5m or [13] 1/3m less than Ptolemy. Hispalensis, on the other band, increased al-Battani's length by the 20th part of an hour, since he determined the tropical year as 365d 5h 49m.
Lest these differences should seem to have arisen from errors of observation, [let me say that] if anyone will study the details carefully, he will find that the discrepancy has always corresponded to the shift in the equinoxes. For when the cardinal points of the universe moved 1° in 100 years, as was found in Ptolemy's time, the length of the year was then what Ptolemy himself reported. When however in the following centuries they moved with greater rapidity in opposition to lesser motions, the year became shorter by as much as the cardinal points' displacement increased. For by their swifter recurrence they encountered the annual motion in a shorter time. Therefore the derivation of the equal length of the year from the fixed stars is more accurate. Thus I used the Spike of the Virgin and discovered that the year has always been 365 days, 6 hours, and about 1/6 hour, the value also found in ancient Egypt. The same reasoning must be employed also with the other motions of the heavenly bodies because their apsides, which are likewise fixed in the firmament, with their true testimony make manifest the laws of the motions as well as heaven itself.
THE MOON
The moon, on the other hand, seems to me to have four motions in addition to the annual revolution which has been mentioned. For on its deferent sphere it revolves once a month about the center of the earth in the order of the signs. That deferent in fact carries what is commonly called the epicycle of the first anomaly or of the argument, but I call the first or larger epicycle. In its upper portion this [larger epicycle] revolves in the direction opposite to the deferent's in a period of a little more than a month. A second epicycle is attached to this larger epicycle, by which it is carried around. Lastly, as the moon clings to this second epicycle, it completes two revolutions a month in the direction opposite to the first epicycle's. As a result, whenever the larger epicycle's center touches the line drawn from the Grand Orb's center through the earth's center (I call this line the Grand Orb's diameter), the moon is then nearest to the larger epicycle's center. This occurs around the new and full moon. But contrariwise at the quadratures, halfway between new and full moon, the moon is most remote [from the larger epicycle's center]. In length, the larger epicycle's radius is to its deferent sphere's radius as 1 1/18:10, and to the smaller epicycle's radius as 4 3/4:1.
By reason of these [arrangements], therefore, the moon appears to be fast at some times, and at other times slow, as well as to drop down and climb higher. Into the first anomaly the smaller epicycle's motion introduces two irregularities. For it withdraws the moon from uniform motion on the larger epicycle's circumference, the maximum inequality being 12 1/4° of a circumference of corresponding size or diameter; and it also brings the larger epicycle's center at times farther from [the moon], at times nearer [to it], within the limits of the [smaller epicycle's] radius. Therefore, since for this reason the moon describes unequal peripheries of circles around the larger epicycle's center, it happens that the first anomaly undergoes complicated variations. Thus, the greatest variation of this kind does not exceed 4°56' near conjunctions and oppositions to the sun, but in the quadratures it increases to 7° 36'.
Those, however, who believe that this [variation] is caused by an eccentric circle improperly treated the motion on that circle as nonuniform and, in addition, they fell into two manifest errors. For, the consequence by mathematical reasoning is that in the quadratures, when the moon drops down to the lowest part of the epicycle, it would appear nearly four times greater (if the entire [disk] were luminous) than when new and full, unless they also irrationally claim that the size of its body increases and decreases. So too, because the earth's size is sensible in comparison with its distance [from the moon], the eccentric makes the parallax increase very greatly near the quadratures. But if anyone investigates rather carefully, he will find that both [the apparent size and parallax] differ very little in the quadratures as compared with new and full moon, and accordingly he will not lightly doubt that my theory is the truer.
Indeed, with these three motions in longitude, the moon passes through the points of its motion in latitude. The epicycles' axes are parallel to the deferent's axis, and therefore the moon does not move away from the [plane of the] deferent. But the deferent's axis is inclined to the axis of the Grand Orb or ecliptic and therefore makes the moon move out of the plane of the ecliptic. Thus the deferent's axis is inclined at an angle which subtends 5° of the circumference of a circle. Its poles revolve [around centers lying on a line that moves] parallel to the ecliptic's axis, in nearly the same manner as was explained regarding declination. Also in the present case they move in the reverse order of the signs but much more slowly, with a revolution being completed in the nineteenth year. It is the common opinion that this [motion] takes place in a higher sphere, to which the poles are attached as they revolve in the manner described. Such a fabric of motions, then, does the moon seem to have.
THE THREE OUTER PLANETS SATURN-JUPITER-MARS
Saturn, Jupiter, and Mars have a similar system of motions, since their spheres completely enclose the Grand Orb associated with the year and revolve in the order of the signs around its center as their common center. But Saturn's sphere completes its revolution in the thirtieth year, Jupiter's in the twelfth year, and Mars' in the twenty-ninth month, just as if these revolutions axe delayed by the spheres' size. For if the Grand Orb's radius is divided into 25 units, the radius of Mars' sphere will be 38, Jupiter's 130 5/12, and Saturn's 230 5/6. By "radius" [of the sphere] I mean the distance from the sphere's center to the center of the first epicycle.
