THE THIRD DAY
SAGREDO. I have been impatiently awaiting your arrival, that I might
hear the novel views about the annual rotation of this globe of ours.
This has made the hours seem very long to me last night and this
morning, though I have not passed them idly. On the contrary, I have
lain awake most of the night running over in my mind yesterday's
arguments and considering the reasons adopted by each side in favor of
these two opposing positions--the earlier one of Aristotle and Ptolemy,
and this later one of Anistarchus and Copernicus. And truly it seems to
me that whichever of these theories happens to be wrong, the arguments
in its favor are so plausible that it deserves to he pardoned--so long as
we pause at the ones produced by its original weighty authors. Yet
because of its antiquity the Peripatetic opinion has had many followers,
while the other has had but few, partly because of its difficulty and
partly because of its novelty. And among the partisans of the former,
especially in modem times, I seem to discern some who introduce very
childish, not to say ridiculous, reasons in maintaining the opinion
which appears to them to be true.
SALV. The same thing has struck me even more forcibly than you. I have
heard such things put forth as I should blush to repeat--not so much to
avoid discrediting their authors (whose names could always be withheld)
as to refrain from detracting so greatly from the honor of the human
race. In the long run my observations have convinced me that some men,
reasoning preposterously, first establish some conclusion In their minds
which, either because of its being their own or because of their having
received it from some person who has their entire confidence, impresses
them so deeply that one finds it impossible ever to get it out of their
heads. Such arguments in support of their fixed idea as they hit upon
themselves or hear set forth by
others, no matter how simple and stupid these may be, gain their instant
acceptance and applause. On the other hand whatever is brought forward
against it, however ingenious and conclusive, they receive with disdain
or with hot rage--if indeed it does not make them ill. Beside themselves
with passion, some of them would not be backward even about scheming to
suppress and silence their adversaries. I have had some experience of
SAGR. I know; such men do not deduce their conclusion from its premises
or establish it by reason, but they accommodate (I should have said
discommode and distort) the premises and reasons to a conclusion which
for them is already established and nailed down. No good can come of
dealing with such people, especially to the extent that their company
may be not only unpleasant but dangerous. Therefore let us continue with
our good Simplicio, who has long been known to me as a man of great
ingenuity and entirely without malice. Besides, he is intimately
familiar with the Peripatetic doctrine, and I am sure that whatever he
does not think up in support of Aristotle's opinion is not I likely to
occur to anybody.
But here, all out of breath, comes the very person who has been wished
for so long today. --We were just now maligning you.
SIMP. Please don't scold me; blame Neptune for my long delay. For in
this morning's ebb he withdrew the waters in such a manner that the
gondola in which I was riding, having entered an unlined canal not far
from here, was left high and dry. I had to stay there over an hour
awaiting the return of the tide. And while I was there, unable to get
out of the boat (which had run aground almost instantly), I fell to
observing an event which struck me as quite remarkable. As the water
slackened, it might he seen to run very swiftly through various
rivulets, the mud being
exposed in many places. While I was watching this effect, I saw this
motion along one stretch come to a halt, and without pausing a moment
the same water would begin to return, the sea turning from retreat to
advance without remaining stationary for an instant. This is an effect
which I have never happened to see before in all the time I have
SAGR. Then you cannot often have happened to be stranded among little
trickles. On account of their having scarcely any slope, the sinking or
rising of the open sea by merely the thickness of a sheet of paper is
enough to make the water flow and return a long distance through such
rivulets. On some seacoasts the rising of the sea only a few yards makes
the water spill over the plains for many thousands of acres.
SIMP. I know that well enough, but I should think that between the
lowest point of the sinking and the first point of the rising, some
perceptible interval of rest would be bound to intervene.
SAGR. It will appear so to you when you have in mind walls or pilings,
upon which this change takes place vertically. But actually there is no
state of rest.
SIMP. It would seem to me that these being two contrary motions, there
would have to be some rest midway between them, in agreement with
Aristotle's doctrine proving that in puncto regressus mediat quies.
SAGR. I remember the passage well, and I also recall that when I was
studying philosophy I was not convinced by Aristotle's proof Indeed, I
have had many experiences to the contrary. I might mention them now, but
I do not want to have us wander into any more abysses. We have met here
to discuss our subject, if possible, without interrupting it as we have
in the past two days.
SIMP. Still it will be good, if not to interrupt it, at least to extend
it somewhat. For upon returning home yesterday evening I fell to
rereading that booklet of theses, where I found some very convincing
proofs against this annual motion which is attributed to the earth. And
since I did not trust myself to quote them exactly, I have brought the
booklet along with me.
SAGR. You have done well. But if we mean to take up our discussion again
in accordance with yesterday's agreement, we must first hear what
Salviati has to say about the book on the new stars. Then, without
further interruptions, we may examine the annual motion.
Now, Salviati, what have you to say in regard to these stars? Have they
really been drawn down from the heavens into these baser regions by
virtue of the calculations made by this author whom Simplicio has
SALV. Last night I undertook to study his procedures, and this morning I
gave them another glance, wondering whether what I thought I had been
reading the night before was really written there, or whether I was the
victim of ghosts and fantastic imaginings of the night. To my great
regret, I found actually written and printed there that which, for the
sake of this philosopher's reputation, I should have wished had not
been. It seems impossible to me that he does not realize the vanity of
his enterprise, both because it Is so obvious and because I remember
having heard our friend the Academician praise him. It also seems to me
very hard to believe that out of deference to others he could be
persuaded to hold his own reputation in such low esteem as to be induced
to publish a work from which nothing but censure could be expected from
SAGR. You might add that there will be rather less than one in a hundred
of these, to offset those who will celebrate and exalt him over all the
most learned men who exist now or ever
have. A man able to sustain the Peripatetic inalterability of the
heavens against a host of astronomers, and one who, to their greater
shame, has done battle against them with their own weapons! And if there
are half a dozen to a province who perceive his trivialities, what are
they against the innumerable multitude who (being able neither to
discover these nor to comprehend them) are taken in by all the shouting,
and applaud the more the less they understand? And even the few who do
understand scorn to make a reply to such worthless and inconclusive
scribbles. With good reason, too; for those who do understand have no
need of this, and upon those who do not understand it is wasted effort.
SALV. Silence would indeed be the most appropriate reprimand for their
worthlessness, were there not other reasons which practically force one
to repudiate them. One reason is that we Italians are making ourselves
look like ignoramuses and are a laughingstock for foreigners, especially
for those who have broken with our religion; I could show you some very
famous ones who joke about our Academician and the many mathematicians
in Italy for letting the follies of a certain Lorenzini appear in print and be maintained as his views
without contradiction. But this also might be overlooked In comparison
with another and greater occasion for laughter that might be mentioned,
which is the hypocrisy of the learned toward the trifling of opponents
of this stripe in matters which they do not understand.
SAGR. I could not ask for a better example of their petulance, or of the
unhappy situation of a man like Copernicus, placed under the carping of
those who do not understand even the rudiments of the position against
which they have declared war.
SALV. You will be no less astonished at their manner of refuting the
astronomers who declare the new stars to be above the orbits of the
planets, and perhaps among the fixed stars themselves (nel firmamento).
SAGR. But how can you have examined this whole book in such a short
time? It is certainly a large volume, and there must be numerous
demonstrations in it.
