New Astronomy Quotes
My aim in the present work is chiefly to reform astronomical theory (especially the motion of Mars) in all three forms of hypotheses, so that our computations from the tables correspond to the celestial phenomena. Hitherto, it has not been possible to do this with sufficient certainty. In fact, in August of 1608, Mars was a little less than four degrees beyond the position given by calculation from the Prutenic tables. In August and September of 1593 this error was a little less than five degrees, while in my new calculation the error is entirely suppressed."
Author’s Introduction, p. 62
"Would it not be correct to say to him that he should regard the Holy Spirit as a divine messenger, and refrain from wantonly dragging Him into physical class?"
Chapter Summary, chapter 45, p. 95
"In what follows, the reader should overlook my credulity, since I am judging everything by my own wits. Inded, the occasions by which people come to understand celestial things seem to me not much less marvellous than the nature of the celestial things itself. I therefore display these occaisions scrupulously, with, no doubt, some attendant difficulty for the reader. Nonetheless, that victory is sweeter that was born in danger, and the sun emerges from the clouds with redoubles splendor. Therefore, O reader, pay heed to the dangers of our army, and contemplate the clouds horrifying in their darkness. Contemplate, I say, for beyond these clouds the sun of truth truly lies hidden, and shortly will emerge."
Chapter 7, p. 183
"It is true that a divine voice, which enjoins humans to study astronomy, is expressed in the world itself, not in words or syllables, but in things themselves and in the conformity of the human intellect and senses with the sequence of celestial bodies and of their dispositions. Nevertheless, there is also a kind of fate, by whose invisible agency various individuals are driven to take up various arts, which makes them certain that, just as they are a part of the work of creation, they likewise also partake to some extent in divine providence."
Chapter 7, p. 185
"I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets."
Chapter 7, p. 185
“At the beginning there was great controversy between us [with Christian Severinus / Longomontanus] as to whether it were possible to set up another sort of hypothesis which would express to a hair's breadth so many positions of the planet, and whether it were possible for the former hypothesis to be false despite its having accomplished this so far over the entire circuit of the zodiac.”
Chapter 11, p. 207
“I shall now add the other way, because of its beauty; I cannot use the Brahean observations in it. Therefore, I am going to give you a clown show, in that I use my own observations, showing by example why Brahe needed such diligence, precision of instruments, assistants, and other equipment.”
Chapter 11, p. 210
“For the wind was blowing so hard that it was only by a glowing coal that we could cast light upon the scale so as to read it.”
Chapter 11, p. 211
“It was, however, the cold and the extremely biting winds that occasioned so much variety in observations made at the same time. For it was impossible to handle the iron and close the clamps with bare hands, and with gloves the arm was not securely enough clamped to allow a very precise reading.”
Chapter 11, p. 213
“I also hope that the nausea evoked by these uncertain observations will lead readers to cling all the more fervently to the extremely certain Tychonic ones. Now, on with the example.”
Chapter 16, p. 253
“The solution is not geometrical, at least if algebra is not geometrical, but proceeds by a double iteration. For algebra, too, forsakes us here, because the categories of art united by [their being concerned with] straight lines do not extend beyond straight lines to angles, unless perchance one would wish to cram the entire theory of sines into this one operation.” -- on the determination of the vicarious hypothesis
Chapter 16, p. 251
“Now I myself could also have taken the bisection of the eccentricity as certainly established, and with better reason than Ptolemy, because in ch. 22 of my Mysterium Cosmographicum I had brought forward a physical cause for the bisection.”
Chapter 16, p. 254
“At the same time, however, it is not unusual, whether in geometry, or arithmetic, or dialectic, to use a form of argument which leads to an absurdity, so that if something absurd is seen to follow from the assumptions, they are rejected as false; and this is carried out until the consequent removal of excesses and defects unveils the exact truth (which in the mathematical disciplines is a mean between the two). In the present case this comes about in the following manner.”
Chapter 16, p. 255
“But it is still not certain that this second correction will directly reconcile your four angles with the exact measure. For the rate of increase of circular variables is not the same as that of straight ones.”