For, each [deferent sphere] has two epicycles. One of these carries the other, in much the same way as was explained in the case of the moon. The arrangement, however, is different. For, the first epicycle revolves in the direction opposite to the deferent sphere's, the periods of both being equal. On the other hand, the second epicycle, revolving in the direction opposite to the first's with twice the velocity, carries the planet around. As a result, whenever the second epicycle is at its greatest distance from the deferent sphere's center, or again at its nearest approach thereto, the planet is then at its closest to the [first] epicycle's center; but it is at its greatest distance therefrom whenever [the second epicycle is] at a quadrant's distance [from the two positions just mentioned and] halfway [between them]. Therefore, through the combination of these motions of the deferent sphere and epicycles, as well as the commensurability of their periods, it happens that these withdrawals and approaches occupy absolutely fixed places of their own in the firmament. [These planets] constantly adhere to unchanging patterns of motion throughout, so that their apsides are immovable: Saturn's, near the star described as being above the Archer's elbow; Jupiter's, 8° east of the star called the end of the Lion's tail; and Mars', 6 1/2° west of the Lion's heart.
The sizes of their epicycles are as follows. In those units of which the Grand Orb's radius was taken to be 25 [25p 0m], the radius of Saturn's first epicycle consists of 19p 41m, while the second epicycle's radius has 6p 34m. Similarly in the case of Jupiter, the first epicycle has a radius of 10p 6m; the second, 3p 22m. As for Mars, its first [epicycle's radius is] 5p 34m; its second [epicycle's radius is 1p] 51m. Thus, the first [epicycle's] radius is throughout three times greater than the second [epicycle's radius].
Now the irregularity imposed by the epicycles' motion upon the deferent sphere's motion bas usually been called the "first anomaly" which, as I said, adheres throughout to unchanging boundaries in the firmament. For there is a second anomaly, in which the planet is seen sometimes to retrograde and often to become stationary. This second anomaly happens by reason of the motion, not of the planet, but of the earth as it changes its observational position on the Grand Orb. For since the earth's speed surpasses the motion of the planet, the line of sight directed toward the firmament regresses, and the earth more than neutralizes the planet's motion. This regression peaks at the time when the earth is nearest to the planet, that is, when it comes between the sun and the planet at the planet's evening rising. On the other hand, about the time when the planet is setting in the evening or rising in the morning, the earth advances the line of sight in the forward direction. But when the line of sight is moving in the direction opposite to the planet's and at an equal rate, the planet seems to stand still because the opposite motions neutralize each other in this way. This generally happens when the angle at the earth between the sun and the planet is about 120°. In all these planets, however, the lower the sphere by which the planet is moved, the greater is this anomaly. Hence in Saturn it is smaller than in Jupiter, and again greatest in Mars, in accordance with the ratio of the Grand Orb's radius to their radii. This anomaly peaks for each of them at the time when the planet is seen along a line of sight tangent to the Grand Orb's circumference. For us, at any rate, these three planets do indeed wander about [in longitude].
In latitude, on the other hand, their digression is twofold. [In the first place,] while the epicycles' circumferences remain in a single plane with their deferent, the planets deviate from the ecliptic in accordance with the axes' inclinations. These do not revolve, as in the case of the moon, but are always directed toward the same region of the heavens. Therefore the intersections of the circles (the deferent's and the ecliptic, these intersections being called the "nodes") also occupy eternal places in the firmament. Thus, the node where the ascent toward the north begins is, for Saturn, 8 1/2° east of the star said to be in the head of the eastern Twin; for Jupiter, 4° west of that star; and for Mars, 6 1/2° west of Vergiliae. Hence in these and the diametrically opposite [nodes] a planet has no latitude.
On the other hand, its maximum latitude, which occurs when these planets are at a quadrant's distance [from the nodes], is quite variable. For, the inclination of the axes and circles seems, as it were, to be attached to those nodes, while oscillating [around them]. In fact, it peaks at the time when the earth is nearest to the planet, that is, when the planet is rising in the evening. For then the axis' inclination is 2 2/3° for Saturn, 1 2/3° for Jupiter, and 1 5/6° for Mars. On the other hand, near evening setting and morning rising, the earth being then at its greatest distance [from the planet], this inclination decreases for Saturn and Jupiter by 5/12°, but for Mars by 1 2/3°. Thus this variation is most notable in the greatest latitudes, and for any latitude it diminishes as the planet's distance from the node lessens, so that the variation increases and decreases in phase with the latitude.
In the second place, it happens that the earth's motion on the Grand Orb causes the apparent latitudes to change for us. Thus, [the earth's] approach toward and withdrawal from [the planet] increase and decrease the angles of the apparent latitude, as mathematical reasoning requires. If in fact this oscillating motion occurs along a straight line, it is nevertheless possible for a motion of this kind to be produced by a combination of two spheres. Although these are concentric, [the higher] one carries around the other one's poles, which are inclined. In addition, the lower sphere makes the poles of the deferent sphere bearing the epicycles revolve with twice the velocity of the upper sphere and in the opposite direction. The deferent's poles are also inclined, their inclination away from the poles of the sphere halfway above being equal to the inclination of this sphere's poles away from those of the highest sphere. So much for Saturn, Jupiter, and Mars as well as the spheres which enclose the earth.
VENUS
What is enclosed within the Grand Orb's embrace, that is, Venus' and Mercury's motions, remains to be investigated. To begin with, Venus has a system of circles closely resembling that of the outer planets, but the motions are executed differently. As was said above, Venus' deferent sphere completes its revolution in the ninth month, which is likewise the period of the larger epicycle. Their composite motion brings the smaller epicycle back in a constant relation to the firmament everywhere, and establishes the higher apse at the point toward which I said the sun is directed. On the other hand, the smaller epicycle's period, while incommensurable with the other two, is commensurable with the Grand Orb's motion: in one revolution of the Orb, the smaller epicycle completes two revolutions. As a result, whenever the earth is in the diameter drawn through the apse, the planet is then nearest to the larger epicycle's center, and farthest from it [when the earth is] on the perpendicular [to the line of apsides] at a quadrant's distance from them. [This arrangement] closely resembles the way in which the moon's smaller epicycle in its aspects is related to the sun. But the radii of the Grand Orb and of Venus' deferent sphere have the ratio 25p:18p; the larger epicycle, 3/4p; and the smaller, 1/4p.