SALV. I stopped after these first refutations of his in which, with
twelve demonstrations founded upon the observations of twelve of the
astronomers who thought that the new star of 1572 (which appeared in
Cassiopeia) was in the firmament, he proves it on the contrary to have
been sublunar. To do this he compares, two by two, the meridian
altitudes taken by different observers in places of different latitude,
proceeding in a manner which you will understand presently. And it seems
to me that in examining this first procedure of his I have detected in
this author a great inability to prove anything against the astronomers
or in favor of the Peripatetic philosophers, and that indeed he only
confirms their opinion more conclusively. Therefore I did not want to
devote myself with equal patience to the examination of his other
methods; having given them a superficial glance, I am positive that the
inconclusiveness which pervades his first refutation would exist in the
others likewise. And the fact is (as you will soon see) that a very few
words suffice to refute this work, although it is built up with so many
laborious calculations, as you have perceived.
Therefore you shall hear how I proceeded. The author, I say, in order to
attack his adversaries with their own weapons, takes a large number of
the observations which they themselves have made, these authors being
twelve or thirteen in number. On a part of these he bases his
calculations, and he deduces such stars to have been below the moon. Now
since I am very fond of proceeding by interrogation, and since the
author is not here himself, you, Simplicio, shall reply to the queries I
am going to make, and say
whatever you believe he would say.
Assuming that we are dealing with the nova of 1572 appearing in
Cassiopeia, tell me, Simplicio, whether you think it might have been in
different places at the same time. That is, could it he amidst the
elements and also be among the planetary orbits, and in addition be
above these among the fixed stars, as well as being infinitely higher?
SIMP. Doubtless one must say that it was located in a single place, at a
unique and determinate distance from the earth.
SALV. Then if the observations made by the astronomers were correct, and
if the calculations made by this author were not erroneous, both the
former and the latter would necessarily have to yield exactly the same
distance; isn't that right?
SIMP. So far as I can see it would necessarily be so, nor do I believe
that the author would contradict this.
SALV. But if, of many computations, not even two came out in agreement,
what would you think of that?
SIMP. I should judge that all were fallacious, either through some fault
of the computer or some defect on the part of the observers. At best I
might say that a single one, and no more, might be correct; but I should
not know which one to choose.
SALV. But would you want to deduce a questionable conclusion and
establish it as true, from a false basis? Surely not. Now this author's
calculations are such that not one of them agrees with any other; you
see, then, bow much faith you can put in them.
SIMP. If that is how matters stand, it is truly a serious defect.
SAGR. I want to help Simplicio and his author out by saying to you,
Salviati, that your case would indeed be conclusive if the author had
undertaken to find out definitely how far the star was from the earth.
But I do not believe that that was his intent; he wished only to show
that the star was sublunar. Now if, from the observations
mentioned and from all the calculations made on these, the height of the
star can always be inferred to have been less than that of the moon,
this would suffice the author to convict of the crassest ignorance all
those astronomers who, whether they erred in geometry or in arithmetic,
could not deduce the true conclusions from their own observations.
SALV. Then I had better turn my attention to you, Sagredo, since you so
cunningly sustain the author's doctrine. And let us see whether I can
also persuade Simplicio (although he is unskilled at calculations and
proofs) that this author's demonstrations are inconclusive to say the
least. Consider first that both he and all the astronomers he is in
conflict with agree that the new star had no motion of its own, but
merely went around with the diurnal motion of the primum mobile. But
they disagree about its place, the astronomers putting it in the
celestial regions (that is, above the moon) and perhaps among the fixed
stars, while he judges it to be near the earth; that is, under the arc
of the moon's orbit. And since the site of the new star of which we are
speaking was toward the north and at no great distance from the pole, so
that for us northerners it never set, it was a simple matter to take its
meridian altitudes by means of astronomical instruments--its minimal
below the pole as well as its maximal above the pole. By combining
these, when the observations were made at different places on the earth
and at different distances from the north (that is, at places differing
among themselves as to polar elevation), the distance of the star could
be reasoned out. For if it was placed in the firmament among the other
fixed stars, its meridian altitudes when taken at different elevations
of the pole would have to differ among themselves in the same way as did
these polar elevations. Thus, for example, if the altitude of the star
above the horizon had been thirty degrees when taken at a place where
the polar elevation was, say, forty-five degrees, then the altitude of
the star ought to be increased four or five degrees in those more northerly lands in which the pole is four
or five degrees higher. But if the distance of the star from the earth
was very small in comparison with that of the firmament, then its
meridian altitudes should have increased noticeably more than the polar
elevations as the pole was approached. From such a greater increase--that
is, from the excess of the increase of the star's elevation over the
increase of the polar altitude, which is called a difference of
parallax--the distance of the star from the center of the earth may be
quickly calculated by a clear and certain method.
Now this author takes the observations made by thirteen astronomers at
different polar elevations, and comparing a part of these (which he
selects) he calculates, by using twelve pairings, that the height of the
new star was always below the moon. But he achieves this by expecting
such gross ignorance on the part of everyone into whose hands his book
might fall that it quite turns my stomach. I can hardly see how the
other astronomers contain themselves in silence. Especially Kepler,
against whom this author particularly declaims; he would not be one to
hold his tongue, unless he considered the matter beneath his notice.
Now for your information I have copied on these pages the conclusions
that he deduces from his twelve investigations.
[p. 329-370. Galileo produces the data that Chiaramonti relied on. There are twelve
pairs of observations which yield observed parallaxes that place the
comet at distances of from one fifth the radius (the radius being
roughly 3,800 miles) of the earth to twenty-five times that radius.
Salviati notes that Chiaramonti dismissed out of hand all data the
yielded results placing the comet well beyond most estimations of the
distance to the stellar sphere.
Salviati explains that it is no doubt true that the data dismissed is
erroneous, but not necessarily anymore so than the sets the author
used, in fact quite the opposite. He reproduces five sets of
observations Chiaramonti ignored and finds them to he reasonably
consist, given the fact that at the extreme distance which the
observations place the comet, the slightest error of even one minute in
the observed angle will yield large variations in the results. He
demonstrate how little he needs to adjust those observations to make the
yield the same results. Meanwhile, he notes, the variations found in the
data Chiaramonti used differ so widely at the much shorter distances of
their results and would require such large adjustments to yield any
consistent result, suggesting some grosser errors, such as failure to
properly take into account refraction.]
SAGR. This is as if I were watching some unfortunate farmer who, after
having all his expected harvest beaten down and destroyed by a tempest,
goes about with pallid and downcast face, gathering up such poor
gleanings as would not serve to feed a chicken for one day.
SALV. Truly, it was with too scant a store of ammunition that this
author rose up against the assailers of the sky's inalterability, and it
is with chains too fragile that he has attempted to pull the new star
down from Cassiopeia in the highest heavens to these base and elemental
regions. Now, since the great difference between the arguments of the
astronomers and of this opponent of theirs seems to me to have been very
clearly demonstrated, we may as well leave this point and return to our
main subject. We shall next consider the annual movement generally
attributed to the sun, but then, first by Aristarchus of Samos and later
by Copernicus, removed from the sun and transferred to the earth.
Against this position I know that Simplicio comes strongly armed, in
particular with the sword and buckler of his booklet of theses or
mathematical disquisitions. It will be good to commence by producing the
objections from this booklet.
SIMP. If you don't mind, I am going to leave
those for the last, since they were the most recently discovered.
SALV. Then you had better take up in order, in accordance with our
previous procedure, the contrary arguments by Aristotle and the other
ancients. I also shall do so, in order that nothing shall be left out or
escape careful consideration and examination. Likewise Sagredo, with his
quick wit, shall interpose his thoughts as the spirit moves him.
