[I.] Hitherto we have treated those Arguments which, leaning on true phenomena, have seemed to win some probability for the annual motion of the Earth. Excepting, however, arguments 1 and 5 of the preceding chapter, which—destitute of the truth of the assumed phenomenon—at once collapsed: but in this chapter [we] must fight with mere shadows and dreams; and therefore the victory will be easier, the very falsity of the assumptions being detected. On which occasion, however, two most famous questions—pertaining partly to the doctrine of the Prime Mobile, and partly to Cosmography—will be dispatched: namely, whether the Meridian Line and the Altitude of the Pole are from time to time changed, as some have thought.

First Argument, from the Change of the Meridian Line

[II.] Joseph Scaliger judged that the Meridian Line is changed, not so much from observation as from the Theory of the precessions of the equinoxes: for in that Diatribe of his on the anticipation of the Equinoxes, he seemed to himself to have demonstrated that the poles of the Equinoctial [circle] are diverse from the poles of the World, and that the poles of the Equinoctial circle are mobile, and that hence is the motion of the equinoctial points into the preceding [signs], on account of which the Fixed [stars] seem to be moved into the consequent [signs]: by this argument most of all, that the star which they call the Polar [star], and which is at the extreme tail of the Lesser Bear, was—as it now is—so also of old, in the time of Eratosthenes and Hipparchus (nay, also of Eudoxus), the most northerly of all the stars of this constellation, and yet was distant from the Pole of the celestial Equator of old indeed by 18 degrees, but in the time of Hipparchus by 12 degrees 24′.

[Margin: Scaliger’s fiction on the change of the Meridian line.]

But in the year of CHRIST 1600 it would be distant only by 3 degrees 24′. From which fiction, among other corollaries, he likewise deduces this—which for him is the fifth in order, and on p. 70, conceived in these words: “The Meridian Lines designated on a plane change [their] position with the progress of time.” For all the Meridian lines, he says there, pass through the poles of the Equator; but the poles of the Equator are mobile; therefore the Meridian lines too are mobile—namely, into the preceding [signs]: and at the end of the Corollary he brings this inference: “As many, therefore, as [there are] equinoctial circles, so many will their poles be; and as often as the poles are changed, so often will the Meridian lines passing through those poles manifestly be changed. For the Meridians do not pass through the poles of the World, but through the poles of the Equinoctial.”

[III.] But how false it is that the star at the extreme tail of the Lesser Bear was of old the Polar star, and the most northerly of all, [just] so false it is that the poles of the World are diverse from the poles of the Equator; and accordingly false is what is deduced thence—namely, that both the poles of the Equator, and the Meridian circles, and the Meridian lines their indices, are changed. But whence that false assumption crept into the mind of Scaliger, and the refutation of this fiction, we have already sufficiently indicated (bk. 3, ch. 28, num. 10; and bk. 6, ch. 4, in the Appendix on the polar star, from num. 3); and Scaliger has been abundantly refuted by the most learned men of our Society—Denis Pétau (bk. 3 of the Dissertations of the Uranology) and Paul Guldin (in the Refutation of the Calvisian Elenchus, written against the Gregorian Calendar, bk. 2, chh. 9 and 10). Besides, this change of the Meridian line has been confirmed by no experiment—[a change] such as it ought to be according to the mind of Scaliger, namely, that the northern part of this line should deflect continually toward the West: nor, from this change, if it were granted, can anything be derived for confirming the motion of the Earth; for a change of this kind does not follow from the motion of the Earth, but from the motion of the poles of the Equator: otherwise, if [it followed] from the annual motion of the Earth, it would be necessary that the whole change of the Meridian lines be completed within any [given] year, and the same return as often as the Earth were in the same place of the Ecliptic.

[Margin: Cesare Marsili, an asserter of the change in the Meridian line.]

[IV.] Let us now hear Galileo, at the end of Dialogue 4 On the System of the World (the second page from the end), narrating thus, under the person of Salviati: “There arises at this time a certain fifth novelty, from which the mobility of the terrestrial globe may be argued, through those [things] which the most illustrious Lord Cesare most subtly detects—[Cesare], born of the most noble family of the Marsili of Bologna, and himself enrolled in the College of the Academic Lyncei [Lynxes], who, in a certain most learned writing, hands down that he has observed a certain continuous change—though very slow—in the Meridian line.” But how great, and toward what region, that change was observed, and by what methods the observation was carried out, Salviati does not there add. But I could not find this writing, although in the papers of the most excellent Lord Carlo Antonio Manzini I have read certain observations, made in the presence of the aforesaid Lord Cesare Marsili, upon that marble line which Master Egnatio Danti had constructed here at Bologna in the great Temple of St. Petronius, as I reported when [treating] of the Bolognese Gnomon (bk. 3, ch. 6, from num. 3), where I exhibited the diagram of this Gnomon and of the aforesaid marble line: from which line perhaps the occasion was taken of suspecting this change. For some Bolognese think that line, or marble path, laid down by Egnatio Danti in the pavement of St. Petronius, was the Meridian Line—although nevertheless it is not, but deflects from the exact Meridian line toward the East, in its northern part, by 9 degrees 6′ 20″, as I, with Fathers Francesco Maria Grimaldi and Francesco Zeno, detected by a most accurate observation. But the cause why that marble path could not be laid upon the meridian line itself was the obstacle of the wall and of the former column, which is near the steps of the great altar; for that line would have turned out very short, and would not have shown the people evidently the days of the Solstices and Equinoxes, as Egnatio Danti wished at that time, when the question of correcting the Roman Calendar was most agitated, on account of the vernal Equinox having retrograded from the 21st of March to the 11th. But Egnatio Danti himself, in the description of that Gnomon (which is annexed to his Anemography, published in the year 1578), teaches clearly enough that that marble path is not the Meridian Line itself, but declines from the Meridian toward the East in its northern part: since he says that the species [image] of the Sun, or [its] ray,