Venus too is sometimes seen to retrograde, particularly when it is nearest to the earth. Its regression occurs for a reason that in a certain way is like the reason for the outer planets' regression, but is its opposite. For their regression occurs because the earth's motion is faster [than theirs], but in this case because it is slower; moreover, in their case the earth's sphere is enclosed, whereas in this case it does the enclosing. Hence Venus is never in opposition to the sun, since the earth cannot come between them. On the contrary, it turns back within fixed elongations to either side of the sun. These are determined by tangents to the circumference drawn from the earth's center, and never exceed 48° in our observations. This in substance is the motion by which Venus is carried around in longitude.
Its latitude also changes for a twofold reason. For Venus too has the axis of its deferent sphere inclined, at an angle of 2 1/2° and the node whence it turns north is in its apse. But although in itself this inclination is one and the same, the digression arising from it appears to us as twofold. For when the earth faces either node of Venus, these digressions are seen on perpendiculars [to the nodal plane] above and below it, and are termed the "reflexions." The deferent sphere's natural inclinations, which are called the "declinations" appear when the earth is at a quadrant's distance [from the nodal line], but they are the same. In all the other positions [of the earth], however, both latitudes mingle and are combined: the larger one prevails over the other, as they augment and eliminate each other by their likeness and difference.
But the axis' inclination is the following. It has an oscillating motion hinged, not on the nodes as in the case of the outer planets, but on certain other points that revolve by performing annual revolutions of their own with reference to the planet. As a result, whenever the earth faces an apse of Venus, at that time the oscillation peaks, and this [affects] the planet itself, no matter what part of its deferent it is in then. Consequently, if the planet is then in an apse or its diametric opposite, it will not completely lack latitude even though it is then in the nodes. From these [peak positions], however, this oscillation decreases until the earth moves through a quadrant of a circle away from the aforesaid [apsidal] location and, their motions being similar, until the peak point of this deviation has moved an equal distance away from the planet, when absolutely no trace of this deviation is found. The deviational swing continues uninterrupted, with that initial [peak] point dropping from north to south and moving as far away from the planet as the earth moves away from the apse. The planet again reaches the peak when a semicircle of the libration is completed. Here the deviation becomes maximal once more, being similar [in sign] and equal to its initial [value]. Thus, finally, the remaining semicircle is traversed in the same way [as the first]. Consequently this latitude, which is usually called the "deviation," never becomes southern. Here too it seems reasonable that these phenomena are produced by two concentric spheres with oblique axes, as I explained in the case of the outer planets.
MERCURY
Of all the orbits in the heaven, however, the most remarkable is that of Mercury, which traverses almost untraceable paths so that it cannot be easily studied. There is the further difficulty that it generally follows a course invisible in the sun's rays and is observable on very few days. Yet Mercury too will be understood, provided that it is investigated by someone of superior ability.
For Mercury too, as for Venus, two epicycles revolving on their deferent sphere will be suitable. For, as in the case of Venus, the larger epicycle has the same period as its deferent sphere, and fixes the position of Mercury's apse at 14 1/2° east of the Spike of the Virgin. The smaller epicycle, on the other hand, revolves with twice the [earth's] speed. But by contrast with the principle governing Venus, in every position of the earth passing over Mercury's [higher] apse or facing it from the opposite direction, the planet is farthest from the larger epicycle's center, and nearest to it [when the earth is] at a quadrant's distance [from the apsidal line]. As I said, Mercury's deferent sphere completes its revolution in the third month, that is, in 88 days. Its radius contains 9 2/5p, of the 25p which I have assumed for the Grand Orb's radius. Of these units, the first epicycle takes 1p 41m, while the second epicycle takes one-third as much, that is, about 34m.
But this combination of circles is not sufficient here, by contrast with the other [planets]. For when the earth passes through the aforementioned positions with respect to the apse, the planet seems to move along a far smaller periphery, and again, when the earth is at a quadrant's distance [from the apsidal line], along an even larger periphery, than is consistent with the aforesaid system of circles. Yet no other perceptible longitudinal irregularity is produced by this [disparity].
Its occurrence, consequently, is reasonably explained by a certain approach [of the planet] toward and withdrawal from the deferent's center along a straight line. This oscillation must be caused by two interlocking small spheres, whose axes are parallel to the deferent's axis. At the same time the center of the larger epicycle, or of this whole [epicyclic structure], is exactly as far away from the center of the small sphere which without any gap contains [the epicycle's center] as the center of this [inner sphere] is from the center of the outer [small sphere]. This distance has been found to be 0p 14 1/2m, the universal measure I have used being 25p 0m. In addition, the outer small sphere's motion 303 performs two revolutions in the course of a year, while the inner one completes four revolutions in the same time with twice the speed in the opposite direction. For by this composite motion the centers of the larger epicycle are carried along a straight line, just as I explained with regard to the oscillating latitudes. In this manner, therefore, when the earth is in the aforementioned positions with respect to the apse, the larger epicycle's center is nearest to the deferent's center, but farthest [from it when the earth is] at a quadrant's distance [from the apsidal line]. However, [when the earth is] at the midpoints, that is, 45° from these [four points, just mentioned], the larger epicycle's center joins the Outer small sphere's center, and both [these centers] coincide. This approach-and-withdrawal amounts to 0p 29m of the aforementioned units. And this ends the discussion of Mercury's motion in longitude.
