[Margin: What a System is.]

[I.] The System of the World is nothing other than the Coordination, or composition, of the great parts of the World—namely the Elements and the Heavens: of which the matter, as it were, is the number of the elements and heavens (both total and partial); but the form is the order and situation of them among themselves, and relatively to the center of the Universe.

[Margin: How manifold the system is.]

Regarded, therefore, by [its] form, the System of the World is divided into two highest kinds—namely, into that which is constructed around the earth immobile at the center of the Universe; and into that which is constructed around the Sun, immobile at the center of the Universe, or immune from the motion τῆς φορᾶς κατὰ τόπον [tēs phorâs katà tópon, “of locomotion according to place”]—namely of translation [local displacement]—but moving the Earth through the annual orb. Again, each [kind], but especially the first, is subdivided into the Homocentric, the Eccentric, and the [system] mixed from some Concentric orbs and some Eccentric. Now, since enough has been done about the Number of the heavens (as the remote matter of the Cosmic system) in the preceding chapter, it follows that we should treat of the order of the heavens and Planets, and of the number of the partial orbs. And we take our beginning from the most ancient [systems].

[Margin: The alternating rise and fall of the systems.]

[II.] It is most worthy of observation that two sects of the Physicists and Mathematicians, alternately—like Castor and Pollux—perished, and again, revived, prevailed in the Schools. For first Pythagoras, with some [members] of his [school], rightly placing the Earth in the center of the World, used Eccentrics and Epicycles, and placed the Sun in the middle of the Planets. But others of the Pythagoreans, retaining Epicycles and Eccentrics, nevertheless placed the Sun in the center of the world, and the Earth in the middle of the seven Planets. Then Plato again restored the earth to the center of the Universe, and so placed the Sun in the middle of the Planets, that nevertheless he reckoned Venus and Mercury to be borne, for the most part, above it [the Sun]; whom Eudoxus, Calippus, and Aristotle followed, [and] strove to explain the whole motion of the Planets through concentric circles—and so judged that neither Venus nor Mercury goes through Epicycles above and below the Sun, but [are] either always above the Sun, or always below. When these were dead, Others again embraced Eccentrics and Epicycles, and the Earth in the middle of the world—such as Archimedes, Hipparchus, Sosigenes, Cicero, Vitruvius, Pliny, Macrobius, Capella—yet with a varying order of the Planets. Others, moving the Earth from [its] place—such as Aristarchus, and Philolaus the Pythagorean—what they thought about Eccentrics and Epicycles, either they did not set forth, or it has not been handed down to posterity. But again Ptolemy, reawakening the most ancient opinion of the Pythagoreans, so established Eccentrics and Epicycles, that he retained the earth in the middle of the World, [and] the Sun in the middle of the Planets; and, persuading the greatest part of the Astronomers of this opinion, extended it down to the fourteenth century. That order of the Planets, however, Alpetragius and Geber judged should be changed. But the homocentrics too were taken up again by Alpetragius, Amici, and Delphinus, with a few others; on the contrary, Turriano and Fracastoro, the Ptolemaic order being retained, nonetheless recalled into the light homocentrics—and indeed more [of them] than the Aristotelians, not to say the Eudoxians. But about the same time Copernicus not only summoned forth from the tomb the figment of Philolaus and Aristarchus, about the annual motion of the earth around the immobile Sun, but adorned it with arguments so probable that he has persuaded very many of it down to this very day; and he carried Venus and Mercury around now below, now above the Sun, with Plato, Vitruvius, Macrobius, Capella, and Bede. Hence Tycho—and with him Longomontanus—having got a most beautiful handle, not only—

[…continues on p. 277 (PDF 312): “…not only [retained the Earth at the center, but]…” — Riccioli proceeds to the Tychonic system and the modern revival of the geo-heliocentric arrangement.]

(printed p. 277 — The historical survey concludes with the modern systems — Tycho, Argoli, Riccioli’s own, and Baliani — and the absurd ancient ones. The chapter then treats the Pythagorean system with its harmonic intervals, Archimedes, and Pliny’s system, and opens the account of Ptolemy.)

…[Hence Tycho, and with him Longomontanus, having got a most beautiful handle,] not only ordered Venus and Mercury, but Mars too, Jupiter, and Saturn, to go around the Sun; but the Sun and Moon, with the Fixed [stars], around the Earth—[the Earth] resting in the middle of the world, free from all motion of translation; and, the Eccentrics being retained, he removed the Ptolemaic Epicycles. Finally Argoli, the Tychonic system being dislocated, tried to move the three superior [planets] around the earth, but Mercury and Venus around the Sun, the earth being left in the middle of the world. But we [hold that] around the earth [are moved] Saturn, Jupiter, the Sun, the Moon, and the Fixed [stars]; but we judge that Venus, Mercury, and Mars can be ordered around the Sun. Finally, Don Giovanni Battista Baliani suspected that the Moon could be placed in the center of the World. It is, therefore, worth the effort to discuss singly so many and so diverse attempts and studies, and to weigh the reasons adduced on either side.