[…continues on p. 348 (PDF 383) with the catchword “paulò”: “…a little [before noon falls upon it]“—the rest of the St. Petronius meridian-line discussion and Riccioli’s reply to the First Argument.]

(printed p. 348 — within Chapter XI, completing the First Argument (meridian-line change): Riccioli replies that no such change has ever been demonstrated, that meridian observation is fallacious, and that a shifting meridian would actually contradict Copernicus’s own axis-parallelism. The Second Argument, from the change of the pole’s altitude, then opens with Pliny’s obelisk account and Domenico Maria of Ferrara’s claim of secularly increasing pole-altitudes.)

[Header: BOOK IX. SECTION IV. — 348]

[the species or ray of the Sun] descends a little after noon to that marble line. His [Danti’s] words are these very [words]: “But since the Sun is not always wont to come at noon (or near [it]) to the points of the Equinoxes, the altitude of the Sun—while it is on the Gnomonic line—will for that cause have to be ascertained, which we shall have from the proportion of the line AB (that is, of the altitude of the Gnomon) to the line from A (the beginning of the Gnomon) and terminated by the Ellipse of the Sun; to which, if there be added that which, after noon, the Sun—by descending to the Gnomon—shall have traversed, and [be compared] with the altitude of the Bolognese Equator, then the Sun will be said,” etc.

[V.] But from whatever [source] at last that suspicion arose to Lord Marsili, so long as the change of the Meridian line shall not be demonstrated, it can by no means be persuaded to us; to us, I say, who have long had it explored [proven] by manifold experiment, how fallacious the observation of this line is; and who, on that account, have been forced to flee to new and subtler ways of verifying it—some of which I indicated (bk. 1, ch. 10, in the scholia), and shall hand down more fully in book 10, in the Cosmographic Problems. Meanwhile, refractions are to be guarded against, and the variety of the Solar declinations, and many other [things] impeding the exact perfection of this practical operation. Wherefore I do not wonder that some—as Father Jacobus Vitta once wrote to me from Germany—found a difference between the Meridian line taken from the Fixed stars and [that] taken from the Sun; and again, between [that] taken from the morning Sun and [that] from the afternoon [Sun]: But if it be once exactly acquired, and afterward, by the same method and diligence, after many years, be investigated in the same place of the Earth, I least doubt that the very same will be found.

[Margin: The site of the House of Loreto.]

Of which thing I have an argument from the site of the Most Holy House of Loreto, of the Most Blessed VIRGIN; for the Angels so placed it that, as then, so also now, it exactly faces the four cardinal points of the World, and by one straight line drawn orthogonally [at right angles] from wall to opposite wall it marks the Meridian; but by another [line], cutting this orthogonally, it designates the parallel of the Equator: so that it might be given to understand that this is the safest Asylum, whither mortals could flee from the four parts of the earthly globe.

[Margin: The Meridian line [is] unchangeable.]

Besides, from Copernicus’s own hypothesis there rather follows the immutability of the Meridian lines: for, to preserve safe and sound, through the motion of the Earth, all the phenomena which in the usual hypothesis are expounded with the Earth resting, he [Copernicus] established that the axis of the terrestrial Equator should advance always parallel to itself, and into the same parts of the heaven, as we expounded (ch. 4, nums. 16, 22, 23, and 25); and hence it follows that the Meridians are always the same on the terrestrial globe, and perpetually regard the same parts of the world, to the sense; nor could a sensible difference ever be discerned between the meridian lines of the same place, provided they be designed with equal diligence.

[Margin: Galileo’s itch in persuading [for] the annual motion of the Earth.]

Wherefore a change of the meridian line would rather stand against [be repugnant to] the Copernican position: which Galileo did not consider, but—from an excessive itch of propping up the annual motion of the Earth from every [source]—as soon as he heard the change of the Meridian line asserted by Marsili, he conceived in [his] mind the hope of hammering out hence too something clever for the annual motion of the Earth. Lastly, the magnetism of the Earth itself—which Galileo did not disapprove—requires that its axis, immovably turned perpetually toward the same points of the heaven, should most constantly keep its position, as William Gilbert teaches clearly (bk. 6 On the Magnet, ch. 2), Cabeo (bk. 2, ch. 4), and

[Margin: The immobility of the terrestrial globe.]