Chapter 18, p. 276
“I therefore proclaim that the acronychal positions displayed by this calculation [the vicarious hypothesis] are as certain as the observations made with the Tychonic sextants can be...
“Finally, you see how nothing prevents the transposition of acronychal observations from the mean to the apparent motion of the sun, so as to keep me from, not just imitating, but even surpassing, the certitude of the Tychonic calculation, which has been raised as an objection against my abandoning the sun's mean motion.”
Chapter 19, p. 281
"For here neither Tycho Brahe nor I have bisected the eccentricity of the equalizing point. Now for Copernicus it was a matter of religion not to neglect this anywhere. For he made very little use of observations, perhaps thinking that Ptolemy used no more than are referred to in his Great Work. Tycho Brahe balked at this. For in imitating Copernicus, he set up this ratio of the eccentricities, which the acronychal observations require. But when this was gainsaid not only by the acronychal latitudes (for these still underwent some increase arising from the second inequality) but also, and much more forcefully, by observations of other positions with respect to the sun which are affected by the second inequality, he stopped here and turned to the lunar theory, and I meanwhile stepped in."
Chapter 19, p. 285
“And Ptolemy too, as was remarked above, had taught us that half of the eccentricity found by acronychal observations is to be assigned to the eccentricity of the eccentric. So it was not without reason that he did so, and we should not rashly reject this bisection, since the observed latitudes support it.”
Chapter 19, p.283
“Therefore, something among those things we have assumed must be false. But what was assumed was: that the orbit upon which the planet moves is a perfect circle; and that there exists some unique point on the line of apsides at a fixed and constant distance from the center of the eccentric about which point Mars describes equal angles in equal times. Therefore, of these, one or the other or perhaps both are false, for the observations used are not false.”
Chapter 19, p. 285
“And from this distance of eight minutes, so small that it is, the reason is clear why Ptolemy, when he made use bisection, was satisfied with a fixed equalizing point. For if the eccentricity of the equant, whose magnitude the very large equations in the middle longitudes fix indubitably, be bisected, you see that the very greatest error from the observations reaches 8', and this in Mars, which has the greatest eccentricity; it is therefore less for the rest. Now Ptolemy professed not to go below 10', or the sixth part of a degree, in his observation. The uncertainty or (as they say) the 'latitude' of the observations exceeds the error in this Ptolemaic computation.
“Since the divine benevolence has vouchsafed us Tycho Brahe, a most diligent observer, from whose observations the 8' error in this Ptolemaic computation is shown, it is fitting that we with thankful mind both acknowledge and honor this benefit of God. For it is in this that we shall carry on, to find at length the true form of the celestial motions, supported as we are by these arguments showing our suppositions to be fallacious. In what follows, I shall myself, to the best of my ability, lead the way for others on this road. For if I had thought I could ignore eight minutes of longitude, in bisecting the eccentricity I would already have made enough of a correction in the hypothesis found in ch. 16. Now, because they could not have been ignored, these eight minutes alone will have led the way to the reformation of all of astronomy, and have constituted the material for a great part of the present work.”
Chapter 20, p. 293
“For the necessary consequence of this inquiry is that there is no single fixed point on the planet's eccentric about which the planet always sweeps out equal angles in equal times.”
Chapter 21, p. 294
“Therefore, our false supposition, although it does put the planet in the right longitudinal position at the right time, does not give it the right altitude...
“Further, even considering the longitude alone, the lack of any perceptible difference in effects between the as yet unknown true hypothesis and the false one assumed by us does not make the effect identical. For there can be a small discrepancy which the senses do not perceive.”
Chapter 21, p. 298
“It is at least now clear to what extent and in what manner the truth may follow from false principles: whatever is false in these hypotheses is peculiar to them and can be absent, while whatever endows truth with necessity is in general aspect wholly true and nothing else. “Further, as these false principles are fitted only to certain positions throughout the whole circle, it follows that they will not be entirely correct outside those positions, except to the extent (as shown in this example) that the difference can no longer be appraised by the acuteness of the senses.”