In latitude it does not differ from Venus, except that it is always in the opposite region. For where Venus turns north, Mercury heads south. But its deferent sphere is inclined to the ecliptic at an angle of 7°. Here too there is a deviation, but it is always southern and never exceeds 3/4°. Otherwise, what was said about Venus' latitudes may be recalled here too, to avoid frequent repetition of the same statements.
Thus, Mercury runs on seven circles in all; Venus, on five; the earth, on three, and around it the moon on four; finally, Mars, Jupiter, and Saturn on five each. Thus altogether, therefore, 34 circles suffice to explain the entire structure of the universe and the entire ballet of the planets.
Translation by Edward Rosen
NICOLAI COPERNICI DE HYPOTHESIBUS MOTUUM CAELESTIUM A SE CONSTITUTISCOMMENTARIOLUS
(PARS INTRODUCTIVA GENERALIS)
Multitudinem orbium caelestium maiores nostros eam maxime ob causam posuisse video, vt apparentem in sideribus motum sub regularitate saluarent. Valde enim absurdum videbatur caeleste corpus in absolutissima rotunditate non semper aeque moueri. Fieri autem posse animaduerterant, vt et compositione atque concursu motuum regularium diuersimode ad aliquem situm moueri quippiam videretur.
Id quidem Calippus et Eudoxus per concentricos circulos deducere laborantes non potuerunt et his omnium in motu sidereo reddere rationem, non solum eorum, quae circa reuolutiones siderum videntur, verum etiam, quod sidera modo scandere in sublime, modo descendere nobis videntur, quod concentricitas minime sustinet. Itaque potiore visa est sententia per eccentricos et epicyclos id agi, in qua demum maxima pars sapientium conuenit. Attamen quae a Ptolemaeo et plerisque alijs passim de his prodita fuere, quamquam ad numerum responderent, non paruam quoque videbantur habere dubitationem. Non enim sufficiebant, nisi etiam aequantes quosdam circulos imaginarentur, quibus apparebat neque in orbe suo deferente, neque in centro proprio aequali semper velocitate sidus moueri. Quapropter non satis absoluta videbatur huiusmodi speculatio neque rationi satis concinna.
Igitur cum haec animaduertissem ego, saepe cogitabam, si forte rationabilior modus circulorum inueniri possit, e quibus omnis apparens diuersitas dependeret, omnibus in se ipsis aequaliter motis, quemadmodum ratio absoluti motus poscit. Rem sane difficilem aggresso ac paene inexplicabilem obtulit se tandem, quomodo id paucioribus ac multo conuenientioribus orbibus, quam olim sit proditum, fieri possit, si nobis aliquae petitiones, quas axiomata vocant, concedantur: quae hoc ordine sequuntur.
Prima petitio
Omnium orbium caelestium seu sphaerarum vnum centrum non esse.
Secunda petitio
Centrum Terrae non esse centrum mundi, sed tantum grauitatis et orbis lunaris.
Tertia petitio
Omnes orbes ambire Solem tamquam in medio omnium existentem, ideoque circa Solem esse centrum mundi.
Quarta petitio
Minorem esse comparationem distantiarum Solis et Terrae ad altitudinem firmamenti, quam semidimetientis Terrae ad distantiam Solis, adeo vt sit ad summitatem firmamenti insensibilis.
Quinta petitio
Quicquid ex motu apparet in firmamento, non esse ex parte ipsius sed Terrae. Terra igitur cum proximis elementis motu diurno tota conuertitur in polis suis inuariabilibus firmamento immobili permanente ac vltimo caelo.
Sexta petitio
Quidquid nobis ex motibus circa Solem apparet, non esse occasione ipsius, sed Telluris et nostri orbis, cum quo circumuoluimur ceu aliquod aliud sidus, sicque Terram pluribus motibus ferri.
Septima petitio
Quod apparet in erraticis retrocessio ac progressus, non esse ex parte ipsarum, sed Telluris. Huius igitur solus motus tot apparentibus in caelo diuersitatibus sufficit.
His igitur sic praemissis conabor breuiter ostendere, quam ordinate aequalitas motuum seruari possit. Hic autem brevitatis causa mathematicas demonstrationes omittendas arbitratus sum, maiori volumini destinatas. Quantitates tamen semidiametrorum orbium in circulorum ipsorum explanatione hic ponentur, e quibus mathematicae artis non ignarus facile percipiet, quam optime numeris et obseruationibus talis circulorum compositio conueniat.
Proinde ne quis temere mobilitatem Telluris asseuerasse cum Pythagoricis nos arbitretur, magnum quoque et hic argumentum accipiet in circulorum declaratione.
Etenim quibus physiologi stabilitatem eius astruere potissime conantur, apparentijs plerumque innituntur: quae omnia hic inprimis corruunt, cum etiam praeter apparentiam versemur eandem.
De ordine orbium
Orbes celestes hoc ordine se complectuntur. Summus est stellarum fixarum immobilis et omnia continens et locans, sub eo Saturnius, quem sequitur Jouius, hunc Martius. Subest huic orbis, in quo nos circumferimur, deinde Venereus, vltimus Mercurialis. Orbis autem Lunae circa centrum Terrae vertitur, et cum eo ceu epicyclus defertur. Eodem quoque ordine alius alium reuolutionis velocitate superat, secundum quod maiora minoraue circulorum spatia emetiuntur. Sic quidem Saturnus anno trigesimo, Iupiter duodecimo, Mars biennio, Tellus annua reuolutione restituitur, Venus nono mense, Mercurius tertio reuolutionem peragit.