Zucchi (in the new Philosophy of Machines, part 5, sect. 10). Wherefore we do not yet believe what Athanasius Kircher (bk. 2 of the Magnet, p. 489) promises he will demonstrate from statical principles—that the terrestrial globe has changed its position through all the ages; for he has not yet demonstrated it, nor indeed do the changes of heavy [bodies] which occur on the surface of the earth suffice for a motion of trepidation, since they are so slight with respect to the whole terrestrial globe (and to the air to be pushed around it) that they do not equal the slenderest atom added to a huge balance. Although this motion of trepidation would do nothing toward the change of the Meridian line, or toward establishing the annual motion of the Earth.

Second Argument, from the Change of the Altitude of the Pole

[VI.] Two [questions] of not least moment offer themselves here for us to inquire into: first, Whether the altitudes of the Pole in the same places of the earth are changed, by some annual or secular variation; then, Whether from such a variation (if we were certain of it) the annual motion of the Earth follows.

[Margin: Pliny’s account of the change of the equinoctial shadow.]

And as to the first, Pliny seems to have furnished a handle to both this question (bk. 36, ch. 10) by this narration: “To the obelisk which is in the Campus Martius, the Divine Augustus added a marvelous use, for ascertaining the shadows of the Sun and the magnitudes of the days and nights—a stone being laid down to the magnitude [length] of the obelisk, to which the shadow at Rome would be made equal on the day completed at the sixth hour, and [which shadow] gradually, by rules [rods] of bronze inset, should decrease day by day, and again increase. A thing worthy to be known, and of fertile genius. Manilius the Mathematician added a gilded ball to the apex, by whose summit the shadow would be gathered into itself, [the shadow] darting forth one increment after another from the apex—the reckoning [being] understood, as they say, from the head of a man. This observation now, for nearly thirty years, does not agree [is no longer consistent]—whether the course of the Sun itself and of the heaven being in some way changed [out of tune]; or the whole earth being somewhat moved from its center, as I gather it has been detected in other places too; or by tremors of the globe, the gnomon there being merely twisted; or by inundations of the Tiber, a settling of the mass being made—although, to [match] the height of the imposed thing [the obelisk], foundations are said to have been cast in the earth too.” From which words nothing certain or probable can be gathered for the motion of the whole Earth, but only the signs of Pliny’s wavering mind. But it is more credible that that error arose partly from the day of the true Equinox, falsely noted in the Calendar and used as immovable—so that accordingly the equinoctial shadow would not seem as great as it was thought it ought to be; partly from the settling of the laid stone, on account of the trodden-down soil over nearly a whole century, so that on that account that marble path did not, in Pliny’s time, make a right angle with the perpendicular line of the Obelisk, as it had made in the time of Augustus. But Scaliger (in the Diatribe of the Equinoxes, p. 72), abusing this passage of Pliny, and asserting that no variation was made in the obelisk or the settling of the stone, refers the whole variety to the change of the meridian line. Dismissing Pliny and Scaliger, therefore, let us descend to more recent Authors.

[Margin: Domenico Maria’s opinion on the changed altitudes of the Pole.]

[VII.] Toward the end of the fourteenth [i.e. fifteenth] century, Domenico Maria of Ferrara, a man endowed with the highest genius, and the teacher of Nicolaus Copernicus, was the first—that I know of—who roused this opinion concerning the change of the altitude of the pole, in a certain treatise or prophecy published at Bologna in the year 1489; from which Magini (Canon 8 of the Secondary Mobiles) and William Gilbert (bk. 6 On the Magnet, ch. 2) selected these words: “I,” says Domenico Maria, “in former years, contemplating Ptolemy’s Geography, found that the elevations of the North pole placed by him, in the individual regions, fall short, by one degree and ten minutes, of those which are of our time: which diversity can by no means be ascribed to a fault of the table. For it is not credible that the whole series of the book was equally corrupted in the numbers of the tables. Therefore it is necessary to concede that the North pole has been carried toward the vertical point [zenith]. And so the observation of a long time has now begun to detect for us [things] which lay hid from our forefathers—not indeed from their sloth, but because they lacked the long-time observation of their predecessors. For very few places, before Ptolemy, were observed in the elevations of the pole; as he himself testifies in the beginning of his Geography: for he says, ‘Hipparchus alone has handed down to us the latitudes of a few places; but very many of the distances—especially those which inclined toward the rising or setting of the Sun—were conceived from a certain general tradition, not from the sloth of the authors themselves, but because there was not yet a use of a more diligent Mathematics.’ It is no wonder, therefore, if the earlier [astronomers] did not perceive this very slow motion: for it manifests itself, in one thousand and seventy years, as carried by nearly one degree toward the zenith of the inhabitants. This is indicated by the narrowness of the Strait of Gades [Gibraltar], where, in Ptolemy’s time, the North pole appeared elevated 36¼ degrees from the horizon, but now [appears elevated] 37 and two-fifths. A like diversity is indicated also by Leucopetra of Calabria, and the individual places of Italy—those, namely, which have not changed up to our times. And so, from this motion, the places which are now inhabited will at last become deserted, and others, which are now baked by the torrid Zone, will (though over a long space of time) be brought to our temperateness of climate.

[Margin: The period of this feigned change.]