SAGR. I shall do so with my customary lack of tact; and since you have
asked for this, you will be obliged to pardon it.
SALV. This favor will oblige me to thank and not to pardon you. But now
let Simplicio begin to set forth those objections which restrain him
from believing that the earth, like the other planets, may revolve about
a fixed center.
SIMP. The first and greatest difficulty is the repugnance and
incompatibility between being at the center and being distant from it.
For if the terrestrial globe must move in a year around the
circumference of a circle--that is, around the zodiac--it is impossible
for it at the same time to be in the center of the zodiac. But the earth
is at that center, as is proved in many ways by Aristotle, Ptolemy, and
SALV. Very well argued. There can be no doubt that anyone who wants to
have the earth move along the circumference of a circle must first
prove that it is not at the center of that circle. The next thing is for
us to see whether the earth is or is not at that center around which I
say it turns, and in which you say it is situated. And prior to this, it
is necessary that we declare ourselves as to whether or not you and I
have the same concept of this center. Therefore tell me what and where
this center is that you mean.
SIMP. I mean by "center," that of the universe; that of the world; that
of the stellar sphere; that of the heavens.
SALV. I might very reasonably dispute whether there is in nature such a
center, seeing that neither you nor anyone else has so far proved
whether the universe is finite and has a shape, or whether it is
infinite and unbounded. Still, conceding to you for the moment that it
is finite and of bounded spherical shape, and therefore has its center,
it remains to be seen how credible it is that the earth rather than some
other body is to be found at that center.
SIMP. Arislotle gives a hundred proofs that the universe is finite,
bounded, and spherical.
SALV. Which are later all reduced to one, and that one to none at all.
For if I deny him his assumption that the universe is movable all his'
proofs fall to the ground, since he proves it to be finite and bounded
only if the universe is movable. But in order not to multiply our
disputes, I shall concede to you for the time being that the universe is
finite, spherical, and has a center. And since such a shape and center
are deduced from mobility, it will be the more reasonable for us to
proceed from this same circular motion of world bodies to a detailed
investigation of the proper position of the center. Even Aristotle
himself reasoned about and decided this in the same way, making that
point the center of the universe about which all the celestial spheres
revolve, and at which he believed the terrestrial globe to be situated.
Now tell me, Simplicio: if Aristotle had found himself forced by the
most palpable experiences to rearrange in part this order and
disposition of the universe, and to confess himself to have been
mistaken about one of these two propositions--that is, mistaken either
about putting the earth in the center, or about saying that the
celestial spheres move around such a center--which of these admissions do
you think that he would choose?
SIMP. I think that if that should happen, the Peripatetics ...
SALV. I am not asking the Peripatetics, I am asking Aristotle himself As
for the former, I know very well what they would reply. They, as most
reverent and most humble slaves of Aristotle, would deny all the
observations in the world, and would even refuse to look at them in
order not to have to admit them, and they would say that the universe
remains just as Aristotle has written; not as nature would have it. For
take away the prop of his authority, and with what would you have them
appear in the field? So now tell me what you think Aristotle himself
SIMP. Really, I cannot make up my mind which of these two difficulties
he would have regarded as the lesser.
SALV. Please, do not apply this term "difficulty" to something that may
necessarily be so, wishing to put the earth in the center of the
celestial revolutions was a "difficulty." But since you do not know to
which side he would have leaned, and considering him as I do a man of
brilliant intellect, let us set about examining which of the two choices
is the more reasonable, and let us take that as the one which Aristotle
would have embraced. So, resuming our, reasoning once more from the
beginning, let us assume out of respect for Aristotle that the universe
(of the magnitude of which we have no sensible information beyond the
fixed stars), like anything that is spherical in shape and moves
circularly, has necessarily a center for its shape and for its motion.
Being certain, moreover, that within the stellar sphere there are many
orbs one inside another, with their stars which also move circularly,
our question is this: Which is it more reasonable to believe and to say;
that these included orbs move around the same center as the universe
does, or around some other one which is removed from that? Now you,
Simplicio, say what you think about this matter.
SIMP. If we could stop with this one assumption and were sure of not
running into something else that would disturb us, I should think it
would be much more reasonable to say that the container and the things
it contained all moved around one common center rather than different
SALV. Now if it is true that the center of the universe is that point
around which all the orbs
and world bodies (that is, the planets) move, it is quite certain that
not the earth, but the sun, is to be found at the center of the
universe. Hence, as for this first general conception, the central place
is the sun's, and the earth is to be found as far away from the center
as it is from the sun.
SIMP. How do you deduce that it is not the earth, but the sun, which is
at the center of the revolutions of the planets?
SALV. This is deduced from most obvious and therefore most powerfully
convincing observations. The most palpable of these, which excludes the
earth from the center and places the sun here, is that we find all the
planets closer to the earth at one time and farther from it at another.
The differences are so great that Venus, for example, is six times as
distant from us at its farthest as at its closest, and Mars soars nearly
eight times as high in the one state as in the other. You may thus see
whether Aristotle was not some trifle deceived in believing that they
were always equally distant from us.
SIMP. But what are the signs that they move around the sun?
SALV. This is reasoned out from finding the three outer planets--Mars,
Jupiter, and Saturn--always quite close to the earth when they are in
opposition to the sun, and very distant when they are in conjunction
with it. This approach and recession is of such moment that Mars when
close looks sixty times as large as when it is most distant. Next, it is
certain that Venus and Mercury must revolve around the sun, because of
their never moving far away from it, and because of their being seen now
beyond it and now on this side of it, as Venus's changes of shape
conclusively prove. As to the moon, it
is true that this can never separate from the earth in any way, for
reasons that will be set forth more specifically as we proceed.
SAGR. I have hopes of hearing still more
remarkable things arising from this annual motion of the earth than were
those which depended upon its diurnal rotation.
SALV. You will not be disappointed, for as to the action of the diurnal
motion upon celestial bodies, it was not and could not be anything
different from what would appear if the universe were to rush speedily
in the opposite direction. But this annual motion, mixing with the
individual motions of all the planets, produces a great many oddities
which in the past have baffled all the greatest men in the world.
Now returning to these first general conceptions, I repeat that the
center of the celestial rotation for the five planets, Saturn, Jupiter,
Mars, Venus, and Mercury, is the sun; this will hold for the earth too,
if we are successful in placing that in the heavens. Then as to the
moon, it has a circular motion around the earth, from which as I have
already said it cannot be separated; but this does not keep it from
going around the sun along with the earth in its annual movement.
SIMP. I am not yet convinced of this arrangement at all. Perhaps I should
understand it better from the drawing of a diagram, which might make it
easier to discuss.
SALV. That shall be done. But for your greater satisfaction and your
astonishment, too, I want you to draw it yourself You will see that
however firmly you may believe yourself not to understand it, you do so
perfectly, and just by answering my questions you will describe it
exactly. So take a sheet of paper and the compasses; let this page be
the enormous expanse of the universe, in which you have to distribute
and arrange its parts as reason shall direct you. And first, since you
are sure without my telling you that the earth is located in this
universe, mark some point at your pleasure where you intend this to be
located, and designate it by means of some letter.
SIMP. Let this be the place of the terrestrial globe, marked A.
SALV. Very well. I know in the second place that you are aware that this
earth is not inside the body of the sun, nor even contiguous to it, but
is distant from it by a certain space. Therefore assign to the sun some
other place of your choosing, as far from the earth as you like, and
designate that also.
SIMP. Here I have done it; let this be the sun's position, marked 0.