[Margin: Ancient systems, but absurd.]

But I have passed over, as of no consideration, those three opinions about which Plutarch (bk. 2 of the Placita, ch. 15) [speaks] in this manner: “Xenocrates thinks the stars are moved in one and the same surface. The rest of the Stoics [place them] with varying lowness and loftiness among themselves. Democritus [places] the fixed [stars] in the supreme [place], hence the wandering [stars], and below these the Sun, Lucifer [Venus], the Moon, etc. Metrodorus of Chios and Crates [held] the Sun set as the supreme of all, after which the Moon, [and] below these the wandering and non-wandering [stars].” So that nothing is so absurd that it does not fortify itself with some patron.

[Margin: Pythagoras’s system.]

[III.] The most ancient, therefore, but of the tolerable systems, was the Pythagorean; in which Pythagoras so disposed the intervals by harmonic ratios, that, beginning from the earth, he ascended thence to the Moon, hence to Mercury, hence to Venus; hence further to the Sun; but from the Sun to Mars, hence to Jupiter, hence to Saturn, and at last from Saturn to the Fixed [stars]—as Pliny plainly relates (bk. 2, ch. 22). For he says: “Pythagoras sometimes, from a musical reckoning, calls ‘a tone’ [the distance] by which the Moon is distant from the earth. From it to Mercury half of that space, and from it to Venus almost as much; from her to the Sun, one and a half times [the amount]. From the Sun to Mars a tone—that is, as much as [from] the earth to the Moon; from it to Jupiter half, and from it to Saturn half, and thence one and a half times to the Zodiac [Signiferum].” With whom Censorinus entirely agrees (in the book On the Natal Day, ch. 11, toward the end), in these words: “Therefore from the earth to the Moon Pythagoras thought there are about 126,000 stadia, and that this is the interval of a tone; from the Moon to the star of Mercury, which is called Stilbon (στίλβων, ‘the gleaming’), half of it, as it were a semitone (ἡμιτόνιον); hence to Phosphoros (φωσφόρος, ‘the light-bringer’), which is the star of Venus, almost as much—that is, another semitone; thence further to the Sun three times as much, as it were a tone and a half; and so the Sun’s star is distant from the earth three tones and a half, which is called a diapente [a fifth]; but from the Moon two and a half, which is called a diatessaron [a fourth]. But from the Sun to the star of Mars, whose name is Pyroeis (πυρόεις, ‘the fiery’), there is just as much interval as from the earth to the Moon, and that makes a tone (τόνος); hence to the star of Jupiter, which is called Phaethon (φαέθων), half of it, which makes a semitone; thence to the highest heaven, where the Signs are, likewise a semitone.” Thus far concerning the order and symmetry of the heavens according to Pythagoras.

[Margin: The Pythagoreans [were] the authors of Eccentrics & Epicycles. Pythagoras’s system [was] not received by all the Pythagoreans.]

That the Pythagoreans first devised Eccentrics and Epicycles, Nicomachus is the authority (in Simplicius, comment. 2 On the Heaven, where he diligently explains the hypotheses of the ancients); and from him, G. B. Amici (ch. 6, On the motions of the celestial bodies), and J. A. Delphinus (On the celestial globes and motions, ch. 4), where he attributes this very [thing] to Pythagoras. From what has been said it is clear that it is not rightly called by Paolo Antonio Foscarini “the system of Pythagoras,” or absolutely “Pythagorean,” that [system] in which the Sun is in the center of the world, and the earth—above Mercury and Venus—is rolled around the Sun, although some disciples of Pythagoras thought thus.

[Margin: Archimedes’s system. And Cicero’s.]

[IV.] To the Pythagorean system, as to [its] order, Archimedes subscribed—if the things are true which Macrobius (bk. 2 on the Dream of Scipio, ch. 3) thus relates about him: “And Archimedes indeed believed that he had detected the number of stadia by which the Moon was distant from the surface of the earth, Mercury from the Moon, Venus from Mercury, the Sun from Venus, Mars from the Sun, Jupiter from Mars, Saturn from Jupiter. But also, from the orb of Saturn all the way to the starry heaven itself, he thought he had measured out the whole space by reason. Which dimension of Archimedes, however, is repudiated by the Platonists.” Nor Archimedes only, but also Cicero (On the Dream of Scipio)—whose words we shall report in a more opportune place, the following chapter, number 4—so that we may dissociate him from Plato.

[Margin: Pliny’s system.]