So that, in the course of three hundred ninety-five thousand [395,000] years, that slowest motion is completed.” Moreover, to this fancy of Domenico Maria there subscribed [agreed] Giordano Bruno of Nola, a zealot of very many novelties, in his books On the Maximum and the Immense, and On the Infinite and In[numerable]

[…continues on p. 349 (PDF 384) with the catchword “ac In”: ”…[On the Infinite and] Innumerable, p. 306”—the rest of the survey of opinions (Bruno, Magini, Stadius, Rothmann, Caligny) and the beginning of Riccioli’s refutation.]

(printed p. 349 — within Chapter XI, the Second Argument (change of pole altitude). Completes the survey of opinions — secular increase (Domenico Maria, Bruno, Magini), secular decrease (Stadius, Pena), annual variation (Rothmann), and Caligny’s plumb-line “diurnal libration” — then begins Riccioli’s refutation: the Earth’s magnetism keeps its axis fixed, and the ancient pole-altitude observations were vitiated by neglected parallax, refraction, and use of the Sun’s limb rather than its center.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 349]

[On the Infinite] and the Innumerable (p. 306). And—what you may wonder at more—Giovanni Antonio Magini, in the tables of the Secondary Mobiles (Canon 8), where he says that he augmented the latitudes of places in his catalogue, on account of the more recent observations of Pietro Pitati and others, who found them increased and greater than in Ptolemy’s time: and he adds, “Nay, [I think] that the latitudes of other places of Ptolemy too ought to be augmented—both for this [reason] and by the authority of Domenico Maria of Ferrara”; whom we judge—[Domenico Maria], endowed with a divine genius, was the teacher of Nicolaus Copernicus, whose opinion on this matter it pleases [me] to communicate to the studious, especially since I know that his writings cannot so easily come to anyone’s hands: for he, in a certain old prophecy printed at Bologna in the year 1489, prefixes these words: “I, in former years,” etc.—which we reported above.

[Margin: Johannes Stadius’s opinion on this change, but a different one.]

[VIII.] A plainly contrary reckoning in this change Johannes Stadius asserted, in the history of Astronomy prefixed to the Bergen tables, following Jean Pena (though with his name suppressed)—(concerning whom enough has been said in ch. 3 of this section, from scholio 2): he affirms that the center of the earth, while the motion of the Fixed [stars] is accelerated, is raised; but while it slows, descends—so that hence it is necessary that the earth be moved up and down, and not be the center of the universe. For the confirmation of which fancy he calls in Pliny (already adduced by us, num. 6), and he says: “It was detected, in Pliny’s century, that the whole earth was somewhat moved from its center; and the same [thing], decreasing hitherto in various places since Ptolemy’s age, and the latitude of cities and regions manifestly betraying itself. And, that we may confirm the matter by an example, Ptolemy reckons the latitude of Rome, in the Geographics, as 41⅔ degrees; and—lest you allege that some error crept into Ptolemy—in the city of Rome, on the day of the Equinox, a ninth part of the gnomon is wanting to the shadow, as Pliny reports and Vitruvius testifies (in the ninth book). But since, two sides of a right-angled triangle around the earth being given, each of the angles is given, [so] here (because 8 and 9 are given) the other of the acute [angles] is also given [as] 48⅓ degrees, which subtends the altitude of the Sun above the horizon; but the other, of 41⅔ degrees, by which the Equator declined from the vertical point of Rome—or [which] defined the latitude of the city of Rome, as Ptolemy recently [did], as 41 degrees 40 minutes. But the observation of the more recent [astronomers], as Erasmus Reinhold reports, yields the same [latitude], in this our century, [as] 41 degrees with a sextant [41°10′]—so that you may doubt whether you would prove that a half of one degree has decreased in the center of the world, or by the obliquation of the earth.” And so Stadius will have it that the altitudes of the pole, from Ptolemy to these times, have been diminished—which Domenico Maria and Magini thought to have been augmented. But as to the part in which he leans on an unequal motion of the fixed [stars], we have already refuted his opinion and Pena’s in the scholia of chapter 3; the rest will be refuted presently, when we shall have reviewed the opinions of others.

[Margin: Rothmann’s opinion on the changed altitude of the Pole.] [Margin: Alexandre Caligny’s observation on the change of the plumb-line.]

[IX.] After this, Christopher Rothmann, the Mathematician of the Landgrave of Hesse, reported to Tycho—as Tycho himself narrates (tome 1 of the Progymnasmata, p. 684)—that “he had sometimes noticed that the altitude of the Pole exhibits itself otherwise, by one or another minute, in summer than in winter; and that at one time rather than another the intervals of certain Fixed [stars]—especially [ones] separated by a great interval—are given [as differing], which undergo a variation of about two minutes.” And hence he judged it [to be] rendered probable that the Earth does not perpetually, immovably, occupy the center of the universe. But at last Pierre Gassendi, at the end of the Judgment on the nine stars seen around Jupiter, narrates a certain observation made by Alexandre de Caligny, which, if it were true, would be an argument that the Earth librates in some meridian, and varies the altitudes of the pole by its libration. For he says that he [Caligny] suspended a plumb-line from a height of thirty feet, and enclosed [it] in a tube, that it might be safe from the agitations of the air; and that he affixed beneath the lead of the plumb-line a point [cusp], and beneath that point inclining downward—when the plumb-line was at rest—he placed another point, perpendicularly erected and fixed in a cube: these [things] being prepared, he observed that the point of the plumb-line, for six hours, was moved from North to South, but bending toward the East; but for six [hours] from South to North, by a bent path toward the West; and that, at noon indeed, it reached the limit of [its] excursion into the South, and again at midnight. From this observation, had through a month, Caligny concluded that there is a certain motion of the Earth from the Southwest [Africus] to the Northeast [Caecias], and from the Northeast to the Southwest; and that to this motion the access and recess of the marine tide is rather to be ascribed than to the Galilean motion of the Earth. To this observation Gassendi, though with suspended assent, nevertheless does not so gainsay [it] but that he doubts whether the observers of celestial things should be admonished that, in taking the altitude of the pole by the meridian altitudes of the Polar star, they should beware of those hours in which the altitude of the culminating star is not the same: for, if the Earth thus nods [librates], the altitude of the stars is not the same at midnight and at the sixth hour; but [that] in this century the greatest altitude of the polar star is to be observed, in Europe, around the sixth hour of evening, but the least around the sixth hour of morning.