DE MOTIBUS QUI CIRCA SOLEM APPARENT
Terra triplici motu circumfertur. Vno quidem in orbe magno, quo Solem ambiens secundum signorum successionem anno reuoluitur, in temporibus aequalibus semper aequales arcus describens: cuius quidem centrum a centro Solis vigesima quinta parte semidiametri sui distat. Cum igitur supponatur semidiametrum huius orbis ad altitudinem firmamenti imperceptibilem habere quantitatem, consequens est, vt hoc motu Sol circumferri videatur, perinde ac si Terra in centro mundi subiaceat, cum tamen id non Solis sed Terrae potius motione contingit: vt exempli causa, dum haec sit sub Capricorno, Sol e directo per diametrum in Cancro cernatur, et sic deinceps. Videbitur etiam Sol eo motu inaequaliter moueri secundum distantiam eius a centro orbis, vt iam dictum est: ex quo maxima diuersitas duobus gradibus et sextante vnius contingit. Declinat autem ab ipso centro Sol ad punctum firmamenti, quod distat a stella lucida, quae est in capite Gemelii splendidior, gradibus fere 10 versus occidentem inuariabiliter. Tunc igitur Sol in summa eius altitudine cernitur quando Terra in loco huic opposito versatur, centro orbis inter eos mediante, et per hunc quidem orbem non Terra solum, sed quicquid simul cum orbe lunari comprehensum est, circumducitur.
Allius Telluris motus est quotidianae reuolutionis et hic sibi maxime proprius in polis suis secundum ordinem signorum hoc est ad orientem labilis, per quem totus mundus praecipiti voragine circumagi videtur. Sic quidem Terra cum circumfluis aqua et vicino aere voluitur.
Tertius est motus declinationis. Axis enim quotidianae reuolutionis non aeque distat axi magni orbis, sed obliquatur secundum circumferentiae partem, nostro quidem saeculo 23 gradibus et medio fere. Igitur centro Terrae in superficie eclipticae semper manente hoc est in circumferentia circuli magni orbis, poli eius circumaguntur circulos vtrobique paruos describentes in centris ab axe orbis magni aequidistantibus. Et hic quoque motus annuas fere complet reuolutiones et cum orbe magno paene compares. At vero axis magni orbis ad firmamentum immutabilem seruat compositionem ad eos quos vocant eclipticae polos. Motus item declinationis cum motu orbis complexus polis quotidianae reuolutionis ad eadem caeli momenta semper retineret, si paribus omnino reuolutionibus cum illo constaret. Nunc longo temporis tractu deprehensum est talem Telluris positionem ad faciem firmamenti mutari, propter quod ipsum firmamentum aliquibus motibus ferri plerisque visum est, lege nondum satis deprehensa. Posse autem haec omnia fieri mutabilitate Telluris minus mirum est. Quibus autem poli inhaereant, ad me non attinet dicere. Video equidem in vilioribus rebus, quod virgula ferrea magnete attrita in vnum semper mundi situm nitatur. Potior tamen sententia visa est, secundum orbem aliquem fieri, ad cuius notum ipsi poli moueantur, quem procul dubio sub Luna esse oportebit.
Quod aequalitas motum non ad aequinoctia, sed ad stellas fixas referatur.
Cum igitur aequinoctialia puncta caeterique mundi cardines plurimum commutentur, falli eum necesse est. Quicunque ab his aequalitatem annuae reuolutionis deducere conatur, quae etiam sub diuersis aetatibus multis experimentis obseruationum diuersa reperta est. Hanc Hipparchus 365 diebus cum quadrante vnius diei, Albategni vero Chaldaeus reperit talem annum ex 365 diebus, 5 horis, 46 minutis, hoc est 13 minutis et 3 quintis Ptolemaico breuiorem. Rursus autem Hispalensis hunc longiorem vigesima parte vnius horae, siquidem ex 365 diebus, 5 horis et 49 minutis annum vertentem constituit.
Ne autem diuersitas ex obseruationum errore processisse videatur si quis singula accuratius animaduertet, inueniet eam cum mutabilitate aequinoctialium punctorum semper correspondisse. Dum enim ipsi mundi cardines in centenis annis vno gradu mutabantur, quemadmodum Ptolemaei aeuo repertum est, erat tunc anni quantitas quae ab ipso Ptolemaeo tradita est. Quando autem subsequentibus saeculis potiori mutabilitate mouerentur motibus inferioribus obuiantes, tanto breuior annus factus est, quanto translatio cardinum esset maior. Nam occursu velociori breuiori tempore anuum excipiebant motum. Rectius igitur agit, quicunque annuam aequalitatem ad stellas fixas referet. Quemadmodum circa Virgini Spicam fecimus inuenimusque annum 365 dierum et 6 horarum et sextantis fere vnius horae semper fuisse, qualis etiam in Aegyptiaca antiquitate reperitur. Eadem ratio in alijs etiam motibus siderum habenda est, quod absides eorum et statae sub firmamento motuum leges docent ac caelum ipsum veraci testimonio.