[V.] Pliny himself too (bk. 2, chapters 5, 6, 8, 15, 16, 17, taken together) expressed the same order, and acknowledged the Apsides of the Eccentrics and Epicycles, or the perigees and apogees of the Planets—surely from Sosigenes, from whom he was wont to draw much. Therefore in ch. 5 he says: “That the Earth is the lowest and the middle [point] in the whole, and that the same, on the hinge of the universe, stands suspended, balancing the [things] by which it hangs: thus alone immobile, with the universe revolving about it.” Soon, in ch. 6: “Between this [earth] and the heaven hang, by the same breath, separated by fixed intervals, seven stars, which from their gait we call ‘wandering,’ though none wander less than they; in the middle of them is carried the Sun.” But with greater distinction, in ch. 8: “Now, the body of the world itself being left aside, let the rest between heaven and the lands be treated. It is certain that the highest is what they call the star of Saturn, and therefore [it] appears the smallest, and goes round in the largest circle, and in the thirtieth year returns to the shortest beginnings of its seat, etc. But the star of Saturn is of a gelid and stiffening nature; and much lower than it [is] the circle of Jupiter, and therefore [it] is carried round by a swifter motion in twelve years. The third, of Mars—which some call Hercules’s—fiery, burning from the nearness of the Sun, is turned round in almost two years; and therefore, by the excessive ardor of this [Mars] and the rigor of Saturn, Jupiter, set between the two, is tempered from each, and made salutary. Then the course of the Sun is of 360 parts [degrees]; but so that the observation of its shadows may return to the marks, five days are added over the years, and over and above a fourth part of a day. For which cause, in the fifth year one intercalary day is added, that the reckoning of the seasons may agree with the Sun’s journey. Below the Sun goes round a huge star called Venus’s, wandering with an alternating course, and a rival of the Sun and Moon by its very surnames. For, going before and rising before the morning, it takes the name of Lucifer [light-bringer], as a second Sun hastening the day; on the contrary, shining from the West [at setting], it is called Vesper [evening-star], as prolonging the light and rendering the office of the Moon. Which nature of it Pythagoras of Samos first detected, about the 42nd Olympiad, etc. But it accomplishes the circuit of the Zodiac in 348 days, never standing off from the Sun farther than 46 parts [degrees], as Timaeus holds. By a like reasoning, but by no means in magnitude, nearest to it [is] the star of Mercury, called by some Apollo’s, [which] is carried in a lower circle, in a swifter circuit by nine days, shining now before the rising of the Sun, now after [its] setting, never more remote from it than 23 parts [degrees], as this same [Pliny] and Sosigenes teach, etc.”

He proceeds hence (ch. 9) to speak of the Moon, and from ch. 15 to 17 he treats of the stations, retrogressions, elevations, depressions, velocity and slowness of the Planets, and refers the causes to [their position] in the circles, according as they approach their apsides or recede from them. But let those words (ch. 15) be noted: “For many causes all these things happen. The first [is] of the circles, which the Greeks call apsides in the stars—for one must use the Greek words. These [apsides] are proper to each of them, and another to the world”; and a little after: “Therefore from another center, for each, their apsides arise, and therefore they have diverse orbs, and dissimilar motions, etc.” Do you see how Pliny designated Eccentric orbs?

[Margin: Ptolemy’s system.]

[VI.] As Pliny grew old, Ptolemy began to flourish, who took over willingly the system of Pythagoras—which he knew had pleased Archimedes, Hipparchus, and Sosigenes—and fortified it with several reasons: both as to the Eccentrics and Epicycles (which he used in bks. 3, 4, 5, and 9 to 13 of the Almagest), and as to the order of the Planets, and the state of the immobile earth in the center of the universe—whose arguments about the situation and immobility of the earth (from bk. 1 of the Almagest, ch. 5 & 7), although they were not neglected by us (bk. 2, ch. 2 & 3), nevertheless below, in section 4, must be more diligently treated and weighed with the solutions of the Copernicans. As regards the order of the Planets: behold his own words (from bk. 9 of the Great Construction, ch. 1): “The sphere of Saturn, which is the greater, and of Jupiter, which is second and nearer to the earth, and of Mars beneath it, are more remote from the earth than the rest. The Solar [sphere] too is said by almost all the first Mathematicians [to be] in nearly the same way. But the spheres of Venus and of Mercury are by the Ancients placed below the Solar [sphere]; by some of the younger [moderns], however, these too are set above it, because the Sun has never been seen to suffer an Eclipse from these Planets. But this reasoning seems weak to us. For some Planets can be below the Sun, and yet not be opposed [interposed] to it, because they are not in the same plane passing through them and our sight—just as also, in the conjunctions of the Moon, for the most part no eclipse of the Sun occurs. But since the understanding of this matter cannot be had otherwise—because none of these stars makes a sensible parallax, from which alone the distances are taken—

[…continues on p. 278 (PDF 313): “…the order of the ancients seems to me to proceed more naturally, when, the Sun being placed in the middle, it separates those Planets which can depart from the Sun by however great a distance, from those which cannot…” — Ptolemy’s defense against Geber and Copernicus, then ¶VII (Ptolemy’s followers, esp. Regiomontanus) and ¶VIII (Clavius’s four arguments for the order).]