[Margin: Epilogue of the three opinions adduced.]

[X.] Three opinions, therefore, have we hitherto obtained concerning the change of the altitudes of the Pole. The first, concerning this change, but [as] secular—that is, not sensible except by the lapse of centuries—whether augmenting these altitudes (as Domenico Maria, Giordano Bruno, and Magini judged), or diminishing [them] (as Johannes Stadius). The second, concerning an annual change, on account of the annual approach and recession of the earth to the Fixed [stars], which was Christopher Rothmann’s. The third, concerning a diurnal change, on account of a libration of the Earth from the Southwest to the Northeast and back, recurring twice daily to the same [point], which Alexandre de Caligny affirmed, and Pierre Gassendi did not deny. These, in order, we now undertake to refute, and much more accurately than [they have done]

[Margin: Authors asserting the Immutability of the altitudes of the Pole.]

against Domenico Maria, Stadius, Magini, and Rothmann—[namely] William Gilbert (bk. 6 On the Magnet, ch. 2), Tycho (tome 1 of the Progymnasmata, p. 684, and in the Mechanics of the Restored Astronomy, p. 8 before the end; and also in a certain Epistle to Giovanni Antonio Magini, given on the Calends of December of the old year, in the year 1590, which we have before the tables of the Directions of the Prime Mobile of Magini himself, p. 82), Kepler (in the Optical Astronomy, p. 148), and Willebrord Snell (bk. 1, ch. 8 of the Batavian Eratosthenes), where, concerning Domenico Maria fabricating great [things] from very few little observations, he says: “Here he makes for us an elephant out of a gnat; for if he had examined Ptolemy a little more diligently, he could have discharged this prophecy with no labor.”

[Margin: First Argument, for the immutability of the altitudes of the Pole.] [Margin: Second Argument.]

[XI.] First, therefore, against Domenico Maria and his followers there is, first, the magnetism of the Earth—which (as Gilbert, Cabeo, and Zucchi, already reviewed above, contend) requires that its axis immovably persist in the same position toward the same points of the heaven, and so that the altitudes of the Pole be not varied. Then, that a just comparison could be made between the altitudes of the Pole of the same place taken anciently and recently, it would be necessary that both were most exact; but it is sufficiently established that those taken anciently were not so exquisite [precise], for many causes: first, on account of the neglected parallax and refraction of the Sun—not only in the solstitial altitudes of the Sun, but also and especially in the measurement of the longest and shortest day of the year, from which it is established that Ptolemy, in the Geography, determined very many altitudes of the pole, or latitudes of places; for the horizontal refractions apparently augment the diurnal quantity [length of day], since, by raising the Sun, they make it seem to rise sooner and set later than the obliquity of the horizon and the declination of the Sun would require; and that more in winter than in summer. It could happen, therefore, that a diversity of refractions—prevailing at diverse times on the same horizon—would produce a diversity of the altitude of the pole: which business, indicated by Gilbert (bk. 6, ch. 2), is illustrated by Kepler (in the Optics, p. 148), and is not omitted by Tycho. Besides, when the altitude of the pole was deduced by the ancients from the proportion of the equinoctial shadow to the Gnomon—the terminus of the shadow being given, and the angle of the Gnomon (right) being applied most exactly—nevertheless, neither did the Equinox occur at noon, and the variation of the declination on the equinoctial days was great, nor even was the day due to the Astronomical Equinox certain to the observers; or assuredly, in all these [matters], some suspicion of error lurks, rendering those altitudes uncertain. But what was most of all a fault in those observations [is that], for the altitude of the center of the Sun, the altitude of the upper limb of the Sun was used—inasmuch as it terminates the extremity of the shadow by its ray—whereas it would be necessary to subtract from that altitude the apparent semidiameter of the Sun. Which we have shown by several examples in our Geographic book, and which we shall make manifest [in] certain [examples] a little below: which very fault in those observations Snell noted in his Batavian Eratosthenes (bk. 1). Suppose, then (which could easily have happened), that there was an error of a whole day in the moment of the Equinox, and that the observation of the equinoctial shadow was begun on the 25th of March—on which the civil Calendar marked the day of the Equinox—but [that] the [true] Equi-

[…continues on p. 350 (PDF 385) with the catchword “Aequi”: ”…[the true] Equinox [was on another day]“—the rest of Riccioli’s refutation of the changed-pole-altitude opinions.]