SALV. These two established, I want you to think about placing Venus in
such a way that its position and movement can conform to what sensible
experience shows us about it. Hence you must call to mind, either from
past discussions or from your own observations, what you know happens
with this star. Then assign it whatever place seems suitable for it to
SIMP. I shall assume that those appearances are correct which you have
related and which I have
read also in the booklet of theses; that is, that this star never
recedes from the sun beyond a certain definite interval of forty degrees
or so; hence it not only never reaches opposition to the sun, but not
even quadrature, nor so much as a sextile
Moreover, I shall assume that it displays itself to us about
forty times as large at one time than at another, greater when, being
retrograde, It is approaching evening conjunction with the sun, and very
small when it is moving forward toward morning conjunction, and
furthermore that when it appears very large, it reveals itself in a
homed shape, and when it looks very small it appears perfectly round.
These appearances being correct, I say, I do not see how to escape
affirming that this star revolves in a circle around the sun, in such a
way that this circle cannot possibly be said to embrace and contain
within itself the earth, nor to be beneath the sun (that is, between the
sun and the earth), nor yet beyond the sun. Such a circle cannot embrace
the earth because then Venus would sometimes be in opposition to the
sun; it cannot be beneath the sun, for then Venus would appear
sickle-shaped at both conjunctions; and it cannot be beyond the sun,
since then it would always look round and never homed. Therefore for its
lodging I shall draw the circle CH around the sun, without having this
include the earth.
SALV. Venus provided for, it is fitting to consider Mercury, which, as
you know, keeping itself always around the sun, recedes therefrom much
less than Venus. Therefore consider what place you should assign to it.
SIMP. There is no doubt that, imitating Venus as it does, the most
appropriate place for it will be a smaller circle, within this one of
Venus and also described about the sun. A reason for this, and
especially for its proximity to the sun, is the vividness of Mercury's
splendor surpassing that of Venus and all the other planets. Hence on
this basis we may draw its circle here and mark it with the letters BG.
SALV. Next, where shall we put Mars?
SIMP. Mars, since it does come into opposition with the sun, must
embrace the earth with its
circle. And I see that it must also embrace the sun; for, coming into
conjunction with the sun, if it did not pass beyond it but fell short of
it, it would appear homed as Venus and the moon do. But it always looks
round; therefore its circle must include the sun as well as the earth.
And since I remember your having said that when it is in opposition to
the sun it looks sixty times as large as when in conjunction, it seems
to me that this phenomenon will be well provided for by a circle around
the sun embracing the earth, which I draw here and mark DI. When Mars is
at the point D, it is very near the earth and in opposition to the sun,
but when it is at the point 1, it is in conjunction with the sun and
very distant from the earth.
And since the same appearances are observed with regard to Jupiter and
Saturn (although with less variation in Jupiter than in Mars, and With
still less in Saturn than in Jupiter), it seems clear to me that we can
also accommodate these two planets very neatly with two circles, still
around the sun. This first one, for Jupiter, I mark EL; the other,
higher, for Saturn, is called FM.
SALV. So far you have comported yourself uncommonly well. And since, as
you see, the approach and recession of the three outer planets is
measured by double the distance between the earth and the sun, this
makes a greater variation in Mars than in Jupiter because the circle DI
of Mars is smaller than the circle EL of Jupiter. Similarly, EL here is
smaller than the circle FM of Saturn, so the variation is still less in
Saturn than in Jupiter, and this corresponds exactly to the appearances.
It now remains for you to think about a place for the moon.
SIMP. Following the same method (which seems to me very convincing),
since we see the moon come into conjunction and opposition with the sun,
it must be admitted that its circle embraces the earth. But it must not
embrace the sun also, or else when it was in conjunction it would not
look homed but always round and full of light. Besides, it would never
cause an eclipse of the
sun for us, as it frequently does, by getting in between us and the
sun. Thus one must assign to it a circle around the earth, which shall
be this one, NP, in such a way that when at P it appears to us here on
the earth A as in conjunction with the sun, which sometimes it will
eclipse in this position. Placed at N, it is seen in opposition to the
sun, and in that position it may fall under the earth's shadow and be
SALV. Now what shall we do, Simplicio, with the fixed stars? Do we want
to sprinkle them through the immense abyss of the universe, at various
distances from any predetermined point, or place them on a spherical
surface extending around a center of their own so that each of them will
be the same distance from that center?
SIMP. I had rather take a middle course, and assign to them an orb
described around a definite center and included between two spherical
surfaces--a very distant concave one, and another closer and convex,
between which are placed at vanious altitudes the innumerable host of
stars. This might be called the universal sphere, containing within it
the spheres of the planets which we have already designated.
SALV. Well, Simplicio, what we have been doing all this while is
arranging the world bodies according to the Copernican distribution, and
this has now been done by your own hand. Moreover you have assigned
their proper movements to them all except the sun, the earth, and the
stellar sphere. To Mercury and Venus you have attributed a circular
motion around the sun without embracing the earth. Around the same sun
you have caused the three outer planets, Mars, Jupiter, and Saturn, to
move, embracing the earth within their circles. Next, the moon cannot
move in any way except around the earth and without embracing the sun.
And in all these movements you likewise agree with Copernicus himself It
now remains to apportion three things among the sun, the earth, and the
stellar sphere: the state of rest which appears to belong to the earth;
the annual motion through the zodiac,
which appears to belong to the sun; and the diurnal movement, which
appears to belong to the stellar sphere, with all the rest of the
universe sharing in it except the earth. And since it is true that all
the planetary orbs (I mean Mercury, Venus, Mars, Jupiter, and Saturn)
move around the sun as a center, it seems most reasonable for the state
of rest to belong to the sun rather than to the earth--just as it does
for the center of any movable sphere to remain fixed, rather than some
other point of it remote from the center.
Next as to the earth, which is placed in the midst of moving object--I
mean between Venus and Mars, one of which makes its revolution in nine
months and the other in two years--a motion requiring one year may be
attributed to it much more elegantly than a state of rest, leaving the
latter for the sun. And such being the case, it necessarily follows that
the diurnal motion, too, belongs to the earth. For if the sun stood
still, and the earth did not revolve upon itself but merely had the
annual movement around the sun, our year would consist of no more than
one day and one night; that is, six months of day and six months of
night, as was remarked once previously.
See, then, how neatly the precipitous motion of each twenty-four hours
is taken away from the universe, and how the fixed stars (which are so
many suns) agree with OUT sun in enjoying perpetual rest. See also what
great simplicity is to be found in this rough sketch, yielding the
reasons for so many weighty phenomena in the heavenly bodies.
SAGR. I see this very well indeed. But just as you deduce from this
simplicity a large probability of truth in this system, others may on
the contrary make the opposite deduction from it. If this very ancient
arrangement of the Pythagoreans is so well accommodated to the
appearances, they may ask (and not unreasonably) why it has found so few
followers in the course of centuries; why it has been refuted by
Aristotle himself, and why even Copernicus is
not having any better luck with it in these latter days.
SALV. Sagredo, if you had suffered even a few times, as I have so often,
from hearing the sort of follies that are designed to make the common
people contumacious and unwilling to listen to this innovation (let
alone assent to it), then I think your astonishment at finding so few
men holding this opinion would dwindle a good deal. It seems to me that
we can have little regard for imbeciles who take it as a conclusive
proof in confirmation of the earth's motionlessness, holding them firmly
in this belief, when they observe that they cannot dine today at
Constantinople and sup in Japan, or for those who are positive that the
earth is too heavy to climb up over the sun and then fall headlong back
down again. There is no need to bother about such men as these, whose
name is legion, or to take notice of their fooleries. Neither need we
try to convert men who define by generalizing and cannot make room for
distinctions, just in order to have such fellows for our company in very
subtle and delicate doctrines. Besides, with all the proofs in the world
what would you expect to accomplish in the minds of people who are too
stupid to recognize their own limitations?