(printed p. 278 — The account of Ptolemy concludes, vindicating him against Geber and Copernicus on the Venus and Mercury parallax. The page then surveys Ptolemy’s followers, especially Regiomontanus, and opens the treatment of Clavius’s system and his arguments for the planetary order.)

[Margin: Ptolemy’s reasoning vindicated from the objections of Geber and Copernicus.]

…[the distances] are taken; the order of the ancients seems to me, in [its] verisimilitude, to proceed more naturally, when, the Sun being placed in the middle, it separates those Planets which can depart from the Sun by however great a distance, from those which cannot so depart, but are always led around near it [the Sun]: although [the hypothesis] does not move them so [far] from the Sun toward the earth, that a parallax—about which one should be concerned—could occur. By which words, indeed, he sufficiently forestalls the objections to be hurled against him afterward by Geber and Copernicus. For he does not deny all parallax to Venus and Mercury, since by this very [fact]—that he places them below the Sun—he is forced to concede [them] a somewhat greater [parallax] than [to] the Sun, and to Venus at perigee about 3′, and to Mercury 7′, as Geber gathers (bk. 7, ch. 1 of his Astronomy). But he denies that this [parallax] is to be cared about in this business, or that it is so evident from observations, that from it, foreknown beforehand, their distances can be established. Moreover, he does not absolutely deny that some little part of the Sun can be eclipsed by Venus or Mercury—for that this follows from the Ptolemaic hypothesis, Geber shows in the same place; but he says that, if this has not been observed, it has happened because the observations of the conjunctions of the Sun with Venus (♀) or Mercury (☿) were made at that time when either, on account of [its] latitude from the Ecliptic, appeared on this side of, or beyond, the Sun’s disc.

Finally Geber too, above, and Copernicus (bk. 1, ch. 10), thus argue: “That argument too of Ptolemy” (the words are Copernicus’s) “—that the Sun ought to be carried in the middle, between those departing in every direction from it and those not departing—how unpersuasive it is, appears from this: that the Moon, itself also departing in every direction, betrays its falsity.” But Ptolemy thought this [argument] probable not absolutely, but on the hypothesis that the knowledge of this matter cannot be had otherwise; whereas the place of the Moon below the Sun is manifest from elsewhere—both from Eclipses, and from the Lunar parallaxes, most evidently exceeding the Solar [ones].

[Margin: Regiomontanus’s system.]

[VII.] To Ptolemy, as to the order of the Planets, subscribed thereafter all the Arabs (except Geber and Alpetragius); and all the Greeks (except Theon); all the Latins, finally, down to Clavius, before the use of the Telescope had grown strong (except Martianus Capella, Macrobius, Apuleius, Sammerius, Bede, Copernicus, and the Copernicans); but especially John Regiomontanus (in the Epitome of the Almagest, bk. 9, prop. 1). Who retained Venus and Mercury below the Sun the more willingly, the more probable he thought it that the space which is between the Sun at perigee and the Moon at perigee—namely [1006] terrestrial semidiameters, as he himself computes—ought not to be empty of every star. He adds—both he himself, and Clavius (on the Sphere, p. 71), and the Conimbrican College (2 On the Heaven, ch. 7, q. 4, art. 2): (1) the Eclipse which the Sun suffers from Venus passing under the Sun’s disc is not sensible, because the disc of Venus, in comparison to the disc of the Sun, is about a hundredth part, as I too computed (bk. 7, sect. 1, ch. 4, num. 4); and much less the Eclipse from tiny Mercury; or, as Copernicus says (bk. 1, ch. 10): “That so small a spot is not easily seen beneath the most excellent light.” But these things, as I said in the same place, must be understood of the naked eye, and before (or apart from) the use of the Telescope; otherwise, that Mercury was seen below [against] the Sun by the help of the Telescope, I related (bk. 3, ch. 3, scholium 3), where also (scholium 2) I taught that that blackish [spot] which was seen below the Sun by Averroes, or Aven Rodan [Ibn Riḍwān], or by others in the time of Charlemagne, was not Mercury, but one or more spots of the Sun.

[Margin: Regiomontanus is vindicated from Copernicus’s insults.]

But Copernicus (bk. 1, ch. 10) refutes the former reasoning of Regiomontanus—(whom, however, whether from forgetfulness or from swelling of mind, he passes over unnamed)—from this, that between the Moon and us there are air and fire, and a space of 52 semidiameters empty of every star. But Regiomontanus would answer that the case is unlike, because Air and Fire are not heaven [celestial], nor a place apt for containing a star. Copernicus adds that the semidiameter of the Epicycle of Venus—by which she departs from the Sun on either side about 45 degrees—occupies a greater space than [the distance] from the earth to Mercury at apogee, and yet is empty of a star; but Regiomontanus would answer that the space within that Epicycle is not empty, since through it Venus runs from apogee to perigee.

[Margin: Clavius’s system. 1st reason of Clavius, from parallax.]