Chapter 21, p. 300
“This mutual tempering of various influences causes one error to compensate for another, brings the calculation within the limits of observational precision, and makes it impossible to perceive the falsity of this particular hypothesis. And so this sly Jezebel cannot float over the dragging of truth (a most chaste maiden) into her bordello. Any honest woman following this false predecessor would stay closely in her tracks owing to the narrowness of the streets and the press of the crowd, and the stupid, bleary-eyed professors of the subtleties of logic, who cannot tell a candid appearance from a shameless one, judge her to be the liar's maidservant.”
Chapter 26, p. 331, p.334
“You thus see how shortening αη helps us in two ways. But to shorten αη is a very easy, small change, because the angles are small: it can be done by saying that the planet was seen in a slightly prior position along a line drawn from η below θ... (p. 331)”
“One might, however, hold suspect such license in making small changes in the data, thinking that by taking the same liberty in changing whatever we don't like in the observations, the full Tychonic eccentricity might also at last be obtained. Anyone who thinks this way should make a try at it, and, comparing his changes with ours, he should judge whether the changes remain within the limits of observational precision. (p.334)”
Chapter 26, p.337
“And finally, when a comparison of hypotheses has been made, and it has appeared that four theories of the sun (or rather, six, as will be said elsewhere) can be generated from a single theory of the earth, like many images from one substantial face, the sun itself, the clearest of truth, will melt all this Ptolemaic apparatus like butter, and will disperse the followers of Ptolemy, some to Copernicus's camp, and some to Brahe's.”
Chapter 28, p. 345
“The reader should not be surprised that in this third turn I am now declining to presuppose the eccentric position of Mars as given by the hypothesis of acronychal observations found above. For I have said that hypothesis was only vicarious, not natural, and thus possesses only as much trustworthiness as is permitted by the observations; and it could deviate somewhat in the intermediate positions between observations.”
Chapter 33, p. 376
"Now it is an axiom in natural philosophy of the most common and general application that of those things which can occur at the same time and in the same manner, and which are always subject to like measurements, either one is the cause of the other or both are effects of the same cause."
Chapter 33, p. 377
"Therefore, the only remaining possibility is that the cause of this intensification and weakening resides in the other endpoint, namely, in that point which is taken to be the center of the world, from which the distances are measured."
Chapter 33, p. 378
"where the weight is farther from the fulcrum, it is thereby rendered heavier, not of itself, but by the power of the arm supporting it at that distance. And this is true, both of the steelyard or lever, and of the motion of the planets: that the weakening of power is in the ratio of the distances.
“But which body is it that is at the center? Is there none, as for Copernicus when he is computing, and for Tycho in part? Is it the earth, as for Ptolemy and Tycho in part? Or finally, is it the sun itself, as I, and Copernicus when he is speculating would have it?”
Chapter 33, p. 379
“But indeed, if this very thing which I have just demonstrated a posteriori (from the observations) by a rather long deduction, if, I say, I had taken this as something to be demonstrated a priori (from the worthiness and eminence of the sun), so that the source of the world's life (which is visible in the motion of the heavens) is the same as the source of the light which forms the adornment of the entire machine, and which is also the source of the heat by which everything grows, I think I would deserve an equal hearing.”
Chapter 33, p. 380
"Therefore, in all respects and in all its attributes, the motive power from th esun coincides with light.
"And although this light of the sun cannot be the moving power itself, I leave it to the others to see whether light bmay perhaps be so constituted as to be, as it were, a kind of instrument or vehicle, of which the moving power makes use."
Chapter 33, pp. 381-2
"The remaining possibility, then, is that, just as light, which lights the whole earth, is an immaterial species of that fire which is in the body of the sun, so this power which enfolds and bears the bodies of the planets, is an immaterial species residing in the sun itself, which is of inestimable strength, seeing that it is the primary agent of every motion in the universe."
Chapter 34, p. 391
“It is therefore plausible, since the earth moves the moon through its species and is a magnetic body, while the sun moves the planets similarly through an emitted species, that the sun is likewise a magnetic body.”
Chapter 36, p. 397
“Nothing is lost in the journey: the entire species carries through to any distance, however remote. It is attenuated only in the extensions of the spheres...”