No, Sagredo, my surprise is very different from yours. You wonder that
there are so few followers of the Pythagorean opinion, whereas I am
astonished that there have been any up to this day who have embraced and
followed it. Nor can I ever sufficiently admire the outstanding acumen
of those who have taken hold of this opinion and accepted it as true;
they have through sheer force of intellect done such violence to their
own senses as to prefer what reason told them over that which sensible
experience plainly showed them to the contrarv. For the arguments
against the whirling of the earth which we have already examined are
very plausible, as we have seen; and the fact that the Ptolemiacs and
Aristotelians and all their disciples took them to be conclusive is
indeed a strong argument of their effectiveness. But the experiences
which overtly contradict the annual movement are Indeed so much greater
in their apparent force that, I repeat, there is no limit to my
astonishment when I reflect that Aristarchus and Copernicus were able to
make reason so conquer sense that, in defiance of the latter, the former
became mistress of their belief
SAGR. Then we are about to encounter still further strong attacks
against this annual movement?
SALV. We are, and such obvious and sensible ones that were it not for
the existence of a superior and better sense than natural and common
sense to join forces with reason, I much question whether 1, too, should
not have been much more recalcitrant toward the Copemican system than I
have been since a clearer light than usual has illuminated me.
SAGR. Well, then, Salviati, let us get down to cases, as they say; for
every word spent otherwise seems to me to be wasted.
SALV. I am at your service ...
SIMP. Gentlemen, please give me a chance to restore harmony to my mind,
which I now find very much upset by certain matters which Salviati has
just touched upon. Then, when this storm has subsided, I shall be able
to listen to your theories more profitably. For there is no use forming
an image in a wavy mirror, as the Latin poet has told us so graciously
... nuper me in lillore vidi,
Cum placidum ventis staret mare.
SALV. You are quite right; tell us your difficulties.
SIMP. Those who deny the diurnal motion to the earth because they do not
see themselves being transported to Persia or Japan have been called
by you just as dull-witted as those who oppose the annual motion because
of the repugnance they feel against admitting that the vast and
ponderous bulk of the terrestrial globe can raise itself on high and
then descend to the depths, as it would have to do if it revolved about
the sun annually. Now I, without blushing to be numbered among such
simpletons, feel in my own mind this very repugnance as to the second
point against the annual motion, the more so when I see how much
resistance is made to motion even over a plain by, I shall not say a
mountain, but a mere stone; and even the former would be but the tiniest
fraction of an Alpine range. Therefore I beg you not to scorn such
objections entirely, but to solve them; and not for me alone, but also
for others to whom they seem quite real. For I think it is very
difficult for some people, simple though they may be, to recognize and
admit that they are simple just because they know themselves to be so
SAGR. Indeed, the simpler they are, the more nearly impossible it will
be to convince them of their own shortcomings. And on this account I
think that it is good to resolve this and all similar objections, not
only that Simplicio should be satisfied, but also for other reasons no
less important. For it is clear that there are plenty of people who are
well versed in philosophy and. the other sciences but who, either
through lack of astronomy or mathematics or some other discipline which
would sharpen their minds for the penetration of truth, adhere to silly
doctrines like these. That is why the situation of poor Copernicus seems
to me lamentable; he could expect only censure for his views and could
not let them fall into the hands of anyone who, being unable to
comprehend his arguments (which are very subtle and therefore difficult
to master), would be convinced of their falsity on account of some
superficial appearances, and would go about declaring them to be wrong
and full of error. If people cannot be convinced by the arguments, which
are quite abstruse, it is good
to make sure that they recognize the vapidity of these objections. From
such knowledge comes moderation in their judgement and condemnation of
the doctrine which at present they consider erroneous. Accordingly I
shall raise two other objections against the diurnal motion, which not
so long ago were to be heard put forward by important men of letters,
and after that we shall look into the annual motion.
The first was that if it were true that the sun and other stars did not
rise over the eastern horizon, but the eastern side of the earth sank
beneath them while they remained motionless, then it would follow that
after a short time the mountains, sinking downward with the rotation of
the terrestrial globe, would get into such a position that whereas a
little earlier one would have had to climb steeply to their peaks, a few
hours later one would have to stoop and descend in order to get there.
The other was that if the diurnal motion belonged to the earth, it would
have to be so rapid that anyone placed at the bottom of a well would not
for a moment be able to see a star which was directly above him, being
able to see it only during the very brief instant in which the earth
traverses two or three yards, this being the width of the well. Yet
experiment shows that the apparent passage of such a star in going over
the well takes quite a while--a necessary argument that the mouth of the
well does not move with that rapidity which is required for the diurnal
movement. Hence the earth is motionless.
SIMP. Of these two arguments, the second really does seem persuasive to
me; but as to the first, I think I could clear that up myself. For I
consider it the same thing for the terrestrial globe to move about its
own center and carry a mountain eastward with it, as for the globe to
stand still while the mountain was detached at the base and drawn along
the earth. And I do not see that carrying the mountain over the earth's
surface is an operation any different from sailing a ship over the
surface of the sea. So if the objection
of the mountain were valid, it would follow I ikeW`1'se that as the ship
continued its voyage and became several degrees distant from our ports,
we should have to climb its mast not merely in order to ascend, but to
move about in a plane, or eventually even to descend. Now this does not
happen, nor have I ever heard of any sailor, even among those who have
circumnavigated the globe, who had found any difference in such actions
(or any others performed on board ship) because of the ship being in one
place rather than another.
SALV. You argue very well, and if it had ever entered the mind of the
author of this objection to consider how this neighoring eastern
mountain of his would, if the terrestrial globe revolved, be found in a
couple of hours to have been carried by that motion to where Mt.
Olympus, for example, or Mt. Carmel is now located, he would have seen
that by his own line of reasoning he would be obliged to believe and
admit that in order to get to the top of the latter mountains one would
in fact have to descend. Such people have the same kind of mind as do
those who deny the antipodes on the grounds that one cannot walk with
his head down and his feet attached to the ceiling; they produce ideas
that are true and that they completely understand, but they do not find
it easy to deduce the simplest solutions for their difficulties. I mean,
they understand very well that to gravitate or to descend is to approach
the center of the terrestrial globe, and that to ascend is to depart
from that; but they fail to understand that our antipodes have no
trouble at all in sustaining themselves or in walking because they are
just like us, having the soles of their feet toward the center of the
earth and their heads toward the sky.
SAGR. Yet we know that men who are profoundly ingenious in other fields
are blind to such ideas. This confirms what I have just said; it is good
to remove every objection, even the feeblest. Therefore the matter of
the well should also be answered.
SALV. This second argument does indeed have some elusive appearance of
cogency. Nevertheless, I think it certain that if one were to
interrogate the very person to whom it occurs, to the end that he might
express himself better by explaining just what results ought to follow
if one assumes the diurnal rotation of the earth, but which appear to
him not to take place; then, I say, I believe that he would get all
tangled up in explaining this question and its consequences--perhaps no
less than he would disentangle it by thinking it over.