[VIII.] Lastly, our Clavius tried to confirm the order of the Pythagorean and Ptolemaic System (in ch. 1 of the Sphere, from p. 65 in my [copy]), and from him Francesco Barozzi (bk. 1 of the Cosmography, p. 9). Which reasons must be weighed. The first is from parallax: for the greater it is (other things being equal), the nearer the star having it is to the earth, as is clear from what was said (bk. 1, ch. 35). But the parallax of the Moon is far greater than that of the Sun, as plainly appears from what was said (bk. 3, ch. 8, & bk. 4, ch. 14). Likewise the parallax of Mercury [is] greater than that of Venus, and of Venus than of the Sun, says Clavius—for as to the three superior [planets] he admits that this argument does not avail. But in reality, as Regiomontanus admits (bk. 9 of the Epitome, prop. 1), and before him Ptolemy (bk. 9 of the Almagest, ch. 1), the motion of Venus and Mercury is not so scrupulously known, that from it—especially using the Ptolemaic or Alfonsine tables—their parallax can be evidently discerned; and rather the distance from the earth must be established from elsewhere, and then from it the parallax is to be gathered by reasoning. Then, since by the Telescope showing [it] it is now established that Venus and Mercury, when they are nearer to apogee, are situated above the Sun, it is false that their parallax is then greater than the Solar; again, because they so go around the Sun that Mercury departs less from the Sun, it follows that Mercury, at its perigee, is higher than Venus at perigee, and therefore undergoes a smaller parallax.

[Margin: 2nd reason, from shadows.]

The second reason is drawn from shadow: for the smaller the shadow of the gnomon, the higher (other things being equal) is the star from whose rays, drawn through the top of the gnomon, the shadow is cast—as is clear from the diagram adduced (bk. 4, ch. 10, num. 1). But at an equal elevation from the horizon, the Solar shadow is shorter than the Lunar; nay (says Barozzi), the shadow of the Sun’s ray is less than that of Venus’s ray, and of Venus’s than of Mercury’s, and of Mercury’s than the Moon’s—and he testifies that this is proved by experience. But concerning Venus at perigee with respect to the Sun, we grant [it]; but concerning her with respect to Mercury, we deny [it]; and concerning either planet situated near apogee, we likewise deny [it]: besides that the experiment of the Mercurial shadow is suspect to me, for Mercury near perigee is wont to lie hidden under the brightness of the Sun—nay, in its greatest digression it does not appear, but [rather] the twilight light dilutes [washes out] its shadows.

[Margin: A slip of Clavius.]

This argument could surely be much more brilliantly accommodated to Jupiter, whose shadow is more evident than Mercury’s: and so I would not have wished those words to have escaped Clavius (p. 68 of the Sphere): “The same which we said of the Moon with respect to the Sun can be accommodated with respect to the other planets; for although the other planets do not shine so [much] as to cast a shadow, yet it can be known how much their rays are cast through the tops of gnomons.” For the rays of Venus and Jupiter do cast a manifest shadow. Then, how slippery is that accommodation and supplement of shadow!—say, by placing the eye in a plane and looking at the Planet through the top of the gnomon; and how difficult, in these Planets, to foreknow the moment at which they are at such and so great an altitude above the astronomical Horizon, independently of their distance from the center of the earth. But it is too easy, from a presupposed hypothesis, to feign experiments, and to reckon [results] that were never produced as [results] that would be, if they were [produced].

[Margin: 3rd reason, from Eclipses.]

The third reason is sought from mutual Eclipses: for that star is nearer to the earth and to us observing from the earth, which, by the interposition of its body, occults the other from us; but the Moon occults from us not only the Sun, but all the other planets: therefore the Moon is the lowest of all. By a like reasoning, Mercury will be below Venus, and Venus below Mars, and so on, says Clavius—namely, from the presumption of this system, not from any experiment concerning Mercury; for Mercury has never been seen to have occulted Venus; nay, perhaps it never could nor will be able even to occult her, but rather Venus [occults] Mercury. See what we have handed down about these occultations of the Planets, established from observation (bk. 5, ch. 2, schol. 2, & bk. 7, sect. 6, ch. 14).

[Margin: 4th reason, from the speed of motion.]

The fourth reason is taken from the velocity of the proper motion, and the slowness of the common motion: for the more a Planet is distant from the prime Mobile and from the Fixed [stars], the more quickly it completes its period, by tending toward the East; whence it happens that, returning daily later to the same Meridian, it seems slower in the motion of the prime mobile and of the Fixed [stars] toward the West. Since, therefore, the Fixed [stars] cannot complete their period except after many thousands of years, but Saturn completes it in about 30 years, and Jupiter in 12, and Mars in about 2 years, and the Sun in a single year, but the Moon within one month, while Venus too and Mercury complete it more quickly than Mars and more slowly than the Moon—it is established that below the Fixed [stars] are—

[…continues on p. 279 (PDF 314): ”…[below the Fixed stars is] Saturn, and below Saturn Jupiter, then Mars, then the Sun, then Venus and Mercury, and lowest of all the Moon” — Clavius’s fourth argument concluded, then the remaining reasons for the Ptolemaic order and Riccioli’s assessment.]