(printed p. 350 — within Chapter XI, continuing the refutation of changed pole-altitudes: equinox-day errors could produce the whole apparent discrepancy, as the spread of modern latitude determinations shows. Domenico Maria’s claimed uniform increase is refuted by worked examples of Rome and Alexandria, where correcting for the solar semidiameter reconciles ancient and modern values; a comparison table is announced.)

[Header: BOOK IX. SECTION IV. — 350]

[the true] Equinox was at noon of the 24th or 26th day. Behold, hence an error of 24 minutes—since indeed from the Table of the solar declinations it is established that, on the days nearest the Equinox, the declination of the Sun is varied by whole single minutes for each single hour; add to this error an error of about 16 minutes, which are in the apparent semidiameter of the Sun: do you not see that there could thence arise an error of 40 minutes in estimating the altitude of the pole, or of a whole degree and more, if the observation was made two days before or after the true Equinox? What if Ptolemy determined some of these from a conjecture of the position of the regions—which Gilbert suspects (bk. 6 On the Magnet, ch. 2), saying: “Since Ptolemy received only certain latitudes from Hipparchus, nor himself observed them in very many places: it is likely that he, the position of the regions being known, estimated the latitude of cities only by a probable conjecture, which he then commended to the tables. So one may see, in our Britain, that the latitudes of cities err by two or three degrees, as experience teaches. Wherefore by no means from these errors is a new motion to be introduced, nor is the renowned magnetic nature of the Earth to be deformed by an opinion so lightly conceived.” And this indeed was the cause why Tycho (in the Mechanics of the Restored Astronomy, p. 8 before the end) vehemently wished, from the Venetian Republic, that it would send to Alexandria of Egypt skilled men who might exactly take the polar altitude of that city—both for other ends, and that, it being compared with the altitude formerly taken by Ptolemy (accurately enough, as it is fair to believe), it might be defined whether the altitudes of the Pole are changed by lapse of time, or not. For other altitudes, not observed by Ptolemy but handed down on the faith of others or by his own conjecture, he judged [we] should by no means trust. But our Clavius too, in the Sphere (p. 284 by my [copy]), professes that the latitudes of places assigned by Ptolemy not rarely stray from the truth by one or another degree. But not even the more recent [astronomers] were always so exact in this business that they incurred the error of no minute, as presently we shall see concerning the altitude of the pole of Rome; and concerning the Parisian [latitude] it is worthy of note—since indeed, by observing it, Oronce [Finé] found it Gr. 48° 40′, Viète Gr. 48° 49′, Gassendi and Hortensius Gr. 48° 42′ or 43′, Hérigone Gr. 48° 55′, Fr. Georg Furner Gr. 48° 50′—whether that arose from the diverse magnitude, placement, and use of the instruments, or from parallax, or from elsewhere.

[Margin: The latitudes of places of Ptolemy variable.] [Margin: The varying altitude of the Pole at Paris.]

It is no wonder, therefore, if Rothmann could obtain the altitude of the pole of Kassel as differing by two minutes at different times of the year; wherefore deservedly Tycho (tome 1, p. 684) reprehends him, in that, on account of this difference—easily arisen from error—he did not hesitate to build up a motion of the Earth. Especially since, from the Hessian observations which Willebrord Snell published, it is established that, on account of a badly-placed instrument, the Kassel altitude of the pole was found to differ from itself by several minutes. Which very [thing] happened to Tycho in the Prague altitude, as the same Snell reports in the Bohemian observations; for first he found it grad. 50° 6′, and so much did Longomontanus, Kepler, [and] Lansberg put in their Catalogues, but afterward he detected Gr. 50° 4′ 30″.

[Margin: Rothmann reprehended on the altitude of the pole. — The Prague altitude of the Pole.]

[XII.] But be it that neither the observations of the Ancients nor of the Recent [astronomers] were erroneous in observing the altitude of the pole: yet, that the divination of Domenico Maria might be true, it would be necessary that all, or very many, altitudes of the pole observed by the ancients, and compared with the more recent, were increased—and indeed by 70 minutes from Ptolemy up to the Year of the Lord 1490; but this is false. For some were rather diminished, some were found of the same quantity as of old; some indeed were increased, but by much fewer, or by more, minutes than 70′. Which is to be shown by several examples; the beginning, as is fitting, being made from Rome. At Rome, therefore, about the times of Augustus, the equinoctial shadow to the Gnomon was found to have the proportion which 8 has to 9, as Vitruvius (bk. 9, ch. 8) and Pliny (bk. 2, ch. 72) expressly affirm. From these two sides, by the rules of rectilinear and right-angled triangles, the meridian altitude of the upper limb of the Sun is gathered to have been, at the Equinoxes, Gr. 48° 22′; but the semidiameter of the Sun being subtracted, or about 16′, there remains G. 48° 6′. So great, therefore, was then the meridian altitude of the Sun at Rome, if we neglect parallax (which for us does not exceed 30″), and suppose [it] to be selected, in that proportion 8 to 9, from many observations—that one [observation] was employed in which the Equinox was celebrated at noon itself, or as nearly as possible; and thus the complement of the altitude to the quadrant—the altitude of the pole—would be Gr. 41° 54′.