SIMP. To be perfectly frank, I am sure that that is what would happen,
although I too find myself right now in this same confusion. For at
first glance it seems to me that the argument is binding, but on the
other hand I am beginning to realize that other troubles would arise if
the reasoning were to continue along the same line For this extremely
rapid Course, which ought to be perceived in the star if the motion
belonged to the earth, should also be discovered in it if the motion
were its own--even more so, since it would have to be thousands of times
as fast in the star as in the earth. On the other hand, the star must be
lost to sight by passing the mouth of the well, which would be only a
couple of yards in diameter, if the well goes along with the earth more
than two million yards per hour. Indeed, this seems to be such a
transitory glimpse that one cannot even imagine it; yet from the bottom
of a well a star is seen for quite a long time. So I should like to be
put in the clear about this matter.
SALV. Now I am strongly confirmed in my belief about the confusion of
the author of this objection, seeing that you too, Simplicio, becloud
what you mean and do not really grasp what you should be saying. I
deduce this principally from your omitting a distinction which is a
principal point in this matter. So tell me whether in carrying out this
experiment (I mean this one of the star passing over the mouth of the
well) you would make any distinction between the well
being deeper or shallower; that is, between the observer being farther
from or closer to its mouth. For I have not heard you make any mention
SIMP. The fact is that I had not thought about it, but your question has
awakened my mind to it, and hints to me that such a distinction must be
quite necessary. Already I begin to see that in order to determine the
time of the passage, the depth of the well may perhaps make no less
difference than its width.
SALV. Still, I rather question whether the width makes any difference to
us, or very much.
SIMP. Why, it seems to me that having to travel 10 yards of breadth
takes ten times as long as to pass I yard. I am sure that a boat 10
yards long will pass beyond my view long before a galley 100 yards long
will do so.
SALV. So, we still persist in that inveterate idea of not moving
unless our legs carry us.
What you are saying is true, my dear Simplicio, if the object you see is
in motion while you remain stationary to observe it. But if you are in a
well when the well and you together are carried along by the rotation of
the earth, don't you see that not in an hour, nor in a thousand, nor in
all eternity will you ever be overtaken by the mouth of the well? The
manner in which the moving or nonmoving of the earth acts upon you in
such a situation can be recognized not from the mouth of the well, but
from some other separate object not sharing the same state of motion--or
I should say, of rest.
SIMP. So far so good; but assume that 1, being in the well, am carried
together with it by the diurnal motion, and that the star seen by me is
motionless. The opening of the well (which alone allows my sight to pass
beyond) being not more than three yards, out of so many millions of
yards in the balance of the terrestrial surface which are hindering my
view, how can the time of my seeing be a perceptible fraction of that of
my not seeing?
SALV. You are still falling into the same quibble, and in fact you will
need someone to help you out of it. It is not the width of the we] I,
Simplicio, which measures the time of visibility of the star, since in
that case you would see it perpetually, as the well would give passage
to your vision perpetually. No, the measure of this time must be
obtained from that fraction of the motionless heavens which remains
visible through the opening of the well.
SIMP. Is not that part of the sky which I perceive the same fraction of
the entire heavenly sphere as the mouth of the well is of the
SALV. I want you to answer that for yourself. Tell me whether the mouth
of the well is always the same fraction of the earth's surface.
SIMP. There is no doubt that it is always the same.
SALV. And how about the part of the sky which is seen by the person in
the well? Is that always the same fraction of the whole celestial
SIMP. Now I am beginning to sweep the darkness from my mind, and to
understand what you hinted to me a little while ago--that the depth of
the well has something to do with this matter. For I do not question
that the more distant the eye is from the mouth of the well, the smaller
Will be the part of the sky which it Will perceive, and consequently the
sooner this will have been passed and become lost to view by whoever is
looking at it from the bottom of the well.
SALV. But is there any place in the well from which he would perceive
exactly that fraction of the celestial sphere which the mouth of the
well is of the earth's surface?
SIMP. It seems to me that if the well were excavated to the center of
the earth, perhaps from there one might see a part of the sky which
would be to it as the well is to the earth. But leaving the center and
rising toward the surface, an ever larger part of the sky would be
SALV. And finally, placing the eye at the mouth of the well, it would
perceive one-half the sky, or very little less, which would take twelve
in passing, assuming that we were at the equator. A while ago I sketched
for you an outline of the Copernican system, against the truth of which
the planet Mars launches a ferocious attack. For If it were true that
the distances of Mars from the earth varied as much from minimum to
maximum as twice the distance from the earth to the sun, then when it is
closest to us its disc would have to look sixty times as large as when
it is most distant. Yet no such difference is to be seen. Rather, when
it is in opposition to the sun and close to us, it shows itself as only
four or five times as large as when, at conjunction, it becomes hidden
behind the rays of the sun.
Another and greater difficulty is made for us by Venus, which, if it
circulates around the sun as Copernicus says, would be now beyond it and
now on this side of it, receding from and approaching toward us by as
much as the diameter of the circle it describes. Then when it is beneath
the sun and very close to us, its disc ought to appear to us a little
less than forty times as large as when it is beyond the sun and near
conjunction. Yet the difference is almost imperceptible.
Add to these another difficulty; for if the body of Venus is
intrinsically dark, and like the moon it shines only by illumination
from the sun, which seems reasonable, then it ought to appear homed when
it is beneath the sun, as the moon does when it is likewise near the
sun--a phenomenon which does not make itself evident in Venus. For that
reason, Copernicus declared that Venus was either luminous in itself or
that its substance was such that it could drink in the solar light and
transmit this through its entire thickness in order that it might look
resplendent to us. In this manner Copernicus pardoned Venus its
unchanging shape, but he said nothing about its small variation in size;
much less of the requirements of Mars. I believe this was because he was
unable to rescue to his own satisfaction an appearance so contradictory
to his view, yet being persuaded by so many other reasons, he maintained
that view and held it to be true.
Besides these things, to have all the planets move around together with
the earth, the sun being the center of their rotations, then the moon
alone disturbing this order and having its own motion around the earth
(going around the sun in a year together with the earth and the whole
elemental sphere) seems in some way to upset the whole order and to
render it improbable and false.
These are the difficulties which make me wonder at Aristarchus and
Copernicus. They could not have helped noticing them, without having
been able to resolve them; nevertheless they were confident of that
which reason told them must be so in the light of many other remarkable
observations. Thus they confidently affirmed that the structure of the
universe could have no other form than that which they had described.
Then there are other very serious but beautiful problems which are not
easy for ordinary minds to resolve, but which were seen through and
explained by Copernicus; these we shall put off until we have answered
the objections of people who show themselves hostile to this position.
Coming now to the explanations and replies to the three grave objections
mentioned, I say that the first two are not only not contrary to the
Copernican system, but that they absolutely favor it, and greatly. For
both Mars and Venus do show themselves variable in the assigned
proportions, and Venus does appear homed when beneath the sun, and
changes her shape in exactly the same way as the moon.
SAGR. But if this was concealed from Copemicus, how is it revealed to
SALV. These things can be comprehended only through the sense of sight,
which nature has not granted so perfect to men that they can succeed in
discerning such distinctions. Rather, the very instrument of seeing
introduces a hindrance of its own. But in our time it has pleased God to
concede to human ingenuity an invention so
wonderful as to have the power of increasing vision four, six, ten,
twenty, thirty, and forty times, and an infinite number of objects which
were invisible, either because of distance or extreme minuteness, have
become visible by means of the telescope.
SAGR. But Venus and Mars are not objects which are invisible because of
any distance Or small size. We perceive these by simple natural vision.
Why, then, do we not discern the differences in their sizes and shapes?