(printed p. 279 — The treatment of Clavius concludes with his remaining reasons (4–9) for the Ptolemaic planetary order. The page then presents the catalogue of authors who subscribed to that order.)

[Margin: 4th reason continued.]

…it is established that immediately below the Fixed [stars] is Saturn, below it Jupiter, below Jupiter Mars, below Mars the Sun, Venus, and Mercury, and below these finally the Moon. But from this argument Clavius denies that anything certain can be gathered about the order of the Sun, Venus, and Mercury among themselves: for the mean motions of the Sun, Venus, and Mercury are equal, but the apparent motion in the Epicycle is longer for Venus than for the Sun, and for the Sun than for Mercury. By which argument Alpetragius (as we shall relate below) contends that Venus ought to be placed below Mars, above the Sun, but Mercury below the Sun. Further, as we said (bk. 7, sect. 3, ch. 11, at the end), the revolution of Venus, the Sun’s motion (which it accompanies) being computed, is 584 days very nearly, and of Mercury about 116; but around the immobile Sun the revolution of Venus is about 225 days, and of Mercury about 88.

[Margin: 5th reason, from the interval between the Moon (☽) and the Sun (☉) [being] not empty.]

The fifth reason is that which I already adduced at number 6, from Regiomontanus—namely, lest the space which is from the Moon to the Sun be empty of a star; which reason avails much more in the hypothesis of Kepler, Ours, and Wendelin, in which between the Moon and the Sun there intervene far more semidiameters of the earth than 1006: for they are, for Kepler, about 3400; for me, 6036; for Wendelin, about 14600. But in the Ptolemaic system the intervals of the Planets are so ordered that nothing superfluous intervenes between heaven and heaven, but the lowest [point] of Saturn, or [its] Perigee, touches the apogee of Jupiter, and so of the rest, as we taught (bk. 7, sect. 6, from ch. 1 to 4). But this reason now ceases in the more recent hypothesis, in which—if, by the Telescope showing [it], we lead Venus around the Sun in a wider circuit, and Mercury in a narrower, and if we wish to keep safe the magnitude of Venus’s Epicycle from [its] greatest digressions from the Sun and from the distance of the Sun from the earth—it is necessary that between the Moon at apogee and Venus at perigee there intervene a great space, empty of every ordinary Planet, as may be seen by [one] comparing the Lunar distances (about which bk. 4, ch. 14) with the least distances of Venus from the earth by the more recent hypotheses (about which bk. 7, sect. 6, ch. 2, in table 2).

[Margin: 6th reason, from the multiplicity of motions.]

The sixth reason is taken from the multiplicity and irregularity of the motions: for Mercury has more motions than Venus and the Sun, and therefore the Ptolemaics attribute to Mercury five orbs and an Epicycle, but to Venus three. But this reason is very weak; for thus the Sun would have to be placed above all the Planets, because by the simplicity of [its] motion it is more similar than all the Planets to the motion of the Fixed [stars] and the Prime mobile. Wherefore Aristotle (bk. 2 On the Heaven, ch. 10, or text 60) said: “It is no less wonderful, for what cause those [bodies] which are more distant from the first motion are not always moved by more motions, etc. For the Sun and Moon are moved by fewer motions than some of the wandering stars, although they are farther from the middle, and nearer to the first of bodies, than these.” Although the latest age has detected far more motions in the Moon, according to what was said (bk. 4, ch. 18). Clavius could, therefore, have neglected this little reason.

[Margin: 7th reason, from the dependence of the Planets on the Sun.]

The seventh reason is drawn from the dependence of the Planets on the Sun in light and motion: for the Sun is, as it were, the King and Heart, the rule and moderator of all the Planets—since all the Planets, in their motions, are bound by a certain admirable harmony to the Sun’s motion, as is clear concerning the synodic revolutions of the Moon; and concerning the periods of the other Planets, whether in the Eccentric or in the Epicycle, it is clear from what was said (bk. 7, sect. 1, ch. 7). [The Sun] ought, therefore, to go in the middle of them, that it might equably direct their motions and illuminate them—since we see Mars and Venus, on account of [their] nearness to the Sun, more strongly illuminated. Nor did Clavius abstain from a likeness and analogy of those [things] which are customary among human polities, so as to set the Sun in the middle place as King; for he says that Saturn, as being an old man, is the counsellor of the Sun; Jupiter, on account of [his] magnanimity, is the Judge; Mars the leader of the soldiery; Venus the mother of the household; Mercury the scribe or chancellor; the Moon, finally, the swiftest messenger—“As most [people] jest,” says Clavius (for he did not wish these [things] to be recounted by himself seriously); “though Stoeffler (on Proclus, p. 44) relates these things seriously.” But these [things] are said too much as commonplaces; and by almost the same argument the Copernicans contend that the Sun ought to have been placed in the middle of the whole Universe, but Tycho in the middle of the five smaller Planets surrounding it; nor must a King, or Master, or Leader always be in the middle of his [people], but often he follows after all [of them], or even sometimes goes before them.