DE LUNA
Luna praeter annalem, vt dictum est, circuitum quatuor motibus videtur peruagari. Nam in orbe suo deferente circa telluris centrum secundum ordinem signorum menstruas complet reuolutiones. Is vero defert, quem vocant epicyclum primae diuersitatis siue augmenti, nos vero primum siue maiorem et qui epicyclum alterum sibi inhaerentem in superiore quidem portione contra motum orbis reflexus paulo tardiore quam menstruo tempore deducit. In hoc demum Luna pendens binas in mense reuolutiones contra motum illius perficit, vt, quandocumque centrum epicycli maioris contingit, lineam a centro orbis magni transeuntem per centrum Terrae, quam diametrum magni orbis vocamus, tunc Luna sit ad centrum maioris epicycli proxima, quod quidem circa nouam et plenam Lunam accidit, at econtra in quadraturis mediantibus ijsdem remotissima. Quantitas autem semidiametri epicycli maioris continet decimam partem de semidiametro orbis sui deferentis cum decima octava vnius particula, minoris vero epicycli semidiametrum quinquies dempta vna quarta ipsius.
Per haec igitur Luna modo concita modo tarda descendens, quoque et ascendens videtur, et primae quidem diversitati, dupliciter variationem motus epicycli minoris ingerit: Lunam enim in circumferentia maioris ab aequalitate distrahit, cuius quidem in hoc maxima diuersitas 12 gradus et quadrantem colligit de circumferentia ipsa quantitatis seu diametric respondentis; eam quoque a centro maioris modo distrahit modo appellit secundum semidiametri magnitudinem. Cum igitur propter hoc circa centrum maioris epicycli inaequales circulorum ambitus Luna describat; contingit primam diuersitatem multipliciter variari. Hinc est quod circa coniunctiones et obiectiones ad Solem maxima huiusmodi diuersitas 4 gradus et 56 minuta non exedat in quadraturis autem ad 7 gradus et 36 minuta extendatur. Qui vero per eccentricum circulum fieri hoc arbitrantur, praeter ineptam in ipso circulo motus inaequalitatem in duos inciderunt manifestos errores. Consequens enim est cum mathematica ratione, quod Luna in quadraturis, dum infima parte epicycli dependet, quadruplo fere maior appareat (si modo tota luceret) quam noua et plena nisi argumentum et diminutionem corporis sui magis temerarie quispiam asserit. Sic quoque diuersitatem aspectus facit propter notabilem terrae magnitudinem ad distantiam eius circa quadraturas plurimum augeri. Si quis autem diligentius perscrutetur, parum valde vtrumque distare comperiet in quadraturis ab his quae interlunio plenaque Luna contingunt, et proinde veriorem hanc speculationem nostram haud facile dubitabit.
His vero tribus motibus longitudinum Luna circumit puncta latitudinis motus, axes quidem epicyclorum aequidistant axi orbis propter quod nullam ab eo agressionem facit. Sed hic orbis axem suum decliuem habet axi magni orbis siue eclipticae, quapropter Lunam a superficie eclipticae digredi facit. Declinat igitur secundum quantitatem anguli, cui de circumferentia circuli 5 gradus supratenduntur, cuius poli circumferentur in aequidistantia axis eclipticae, propemodum sicut in declinatione dictum est: sed hic contra signorum ordinem et longo tardiore motu, vt ad vnam reuolutionem decimum nonum annum expectet. Et hoc in orbe quidem eminentiore fieri plerisque videtur, cui poli inhaerentes ad hunc modum ferantur. Talem igitur videtur habere Luna motuum fabricam.
DE TRIBUS SUPERIORIBUS: SATURNO, IOUE ET MARTE
Saturnus, lupiter et Mars similem habent motuum rationem, siquidem orbes eorum annalem illum magnum penitus includentes in centro communi ipsius magni orbis ad ordinem signorum voluuntur. Sed orbis quidem Saturnius trigesimo anno reducitur, Iouianus duodecimo, Martius autem vigesimo nono mense, perinde ac si tales reuolutiones magnitudo orbium remoraretur. Nam semidiametro magni orbis ex 25 partibus constituto, semidiameter orbis Martij 38 partes obtinet, Iouis 130 et vnius particulae quincuncem, Saturni 230 et sextantem vnius. Dico autem semidiametrum a centro orbis ad centrum primi epicycli distantiam. Habet enim quisque duos epicyclos, quorum alter alterum defert, propemodum sicut in Luna dictum est, sed lege diuersa. Primus enim epicyclus contra motum orbis reflexus pares facit cum eo reuolutiones, altero vero obuians primi motum reuolutionibus duplicatis circumagit sidus, adeo vt quandocunque sit in summa a centro orbis distantia vel rursus in maxima vicinitate, tunc sidus sit centro epicycli quam proximum, in quadrantibus autem mediantibus remotissimum. Igitur ex talium motuum compositione orbis et epicyclorum et reuolutionum paritate contingit, vt huiusmodi elongationes et accessiones maxime statas sibi sub firmamento sedes obtineant, ac deinceps certas vbique obseruant motuum conditiones. Itaque absides suas inuariabiles habent, Saturnus quidem circa stellam quae super cubitum esse dicitur Sagittatoris, Iupiter gradibus 8 post stellam quae extremitas caudae Leonis appellatur, Mars vero gradibus 6 et medio ante Cor Leonis.
Magnitudines autem epicyclorum hae sunt. In Saturno quidem primi semidiameter constat ex partibus 19 et 41 minutis, qualium semidiameter orbis magni ex 25 supponebatur; secundus autem epicyclus partium 6 et minutorum 34 semidiametrum habet. Sic quoque in Ioue primus partium 10 et minutorum 6, secundus partium 3 et minutorum 22 semidiametros continerent. In Marte autem primus partium 5 minutorum 34, secundus partis 1 minutorum 51. Sic igitur vbique ad primum semidiameter triplo maior est secundo.