SALV. In this the impediment of our eyes plays a large part, as I have
just hinted to you. On account of that, bright distant objects are not
represented to us as simple and plain, but are festooned with
adventitious and alien rays which are so long and dense that the bare
bodies are shown as expanded ten, twenty, a hundred, or a thousand times
as much as would appear to us if the little radiant crown which is not
theirs were removed.
SAGR. Now I recall having read something of the sort, but I don't
remember whether it was in the Solar Letters or in Il Saggiatore by our
friend. It would be a good thing, in order to refresh my
memory as well as to inform Simplicio, who perhaps has not read those
works, to explain to us in more detail how the matter stands. For I
should think that a knowledge of this would be most essential to an
understanding of what is now under discussion.
SIMP. Everything that Salviati is presently setting forth is truly new
to me. Frankly, I had no interest in reading those books, nor up till
now have I put any faith in the newly introduced optical device.
Instead, following in the footsteps of other Peripatetic philosophers of
my group, I have considered as fallacies and deceptions of the lenses
those things which other people have admired as stupendous achievements.
If I have been in error, I shall be glad to be lifted out of
it; and, charmed by the other new things I have heard from you, I shall
listen most attentively to the rest.
SALV. The confidence which men of that stamp have in their own acumen
is as unreasonable as the small regard they have for the judgments of
others, It is a remarkable thing that they should think themselves
better able to judge such an instrument without ever having tested it,
than those who have made thousands and thousands of experiments with it
and make them every day. But let us forget about such headstrong people,
who cannot even be censured without doing them more honor than they
Getting back to our purpose, I say that shining objects, either because
their light is refracted in the moisture that covers the pupil, or
because it is reflected from the edges of the eyelids and these
reflected rays are diffused over the pupil, or for some other reason,
appear to our eyes as if surrounded by new rays. Hence these bodies look
much larger than they would if they were seen by us deprived of such
irradiations. This enlargement is made in greater and greater proportion
as such luminous objects become smaller and smaller, in exactly such a
manner as if we were to suppose a growth of shining hair, say four
inches long, to be added around a circle four inches in diameter, which
would increase its apparent size nine times; but ...
SIMP. I think you meant to say "three times," since four inches added on
each side of a circle four inches in diameter would amount to tripling
its magnitude and not to enlarging it nine times.
SALV. A little geometry, Simplicio; it is true that the diameter increases
three times, but the surface (which is what we are talking about) grows
nine times. For the surfaces of circles, Simplicio, are to each other as
the squares of their diameters, and a circle four inches in diameter has
to another of twelve inches the same ratio which the square of four has
to the square of twelve; that is, 16 to 144. Therefore it will be nine
times as large, not three. This is
for your information, Simplicio.
Now, to continue, if we add this coiffure of four inches to a circle of
only two inches in diameter, the diameter of the crown will be ten
inches and the ratio of the circle to the bare body will be as 100 to 4
(for such are the squares of 10 and of 2), so the enlargement would be
twenty-five times. And finally, the four inches of hair added to a tiny
circle of one inch in diameter would enlarge this eighty-one times. Thus
the increase is continually made larger and larger proportionately,
according as the real objects which are increased become smaller and
SAGR. The question which gave Simplicio trouble did not really bother
me, but there are some other things about which I desire a clearer
explanation. In particular I should like to team the basis upon which
you affirm such a growth to be always equal in all Visible objects.
SALV. I have already partly explained by saying that only luminous
objects increase; not dark ones. Now I shall add the rest. Of shining
objects, those which are brightest in light make the greatest and
strongest reflections upon our pupils, thereby showing themselves as
much more enlarged than those less bright. And so as not to go on too
long about this detail, let us resort to what is shown us by our
greatest teacher; this evening, when the sky is well darkened, let us
look at Jupiter; we shall see it very radiant and large. Then let us
cause our vision to pass through a tube, or even through a tiny opening
which we may leave between the palm of our hand and our fingers,
clenching the fist and bringing it to the eye; or through a hole made by
a fine needle in a card. We shall see the disc of Jupiter deprived of
rays and so very small that we shall indeed judge it to be even less
than one-sixtieth of what had previously appeared to us to be a great
torch when seen with the naked eye. Afterwards, we may look at the Dog
Star, a very beautiful star and larger than any other fixed star. To the
naked eye it looks to be not
much smaller than Jupiter, but upon taking away its headdress in the
manner described above, its disc will be seen to be so small that one
would judge it to be no more than one-twentieth the size of Jupiter.
Indeed, a person lacking perfect vision will be able to find it only
with great difficulty, from which it may reasonably be inferred that
this star is one which has a great deal more luminosity than Jupiter,
and makes larger irradiations.
Next, the irradiations of the sun and of the moon are as nothing because
of the size of these bodies, which by themselves take up so much room in
our eye as to leave no place for adventitious rays, so that their discs
are seen as shorn and bounded.
We may assure ourselves of the same fact by another experiment which I
have made many times--assure ourselves, I mean, that the resplendent
bodies Of More vivid illumination give out many more rays than those
which have only a pale light. I have often seen Jupiter and Venus
together, twenty-five or thirty degrees from the sun, the sky being very
dark. Venus would appear eight or even ten times as large as Jupiter
when looked at with the naked eye. But seen afterward through a
telescope, Jupiter's disc would be seen to be actually four or more
times as large as Venus. Yet the liveliness of Venus's brilliance was
incomparably greater than the pale light of Jupiter, which comes about
only because Jupiter is very distant from the sun and from us, while
Venus is close to us and to the sun.
These things having been explained, it will not be difficult to
understand how it might be that Mars, when in opposition to the sun and
therefore seven or more times as close to the earth as when it is near
conjunction, looks to us scarcely four or five times as large in the
former state as in the latter. Nothing but irradiation is the cause of
this. For if we deprive it of the adventitious rays we shall find it
enlarged in exactly the proper ratio. And to remove its head of hair
from it, the telescope is the unique and supreme means.
Enlarging its disc nine hundred or a thousand times, it causes this to
be seen bare and bounded like that of the moon, and in the two positions
Varying in exactly the proper proportion.
Next in Venus, which at its evening conjunction when it is beneath the
sun ought to look almost forty times as large as in Its morning
conjunction, and is seen as not even doubled, it happens in addition to
the effects of irradiation that it is sickle--shaped, and its horns,
besides being very thin, receive the sun's light obliquely and therefore
very weakly. So that because it is small and feeble, it makes its
irradiations less ample and lively than when it shows itself to us with
its entire hemisphere lighted. But the telescope plainly shows us its
horns to be as bounded and distinct as those of the moon, and they are
seen to belong to a very large circle, in a ratio almost forty times as
great as the same disc when it is beyond the sun, toward the end of its
SAGR. 0 Nicholas Copernicus, what a pleasure it would have been for you
to see this part of your system confirmed by so clear an experiment!
SALV. Yes, but how much less would his sublime intellect be celebrated
among the learned! For as I said before, we may see that with reason as
his guide he resolutely continued to affirm what sensible experience
seemed to contradict. I cannot get over my amazement that he was
constantly willing to persist in saying that Venus might go around the
sun and be more than six times as far from us at one time as at another,
and still look always equal, when it should have appeared forty times
SAGR. I believe then that in Jupiter, Saturn, and Mercury one ought also
to see differences of size corresponding exactly to their varying
SALV. In the two outer planets I have observed this with precision in
almost every one of the past twenty-two years. In Mercury no
observations of importance can be made, since it does not allow itself
to be seen except at its maximum angles with the sun, in which the
its distances from the earth are imperceptible. Hence such differences
are unobservable, and so are its changes of shape, which must certainly
take place as in Venus. But when we do see it, it would necessarily show
itself to us in the shape of a semicircle, just as Venus does at its
maximum angles, though its disc is so small and its brilliance so lively
that the power of the telescope is not sufficient to strip off its hair
so that it may appear completely shorn.