[Margin: 8th reason, from the Sun’s activity.]

The eighth reason, which Albumasar adduces (in his Great Introductory [work], tract. 3, diff. 3), rests on the activity of the Sun: for it ought to be placed in the middle of the Planets, lest, if it were higher, [it should fail in heat]; but if too low, it would act too much upon these lower [things, and scorch them here too]. Clavius thinks Ovid alluded [to this] (Metamorphoses 2), when he brings in Phoebus moderating, by [his] counsel, Phaethon [who was] guiding the solar chariot:

“Going too high, you will burn the heavenly signs; too low, the lands: in the middle you will go most safely.”

But this reason, if it held, would require the Sun to be precisely in the middle of the interval which is from the earth to the Fixed [stars], as to quantity; whereas in no hypothesis—much less the Ptolemaic—can this be true, as is clear from the distances of the Planets from the earth, reduced by us into a table (bk. 7, sect. 6, ch. 2).

[Margin: 9th reason, from the week of days and the dominion of the Planets.]

The ninth reason is taken from the order and nomenclature of the days of the week—which order Xiphilinus relates (from bk. 36 of Dio, in [the life of] Pompey) to have been instituted by the Egyptians. For, beginning from Saturn, and attributing to it the dominion over the first hour of the day, and running through the hours according to this order of the Planets—Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon—the dominion falls upon the first hour of the following day to the Sun, and of the [next] following to the Moon, then to Mars, afterward to Mercury, hence to Jupiter, and at last to Venus, according to what was said (bk. 1, ch. 30). But Dio in the same place, and Xiphilinus, indicate also another reason for this order, taken from the harmonic intervals—which [reason], also from Pythagoras, Pliny and Censorinus hinted to us (we adduced [it] at number 3). And that distribution [of the days] presupposes the aforesaid order of the Planets, but does not produce [prove] it; for neither is it true—nay, [it is] a most vain figment—that the dominion of the first hour of the Lord’s day [Sunday] is given to the Sun rather than to another Planet, and so of the rest. The other [matters] about the harmonic intervals, which everyone tries to drag over to his own system, must be discussed in section [4] of this book.

For these causes, then—and especially on account of [its] antiquity and authority—this system prevailed over all others, from Pythagoras down to our own century; and so, for about 20 centuries, it had on its side the greater part of the Astronomers, and many of the Theologians and Physicists [Natural Philosophers]; of whom it is fitting to review the chief.

Authors who subscribed to Pythagoras and Ptolemy as to the Order of the Planets

[IX.] I said “as to the order”; for as to the multitude of the total or partial heavens some have dissented, as is clear from what was said here in chapter 1; and as to the hypothesis of Eccentrics, the Homocentrists [dissented], as I already said (sect. 2, ch. 2). But as to the order of the Planets, to this system have given their vote: Archimedes (in Macrobius, bk. 2 on the Dream of Scipio, ch. 3); the Chaldeans (in Bede, [the book] On the Elements of Philosophy); Cicero (On the Dream of Scipio); Pliny (bk. 2, ch. 6 & 7); Cleomedes (bk. 1 of the Cyclic Theory, ch. 3); Sosigenes (in Simplicius, on 2 On the Heaven); Albategnius [al-Battānī] (On the science of the stars, ch. 50); Alfraganus (difference 12, where he says he follows the opinion of the ancients); Albumasar (in his Introductory [work], tract. 3, diff. 3). And these were followed by the greater part of the Arabs, and the Alfonsines in [their] tables; John Fernel (bk. 1 of the Cosmotheoria); Peurbach (in the Theorics of the Planets) and its expositors, especially Pedro Nunes, Erasmus Reinhold, Erasmus Oswald, and Christian Wurstisius. Besides, John Regiomontanus (in the Epitome of the Almagest, bk. 4, prop. 1); John Stoeffler (on Proclus’s Sphere, p. 44); Julius Firmicus (bk. 3 of the Mathesis, from ch. 3 to 9); Giovanni Pontano (bk. 7, On celestial things); John of Sacrobosco (on ch. 1 of the Sphere, and there his commentators enumerated at the beginning of bk. 1 of our Almagest); Orontius [Finé] (on the Sphere, bk. 1, ch. […]); G. B. Amici (opusculum On the motions of the celestial bodies); J. A. Delphinus (On the celestial Globes); Fracastoro (in the Homocentrica, sect. 2 & 3); Egnatio Danti (in [his] tables, from table 12); Peter Apianus (in the Astronomicum Caesareum); Gemma Frisius (On the principles of Cosmography, bk. 1); Maurolyco (Dialogue 1 & 3 of the Cosmography, and at the end of the same); John Anthony Magini (in the Theorics of the Planets); Clavius (on the Sphere, from p. 64); Barozzi (in the Cosmography, bk. 1—

[…the author-catalogue continues on p. 280 (PDF 315): “…p. 8; Rudolph Goclenius, Michael Neander, Cardano, Ascanio Martinengo; and, to add a Father or two, St. John Damascene and Bede” — then the System I diagram (the Ptolemaic/Pythagorean order), and ¶X: Clavius’s “swan-song,” on seeing Galileo’s telescopic discoveries.]