[Margin: The altitude of the Pole of Rome examined.]

But Ptolemy puts it Gr. 41° 40′; because from the Almagest (bk. 2, chh. 5 & 6) it is established that he, from the altitude of the pole, deduced the meridian equinoctial and solstitial shadow, and conversely from these shadows the altitude of the pole—no account or mention being made of the solar semidiameter; wherefore he used the equinoctial shadow made from the upper limb, which gives the altitude of the limb Gr. 48° 22′, or roundly 20′, and assumed for the altitude of the pole the complement Gr. 41° 38′, or roundly 40′. Therefore, the semidiameter of the Sun, 16′, being added to this altitude of the pole, it comes out, as above, the altitude of the pole Gr. 41° 54′ or 56′; nor can Ptolemy otherwise be reconciled with Vitruvius and Pliny. But now Clavius in the Sphere, from more recent observations, puts it Gr. 41° 56′. But Latino Orsini (part 3 of the Latin Radius, ch. 5), from his own observation, puts it Gr. 41° 54′—as much as Bellarmato and Magini also put in their Geographic tables. Be it that Tycho, in the Epistle to Magini (which is had on folio 81 in Magini’s Directions of the Prime Mobile), from the observation of Regiomontanus when he was at Rome, gathers it [as] Gr. 42°—as much as the Alphonsine and Rudolphine tables put.

[Margin: Ptolemy’s errors in the altitudes of the Pole.]

So great, therefore, is it now as of old; nor, as Domenico Maria will have it, is it increased by a sensible and evident difference, if we follow Ptolemy corrected and reconciled with Vitruvius and Pliny; and much less is it increased by 70 minutes. But if Domenico Maria should contend that Ptolemy is not to be corrected, but that his numbers are to be taken as they lie, I shall show too either that Ptolemy contradicts himself, or that the altitude of the Pole of Rome was not less of old than now. For indeed in table 6 of Europe Ptolemy says the longest day observed at Rome [was] of 15 hours 5′; therefore the semidiurnal arc was of 7 hours 32½′, or of 113° 7′, whose complement to the semicircle gives the inferior angle at the pole of the world Gr. 66° 53′; with which, and with the complement of the maximum declination of the Sun (which in truth was then also Gr. 66° 30′, as I showed bk. 3, ch. 27), there follows—by the second [case] of right-angled spherical triangles—the altitude of the pole of Rome Gr. 42° 5′. But if the semidiurnal time, on account of the refractions augmenting it, we diminish (from our observation) by about 4′—that is, increase the inferior angle at the pole of the world by one degree—the altitude of the pole comes out Gr. 40° 53′, which is repugnant to Ptolemy, who puts it in his Tables Gr. 41° 40′; nay, if we were to use the obliquity of the Ecliptic asserted by him, Gr. 23° 51½′, the altitude of the pole of Rome would come out Gr. 40° 25′, which is much more repugnant to Ptolemy. Thus it does not profit Domenico Maria to adhere to an uncorrected Ptolemy.

[Margin: The altitude of the Pole of Alexandria examined.]

But behold another argument of a correction to be applied to Ptolemy, on account of the neglected semidiameter of the Sun. And indeed in the altitude of the Pole of Alexandria of Egypt. For there, by the testimony of Vitruvius (bk. 9, ch. 8), the equinoctial shadow to the gnomon was found as 3 to 5. Let it now be made: as 3 to 5, so the whole Sine of seven ciphers [10,000,000] to 16,666,666, which is the Tangent of Gr. 59° 2′; and the altitude of the upper limb of the Sun is had, namely Gr. 59° 2′; from which, if you take away the semidiameter of the Sun, 16′, there is left Gr. 58° 46′; and therefore the altitude of the Pole of Alexandria [is] Gr. 31° 14′. But if the Sun’s semidiameter be not taken away, the altitude of the Pole would be Gr. 30° 58′, as much as Ptolemy precisely puts (bk. 5 of the Almagest, ch. 13, and bk. 4 of the Geography, table 13). It appears therefore that he, on account of the neglected semidiameter of the Sun, erred by 16 minutes.

[Margin: Gemma Frisius and Snell fallen [into the same error].]

Into which error—what is more to be wondered at—fell not only Gemma Frisius (ch. 21 of the Astronomical Radius), but also Willebrord Snell (bk. 1 of the Batavian Eratosthenes, ch. 8); for from the proportion 3 to 5 they gathered the altitude of the Sun Gr. 59° 2′ and of the pole Gr. 30° 58′, whereas that was the altitude of the limb, not of the center, of the Sun. Into a similar error to this I detected a man here at Bologna had fallen—otherwise most consummate in Geometry and Astronomy—who, measuring the altitude from the reversed shadow [umbra versa], and taking from the altitude of the lower limb the semidiameter of the Sun (which he ought to have added), differed from us by a whole 32′.

[XIII.] But that the inconstant difference between the altitudes of the Pole handed down by Ptolemy, and [those] more accurately observed in these last times, may appear, I shall select from my Geographic book the following [ones], that the falsity of the opinion of Domenico Maria may be made manifest.