Chapter 37, p. 402
“It would be preferable to attribute to the earth a force that retains the moon, like a sort of chain, which would be there even if the moon did not circle the earth at all.”
Chapter 38, pp. 404-405
“[H]ow does the planet come to ascend from and descend towards the sun? Can this, too, come from the sun? My answer is that it is to some extent from the sun, and to some extent not from the sun.
“Examples of natural things, and the kinship of celestial things for these terrestrial ones which has hitherto been gathered to exist ,cry out that in a simple body the operations which are more general are simpler, while the variables, if any (such as, in the motion of the planets, the varying distance from the sun, or the eccentricity), arise from the concurrence of extrinsic causes.
“Thus, in a river, the simple property of water is to descend towards the center of the earth. But because its path is not direct, it flows in to those places where it finds a lower bed, stagnates where it meets with level ground, and is carried along with a roar where it comes upon steeper slopes; and there is a whirlpool where it dashes headlong into projecting rocks. Where water itself, by its inherent force, endeavors to do nothing but descend towards the center of the earth, a simple task for a simple property, flow and stagnation and waves and whirlpools and all the variety [of phenomena] arise from the causes described, which are extraneous and accidental.”
Chapter 39, p. 410
“In adopting this account, we would indeed approach more closely the geometrical suppositions of the ancients, but we would stray very far from the physical theory, as is shown in ch. 2. Neither have my thoughts on the matter sufficed to discover a way in which these things can happen naturally.”
Chapter 39, pp. 412-413
“For example, sailors cannot know from the sea itself how far they have traveled over the waters, since the course, viewed in that way, has no distinct limits... In just the same way, the mind of the planet cannot by itself measure its position, or the distance between itself and the sun, since between them there is pure ethereal air, devoid of any means of indication.”
Chapter 40, p.417
“My first error was to suppose that the path of the planet is a perfect circle, a supposition that was all the more noxious a thief of time the more it was endowed with the authority of all philosophers, and the more convenient it was for metaphysics in particular.”
Chapter 40, p. 417
“For unless we can find the sum of all of them (and they are infinite in number) we cannot say how much time has elapsed for any one of them.”
Chapter 40, pp. 419-420
"it therefore seemed to me I could conclude that by computing the area CAH or CAE I would have the sum of the infinite distances in CH or CE, not because the infinite can be traversed, but because I thought that the measure of the faculty by which the collected distance smete out the times is contained in this area, so that we would be able to obtain it by knowing the area without an enumeration of least parts...
“Thus the area CGA becomes a measure of the time or mean anomaly corresponding to the arc of the eccentric CG, since the mean anomaly measures the time.”
Chapter 40, p. 426
“It has been shown that this second inequality itself shares something in common with the first inequality, and that the theory of the sun or earth (for Copernicus) or of the epicycle (for Ptolemy) is like the theory of the other planets.”
Chapter 44, p. 452
“I am addressing this to you who are experienced in matters astronomical, who know that in astronomy there is no tolerance for the sophistical loopholes that beset other disciplines.”
Chapter 44, p. 453
“Therefore, the times, when they are abstracted from the plane and adjusted upward and downward, will be accumulated at aphelion and perihelion in much the same manner as, if one were to squeeze a fat-bellied sausage at its middle, he would squeeze and squash the ground meat, with which it is stuffed, outwards from the belly towards the two ends, emerging above and below from beneath his hand.”
Chapter 45, p, 458
“You are merry indeed now, but I was straining and gnashing my teeth then.”
Chapter 46, p. 462
“Therefore, even though it might be of use to those who want to use numbers, to know that εβδ is a mean between εαδ and μβδ, nevertheless, for us, who strive after a geometrical way, this passage does not lie open.
Chapter 47, p. 478
“So we have ... not yet done justice to the hypothesis we took up there, because we have been abandoned by geometry.”
Chapter 48, p. 482
“I can't imagine anyone reading this not being overcome by the tedium of it even in the reading. So the reader may well judge how much vexation we (my calculator and I) derived hence, as we thrice followed this method through the 180° of anomaly, changing the eccentricity each time.”