(printed p. 280 — The author-catalogue concludes, followed by the System I diagram and Clavius’s “swan-song” on the telescope, which ends Chapter II. Chapter III then opens, on the Platonic, Geber, and Theon systems. A large engraved diagram of the Ptolemaic system spans both columns.)

…[Barozzi, in the Cosmography, bk. 1,] p. 8; Rudolph Goclenius (in the Urania, ch. 4); Michael Neander (in the Elements of the spherical doctrine, ch. […]); Cardano (On Variety, bk. 1, ch. 1); Ascanio Martinengo (in the Great Gloss, p. 968). Finally, to add one or another Father: St. [John] Damascene (bk. 2 of the Orthodox Faith, ch. 7) supposes that in the First circle of heaven—that is, the supreme—is Saturn; in the second, Jupiter; in the third, Mars; in the fourth, the Sun; in the fifth, Venus; in the sixth, Mercury; but in the seventh and lowest, the Moon. And Bede (in the book On the Nature of Things, ch. 13, and On the reckoning of times, ch. 24), following Pliny, proposed the same order—although (bk. 2 On the Elements of Philosophy) he teaches that Venus and Mercury go around the Sun.

If anyone desires a figure—though not a necessary one—of the system of Pythagoras, Ptolemy, etc. (which one may call the common and most ancient [system], and the Chaldean or Babylonian, as we shall learn from Bede, ch. 4, num. 4), behold it [here]—in which, however, Eccentrics and Epicycles are to be understood [as implied], according to the figures handed down in bk. 7, sect. 2 & 3.

System I — The Most Ancient and Common [System] of Pythagoras, Ptolemy, and Very Many

[Translator’s note — engraved diagram: A geocentric world-system. At the center sits the Earth (drawn as a small globe with lands and seas). Around it run concentric circles, labelled outward in order by their planetary symbols: ☽ Moon, ☿ Mercury, ♀ Venus, ☉ Sun, ♂ Mars, ♃ Jupiter, ♄ Saturn. The outermost band is the starry firmament / zodiac (Signiferum), divided into the twelve signs (Gemini ♊, Cancer ♋, Leo ♌, Virgo ♍, … Capricorn ♑, etc.) and studded with stars. This is the standard Ptolemaic order; per Riccioli’s caption, the eccentrics and epicycles are to be supplied mentally.]

[Margin: Clavius’s last word on the system, the Telescope having been seen.]

[X.] Thus far the Astronomers, down to Clavius—as long as the heaven was explored with unarmed eyes. But when the Belgian spyglass [telescope] was first brought [to us], and Venus was seen to be illumined by the Sun in the manner of the Moon, so that it must go around the Sun, and similar [things], the good and candid old man Clavius exclaimed—nay, like a Swan near to death, he sang of the change of the ancient system in these words (which, from the last edition, on chapter 1 of the Sphere, Scheiner recites, num. 22 of the Mathematical Disquisitions, and Tanner, On the Heaven, q. 10): “Yet I do not wish this to be hidden from the Reader: that not long ago there was brought from Belgium a certain instrument, in the manner of a certain oblong tube, in whose ends are fitted two glasses, or lenses, by which objects remote from us appear very near, and indeed far larger than they really are. With this instrument very many stars are discerned in the firmament, which without it can in no way be seen, etc. The Moon too, when it is horned [crescent] or half-full, appears, in a wonderful way, broken and rough—so that one cannot sufficiently wonder that there are such great inequalities in the Lunar body. But on this matter, consult the booklet of Galileo Galilei which he entitled the Sidereal Messenger, printed at Venice in the year 1610. Among the other [things] which are seen by this instrument, this holds not the last place—namely, that Venus receives [its] light from the Sun in the manner of the Moon, so that it appears now more, now less, horned, according to its distance from the Sun: which I have observed not once, with others, here at Rome. Saturn too has other stars conjoined [to it], smaller than itself—one toward the East, the other toward the West. Jupiter, finally, has four wandering stars, which vary their position in a wonderful way, both among themselves and with Jupiter, as Galileo diligently and accurately describes. SINCE these things are so, let the Astronomers see in what way the celestial orbs are to be constituted, that these Phenomena may be saved [accounted for].” Thus Clavius. But let us proceed to the other systems.