[…continues on p. 351 (PDF 386) with the catchword “Alti[tudines]”: the comparison table “Altitudes of the Pole according to Ptolemy compared with the Observations of more recent [astronomers],” followed by the close of the refutation and the opening of Chapter XII.]

(printed p. 351 — closes Chapter XI with a comparison table of some 22 places proving the pole-altitude differences are inconstant, not a uniform secular change; Rothmann’s annual variation is dismissed as instrument error, and Caligny’s plumb-line is answered by Riccioli’s own contrary experiment. The Second Argument receives its formal two-fold response. Chapter XII then opens: an Epitome of the sunspot argument from Galileo and Scheiner.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 351]

[XIV.] Thus far against the first opinion—[namely] of the altitude of the pole varying, but after many years, by a certain quasi-secular change—which, however, [even if] granted, nothing would be concluded for the annual motion of the Earth. But there followed the second opinion, of Rothmann, asserting that the altitudes of the pole are varied yearly, on account of the annual motion of the Earth, so that one [altitude] is taken in winter, another in summer, as the greatest; which, however, since it does not extend beyond 2 minutes, it is very easy to reject that variety upon the instruments, or the use of the instruments, as we have already said: yet, this being admitted, Tycho judged (tome 1 of the Progymnasmata, p. 685) that thence the annual motion of the earth could probably be gathered.

[Margin: Galileo’s doctrine on the change of the altitude of the Fixed [stars] on account of the annual motion of the Earth.]

But Galileo (Dialogue 3 On the System of the World, from Latin p. 276) teaches that no change in the pole would hence be detected, because the axis of the Earth does not regard the fixed pole itself in the heaven, but one point and another; but that a change would appear in the altitude of some fixed star seen, and in its distance from the pole, if by Copernicus some sensible parallax in the fixed [stars] were admitted on account of the diameter of the annual orb: such a change, however, he tries to show (p. 282) would not appear, by force of the annual motion, in any Fixed [stars] which are in the Ecliptic—granted that they would appear larger than themselves, the Earth approaching them; but in stars placed outside the plane of the Ecliptic, a change would appear in the meridian altitude the greater, the more they were distant from the Ecliptic; but in the apparent magnitude so much the smaller a change, so that, if any star be nearest the pole of the world, it would appear of the same magnitude the whole year, but in the elevation above the horizon so much the greater a diversity would appear to one observing the same star once, and again after six months, [by] how much greater the proportion of the annual orb to the Eighth sphere will be.

[Margin: Galileo’s lapse.]

But here Galileo errs (says Fr. Francesco Maria Grimaldi): for, for example, to an inhabitant of the right sphere, a Fixed [star] in the beginning of Cancer ♋—though in the Ecliptic itself—if the annual orb be supposed very great, will have a much smaller meridian altitude when the Earth is placed in the beginning of Cancer ♋ than when placed in Libra ♎ or Aries ♈. Nay, while the earth is under Aries ♈, that Fixed [star] will rise to this inhabitant at midnight itself, and after 6 hours will be in the Meridian, if the annual orb have no proportion to the sphere of the Fixed [stars]; but far otherwise if [it be] great: as will easily be clear to one viewing the Copernican sphere. But since Copernicus—as Tycho too noted above—knew that these diversities do not appear, nor could the immutability of these altitudes and magnitudes consist [with each other], the Earth’s annual motion being posited, if the proportion of the diameter of the annual orb to the diameter of the Fixed [stars] were sensible—for that reason he established that proportion to be insensible, and the diameter of the annual orb to be, with respect to the diameter of the Sphere of the Fixed [stars], as a point.

[XV.] To the experiment of Alexandre Caligny we answer with an experiment made by us quite to the contrary: For a plumb-line, suspended by us from a similar height in a chamber closed on every side, and a little line drawn perpendicularly and most subtly against the silken thread upon a white little board, near the lead—within half an hour so came to rest that the thread coincided exactly with that line, nor wavered hither and thither with any sensible quivering, even if, a mirror being placed beneath and a point [cusp] fixed in the lead, it were observed from below [to see] whether any motion were detected in it; which I formerly experienced at Ferrara, and afterward at Bologna, more than once, Fr. Francesco Maria Grimaldi being witness. Wherefore I cannot but believe my own eyes; and perhaps to Caligny the opposite befell, on account of a twisted thread of the plumb-line, or a tremor of the place whence he had suspended the plumb-line, or [for] another cause. But see what I have said about these [things] (bk. 2, ch. 21, scholia 2 & 3). Although, even if we should concede this to him, not thence [could] the annual motion of the Earth, but a diurnal libration at most, be gathered. Let now Argument 2 be of this kind, with its response.

[Margin: Second Argument and Response.]

[XVI.] The altitudes of the Pole are changed, either by a long course of ages, or yearly, or daily; therefore the Earth is moved by an annual motion.

It is answered, first: by denying the Antecedent—as concerning the secular change is clear from the things said from number 11 to 13 inclusive; concerning the annual indeed, under the end of num. 11 and num. 14; but concerning the diurnal, from the things said at num. 15.

I answer, secondly: the Antecedent being granted as to the first and last part, I deny the Consequence; for from those changes there would not be gathered an annual motion of the Earth in the Ecliptic, but some libration, requiring for its period either many ages, or a day or half a day only.