Hanc autem diuersitatem quam epicyclorum motus inducit super motum orbis, primam appelare placuit, quae vbique sub firmamento certos, vt dictum est, obseruat limites. Alia siquidem est diuersitas, secundum quam sidus interdum regredi, saepe etiam subsistere cernitur, quae non ex motu sideris contingit, sed Telluris in orbe magno aspectum variantis. Haec enim motum sideris velocitate superans radio visuali ad firmamenti aspectum obuiante motum sideris vincit. Quod tunc maxime fit, quando proxima fuerit sideri Terra, dum videlicet inter Solem et sidus mediat vespertini sideris ortu. Econtrario autem circa vespertinum occasum ortumue matutinum praeuentione antefert visum. Vbi vero visus contra motum aequali cursu obuiat, stare videtur aduersis motibus inuicem se sic perimentibus, quod plerumque circa triquetrum Solis radium contingit. In his autem omnibus tanto maior contingit talis diuersitas, quanto inferiore orbe sidus mouetur, vnde minor in Saturno quam Ioue, et rursus in Marte maxima, secundum proportionem semidiametri magni orbis ad illorum semidiametros. Fit autem tunc vniuscuiusque maxima, quando sidus per radium aspicitur circumferentiam magni orbis contingentem, equidem tria haec sidera nobis pererrant.
In latitudine vero duplicem digressionem faciunt circumferentijs quidem epicyclorum in vna superficie permanentibus, cum orbe suo ab ecliptica declinant secundum axium deflexiones, non sicut in Luna circumducibiles, sed in eundem caeli tractum semper vergentes. Igitur et sectiones circulorum orbis et eclipticae, quas nodos vocant, aeternas in firmamento sedes occupant. Sic quidem Saturnus nodum suum habet, vnde ad septentriones scandere incipit, partibus 8 et media post stellam, quae in capite Geminorum orientalis dicitur; Iupiter ante eam ipsam stellam partibus 4, Mars vero Vergilias antecedentem partibus 6 et medio. In his igitur ac e diametro positis sidus existens nullam habet latitudinem, maximam vero, quae in his in quadraturis contingit, valde diuersam. Nam axium circulorumque inclinatio tanquam nodis illis pensilis instare videtur: tunc equidem maxima fit, quando Tellus sideri proxima est, hoc est in ortu sideris vespertino. Tunc enim in Saturno partibus duabus et besse axis inclinatur, in Ioue partibus 2 dempto triente, in Marte vero parte l et dextante. Econtra autem circa vespertinum occassum ortumque matutinum: plurimum tunc absente Terra Saturno quidem et Ioui quincunce vnius partis minor est huiusmodi inclinatio, Marti vero parte 1 et besse. Sic quidem diuersitas haec in maximis latitudinibus apprime percipitur, ac allicui tanto minor, quanto minus a nodo sidus distat pariter cum latitudine crescens et decrescens.
Accidit etiam motu Telluris in orbe magno latitudines visibiles nobis variari, ita sane propinquitate et distantia visibilis latitudinis angulos augente et minuente, sicut mathematica ratio exposcit, siquidem hic motus librationis secundum lineam rectam contingit. Fieri autem potest, vt ex duobus orbibus huiusmodi motus componatur, qui cum sint concentrici, alter alterius deflexos circumducit polos et inferior contra superiorem duplici velocitate polos orbis epicylos deferentis reuoluat; et hi quoque poli tantam habeant deflexionem a polis orbis mediate superioris, quantum huius a polis supremi orbis. Et haec de Saturno, Ioue et Marte ac orbibus Terram abientibus.
QUAE MAGNI ORBIS AMBITU INCLUDUNTUR
De Venere
Reliquum est eorum speculationem aperire, quae magni orbis ambitu includuntur, hoc est de motibus Veneris et Mercurij. Venus quidem persimilem habet circulorum compaginem qualem illi superiores, sed alia motum obseruantia.
Orbis quidem cum epicyclo suo maiori pares facit reuolutiones nono mense, vt praedictum est, eoque motu composito minorem epicyclum certa ubique habitudine firmamento restituit, summam eius absidem ad punctum, quo Solem vergere diximus, constituens. Minor autem epicyclus, impares cum illis reuolutiones habens, motui orbis magni imparitatem reseruauit. Ad huius quidem reuolutionem duos omnino circuitus perficit, vt, quandocunque Tellus in linea ad absidem diametro porrecta fuerit, sidus tunc centro maioris epicycli proximum sit et in transuerso quadrantum remotissimum simili fere modo, quemadmodum in Luna minor epicyclus Solem respicit, obseruans. Est autem proportio semidiametrorum orbis magni et Veneris sicut 25 ad 18, et maior epicyclus dodrantem suscipit vnius particulae, minor vero quadrantem.
Retrocedere quandoque et haec cernitur, tunc maxime quando sidus Terrae proximum est, simili quodammodo ratione vt in superioribus, sed conuersa. In illis enim accidit motu Terrae superante, hic autem superato, ac illic orbe Telluris contento, hic vero continente. Quapropter nec unquam Soli opponitur, cum Tellus intermediari non possit, sed ex certis a Sole distantijs, quae fiunt in contactibus circumferentiae lineis a centro Telluris prodeuntibus, vtrobique reuertitur, 48 gradus nunquam excedens ad nostrum aspectum. Et haec est Venerei motus summa, quo in longitudinem circumducitur.