Chapter 49, p. 494
“You will say that we have come out worse, since in ch. 48 we came nearer the truth in our results. But, my good man, if I were concerned with results, I could have avoided all this work, being content with the vicarious hypothesis. Be it known, therefore that these errors are going to be our path to the truth.”
Chapter 50, p. 495
“How small a heap of grain we have gathered from this threshing! But you also see what a huge cloud of husks there is now. They ought to have been hauled back to the beginning of ch. 48, since before I investigated the arcs of the oval path I would have dealt with them. But for the sake of bringing light, they ought to be winnowed. Besides, we might end up finding a few useful grains.”
Chapter 51, p. 508
“While I am thus celebrating a triumph over the motions of Mars, and getter him in the prison of tables and the leg-irons of eccentric equations, considering him utterly defeated, it is announced in various places that the victory is futile, and war is breaking out again with full force. For while the enemy was in the house as a captive, and hence lightly esteemed, he burst all the chains of the equations and broke out of the prison of the tables. That is, no method administered geometrically under the direction of the opinion of ch. 45 was able to emulate in numerical accuracy the vicarious hypothesis of chapter 16 (which has true equations derived from false causes). Outdoors, meanwhile, spies positioned throughout the whole circuit of the eccentric – I mean the true distances – have overthrown my entire supply of physical causes called forth from ch. 45, and have shaken off their yoke, retaking their liberty. And now there is not much to prevent the fugitive enemy's joining forces with his fellow rebels and reducing me to desperation, unless I send new reinforcements of physical reasoning in a hurry to the scattered troops and old stragglers, and, informed with diligence, stick to the trail without delay in the direction whither the captive has fled. In the following few chapters, I shall be telling of both these campaigns in the order in which they were waged.”
Chapter 53, p. 529
“Since we are establishing new hypotheses here, in that we are inquiring into the natural cause of the eccentric equations, it is appropriate that we should explore everything as carefully as possible, lest in neglecting the foundations we build upon them a building doomed to ruin.”
Chapter 52, p. 528
“[E]ven though no astronomer should try anything with numbers whose foundations he has not previously seen in geometry...”
Chapter 55, p. 542
“So the physical causes of ch. 45 go up in smoke.”
Chapter 57, p. 550
“Therefore, the comparison with the planets ought to be different: they need no oar, no physical instrument, for catching hold of the force of some weighty thing (for that motive species of the sun has no weight). Nor do we deem it fitting that the stars have corporeal oars...”
Chapter 57, p. 565
“And thus this putative center B is actually secondary to the path CD. But if it were watched by the planet, it would have to be prior to the path.
For these reasons, therefore, I deny that the versed sine of the eccentric anomaly provides the planet with a measure of its reciprocation, not because this is not such a measure, but because even if it is, it cannot be discerned by the planet's mind.”
Chapter 58, p. 573
“Galatea seeks me mischievously, the lust wench:
She flees to the willows, but hopes I'll see her first.
It is perfectly fitting that I borrow Virgil's voice to sing this about Nature. For the closer the approach to her, the more petulant her games become, and the more she again and again sneaks out of the seeker's grasp just when he is about to seize her through some circuitous route. Nevertheless, she never ceases to invite me to seize her, as though delighting in my mistakes.”
Chapter 58, p. 575
“The very truth, and the nature of things, though repudiated and ordered into exile, sneaked in again through the back door, to be received by me under an unwonted guise.”
Chapter 59, p. 591
“If anyone thinks that the obscurity of this presentation arises from the perplexity of my mind, I shall myself only thus far acknowledge to him my guilt, that I was unwilling to leave anything untested, no matter how utterly obscure, and no matter how irrelevant to the practice of astrology, which many deem the sole end of this celestial philosophy. But as for the subject matter, I urge any such person to read the Conics of Apollonius. He will see that there are some matters which no mind, however gifted, can present in such a way as to be understood in a cursory reading. There is need of meditation, and a close thinking through of what is said.”
Chapter 68, p. 640
“Therefore, as long as we are wanting suitable observations from antiquity, circumstances compel us to leave this discussion of the motion of the nodes, along with many other matters, to posterity, if, indeed, it should please God to vouchsafe the human race a length of time in this world sufficient to work through such remaining questions thoroughly.”