Latitudinem quoque duplici causa scandit. Habet enim et haec axem orbis inclinatum quantitate anguli graduum duorum cum semissi. Et nodum suum, vnde septentriones petit, in abside sua habet. Digressio autem, quae ex tali inclinatione procedit, quamquam eadem in se ipsa sit, duplex ostenditur. Nam in alterutro nodorum Veneris incidente Terra transversis sursum et deorsum aspiciuntur: has reflexiones vocant; naturales apparent orbis obliquitates, et has vocant declinationes, eadem vero in quadrantibus. Caeteris autem locis ambae latitudines permixtae confunduntur ac alia aliam superans vincit ac similitudine ac dissimilitudine mutuo se augent et perimunt. Haec vero axis inclinatio est: habet librationem mobilem, non autem sicut in superioribus illis ad nodos pendentem, sed in alijs quibusdam volubilibus punctis, quae reuolutiones suas ad sidus annuas faciunt, vnde, quandocunque Tellus contra absidem Veneris steterit, maxima tunc fit librationis inflexio et haec in ipso sidere, in quacumque tunc parte sui orbis fuerit. Quapropter si tunc sidus in abside sit vel ei diametraliter opposito, latitudine non penitus carebit, tametsi in nodis tunc versetur. Hinc vero decrescente hac inflexione quoadusque Tellus per quadrantem circuli dicto loco amoueatur et similitudine motuum maximae illius deuiationis punctus a sidere tantundem destiterit, nullum prorsus huiusce deuiationis vestigium vsquam reperitur. Et deinceps deuiationem libramento continuato et illo principio a septentrionibus ad austrum declinante ac identidem a sidere sese elongante secundum Telluris ab abside remotionem sidus ad eam perducitur partem, quae prius australis fuerat, nunc autem oppositionis lege septentrionalis facta, donec iterum ad summam perueniat librationis circulo peracto, vbi rursum maxima fit deuiatio et primae similis et aequalis. Sic demum pari modo per reliquum semi circulum pergit. Quapropter nunquam fit meridiana haec latitudo, quam plerumque deuiationem vocant. Et haec duobus orbibus fieri concentricis et axibus obliquis, sicut in superioribus orbibus dieebamus, hic quoque consentaneum esse videtur.
De Mercurio
Sed omnium in caelo mirabilissimus est Mercurij cursus, qui paene imperuestigabiles permeat vias, vti perscrutari non facile queat. Addit praeterea difficultatem, quod sub radijs Solis inuisibiles plerumque meatus occupat et paucis admodum diebus visibilem se exhibet: attamen comprebendetur et ipse, modo altiori ingenio quispiam incumbat. Conuenient et huic epicycli duo, vt in Venere, in orbe suo reuolubiles. Nam maior epicyclus cum orbe suo pariter facit reuolutiones, vt illic, absidis eius sedem gradibus 14 et medio post Virginis Spicam constituens, Minor autem epicyclus contraria illius lege duplici vero reuolutione relfectitur, vt in omni situ Telluris, quo absidem huius superauerit vel ex aduerso respicit, sidus a centro maioris epicycli remotissimum sit atque in quadrantibus proximum. Et huius quidem orbem tertio mense diximus reuerti, hoc est 88 diebus, cuius semidimetiens partes capit 9 et duas quintas vnius partis, quarum semidiametrum magni orbis 25 posuimus. Ex his autem primus epicyclus accipit 1 et 41 minuta, secundus autem tertiam eius partem, hoc est minuta 34 fere. Sed is quidem circulorum concursus hic non sufficit vt in caeteris. Terra siquidem in supradictis absidis respectibus permeante, longo minori apparet ambitu sidus moueri, quam ratio circulorum iam dicta sustinet, et rursus in quadraturis longe etiam maiore. Cum vero nullam aliam in longitudine diuersitatem ex hoc fieri parcipiatur, consentaneum est per accessum quendam et recessum a centro orbis secundum lineam rectam contingere. Quod quidem fieri oportet duobus orbiculis circumdatis habentibus axes aequidistantes axi orbis, dum centrum epicycli maioris siue totius illius asse tantum distat a centro orbiculi immediate continentis, quantum centrum huius a centro extremi. Id quidem repertum est minutis 14 et medio vnius partis de 25, quibus omnium contextum mensi sumus: quodque motus extremi orbiculi binas in anno vertente reuolutiones faciat, interior autem motu reflexo duplo recursu quater interim reuertatur. Perferuntur enim hoc motu composito centro maioris epicycli secundum lineam rectam, quemadmodum circa latitudines libratas diximus. Sic igitur in memoratis ad absidem Telluris sitibus centrum epicycli maioris centro orbis proximum est, in quadraturis autem remotissimum. In locis autem mediantibus, hoc est 45 gradus ab his, centrum maioris epicycli centro exterioris orbiculi se applicat amboque in vnum concurrunt. Quantitas autem huiusce recessus et accessus constat minutis 29 vnius praedictarum partium. Et hactenus motus Mercurij longitudinalis sic se habet.
Latitudinem vero haud secus facit quam Venus, sed tractu semper contrario. Vbi enim illa septentrionalis fit, hic austros petit. Declinat autem orbis eius ab ecliptica quantitate anguli partium 7. Deuiatio autem hic quoque semper australis dodrantem vnius gradus nunquam excedit. Caeterum quae circa latitudinem Veneris dicta sunt, hic quoque commemorasse conuenit, ne eadem saepe repetantur.
Sicque septem omnino circulis Mercurius currit, Venus quinque, Tellus tribus et circa eam Luna quatuor. Mars demum, Iupiter et Saturnus singuli quinque. Sic igitur in vniuersum 34 circuli sufficiunt, quibus tota mundi fabrica totaque siderum chorea explicata sit.
Further reading:
- Kopernik Mikołaj, Pisma pomniejsze, Warszawa 2007.