It remains for us to remove what would seem to be a great objection to
the motion of the earth.. This is that though all the planets turn about
the sun, the earth alone Is not solitary like the others, but goes
together in the company of the moon and the whole elemental sphere
around the sun in one year, while at the same time the moon moves around
the earth every month. Here one must once more exclaim over and exalt
the admirable perspicacity of Copernicus, and simultaneously regret his
misfortune at not being alive in our day. For now Jupiter removes this
apparent anomaly of the earth and moon moving conjointly. We see
Jupiter, like another earth, going around the sun in twelve years
accompanied not by one but by four moons, together with everything that
may be contained within the orbits of its four satellites.
SAGR. And what is the reason for your calling the four Jovian planets
SALV. That is what they would appear to be to anyone who saw them from
Jupiter. For they are dark in themselves, and receive their light from
the sun; this is obvious from their being eclipsed when they enter into
the cone of Jupiter's shadow. And since only that hemisphere of theirs
is illuminated which faces the sun, they always look entirely
illuminated to us who are outside their orbits and closer to the sun;
but to anyone on Jupiter they would look completely lighted only when
they were at the highest points of their circles. In the lowest
part--that is, when between Jupiter and the sun--they would appear homed
from Jupiter. In a word, they would make for
Jovians the same changes of shape which the moon makes for us
Now you see how admirably these three notes harmonize with the
Copernican system, when at first they seemed so discordant with it. From
this, Simplicio will be much better able to see with what great
probability one may conclude that not the earth, but the sun, is the
center of rotation of the planets. And since this amounts to placing the
earth among the world bodies which indubitably move about the sun (above
Mercury and Venus but beneath Saturn, Jupiter, and Mars), why will it
not likewise be probable, or perhaps even necessary, to admit that it
also goes around?
SIMP. These events are so large and so conspicuous that it is impossible
for Ptolemy and his followers not to have had knowledge of them. And
having had, they must also have found a way to give reasons sufficient
to account for such sensible appearances; congruous and probable
reasons, since they have been accepted for so long by so many people.
SALV. You argue well, but you must know that the principal activity of
pure astronomers is to give reasons just for the appearances of
celestial bodies, and to fit to these and to the motions of the stars
such a structure and arrangement of circles that the resulting
calculated motions correspond with those same appearances. They are not
much worried about admitting anomalies which might in fact be
troublesome in other respects. Copernicus himself writes, in his first
studies, of having rectified astronomical science upon the old Ptolemaic
assumptions, and corrected the motions of the planets in such a way that
the computations corresponded much better with the appearances, and vice
versa. But this was still taking them separately, planet by planet. He
goes on to say that when he wanted to put together the whole fabric from
all individual constructions, there resulted a monstrous chimera
composed of mutually disproportionate members, incompatible as a
whole. Thus however well the astronomer might be satisfied merely as a
calculator, there was no satisfaction and peace for the astronomer as a
scientist. And since he very well understood that although the celestial
appearances might be saved by means of assumptions essentially false in
nature, it would be very much better if he could derive them from true
suppositions, he set himself to inquiring diligently whether any one
among the famous men of antiquity had attributed to the universe a
different structure from that of Ptolemy's which is commonly accepted.
Finding that some of the Pythagoreans had in particular attributed the
diurnal rotation to the earth, and others the annual revolution as well,
he began to examine under these two new suppositions the appearances and
peculiarities of the planetary motions, all of which he had readily at
hand. And seeing that the whole then corresponded to its parts with
wonderful simplicity, he embraced this new arrangement, and in it he
found peace of mind.
SIMP. But what anomalies are there in the Ptolemaic arrangement which
are not matched by greater ones in the Copernican?
SALV. The illnesses are in Ptolemy, and the cures for them in
Copernicus. First of all, do not all philosophical schools hold it to be
a great Impropriety for a body having a natural circular movement to
move irregularly with respect to its own center and regularly around
another point? Yet Ptolemy's structure is composed of such uneven
movements, while in the Copernican system each movement is equable
around its own center. With Ptolemy it is necessary to assign to the
celestial bodies contrary movements, and make everything move from east
to west and at the same time from west to east, whereas with Copernicus
all celestial revolutions are in one direction, from west to east. And
what are we to say of the apparent movement of a planet, so uneven that
it not only goes fast at one time and slow at another, but sometimes
stops entirely and even goes backward a long way after doing so?
To save these appearances, Ptolemy introduces vast epicycles, adapting
them one by one to each planet, with certain rules about incongruous
motions--all of which can be done away with by one very simple motion of
the earth. Do you not think it extremely absurd, Simplicio, that in
Ptolemy's construction where all planets are assigned their own orbits,
one above another, it should be necessary to say that Mars, placed above
the sun's sphere, often falls so far that it breaks through the sun's
orb, descends below this and gets closer to the earth than the body of
the sun is, and then a little later soars immeasurably above it? Yet
these and other anomalies are cured by a single and simple annual
movement of the earth.
SAGR. I should like to arrive at a better understanding of how these
stoppings, retrograde motions, and advances, which have always seemed to
me highly improbable, come about in the Copernican system.
SALV. Sagredo, you will see them come about in such a way that the
theory of this alone ought to be enough to gain assent for the rest of
the doctrine from anyone who is neither stubborn nor unteachable. I tell
you, then, that no change occurs in the movement of Saturn in thirty
years, in that of Jupiter in twelve, that of Mars in two, Venus in nine
months, or in that of Mercury in about eighty days. The annual movement
of the earth alone, between Mars and Venus, causes all the apparent
irregularities of the five stars named. For an easy and full
understanding of this, I wish to draw you a picture of it.
Now suppose the sun to be located in the center 0, around which we shall
designate the orbit described by the earth with its annual movement,
BGM. The circle described by Jupiter (for example) in 12 years will be
BGM here, and in the stellar sphere we shall take the circle of the
zodiac to be PUA. In addition, in the earth's annual orbit we shall take
a few equal arcs, BC, CD, DE, EF, FG, GH, H1, IK, KL, and LK and in the
circle of Jupiter we shall indicate these other arcs passed over in
the same times in which the earth is passing through these. These are
BC, CD, DR, EF, FG, GH, Hf, IK, KL, and LM, which will be
proportionately smaller than those noted on the earth's orbit, as the
motion of Jupiter through the zodiac is slower than the annual celestial
Now suppose that when the earth is at B, Jupiter is at B, then it will
appear to us as being in the zodiac at P, along the straight line BBP.
Next let the earth move from B to C and Jupiter from B to C in the same
time; to us, Jupiter will appear to have arrived at Q in the zodiac,
having advanced in the order of the signs from P to Q. The earth then
passing to D and Jupiter to D, it will be seen in the zodiac at R; and
from E, Jupiter being at E, it will appear in the zodiac at S, still
advancing. But now when the earth begins to get directly between Jupiter
and the sun (having arrived at F and Jupiter at F), to us Jupiter will
appear to be ready to commence returning backward through the zodiac,
during the time in which the earth will have passed through the arc EF,
Jupiter will have been slowed down between the points S and T, and will
look to us almost stationary. Later the earth coming to G, Jupiter at G
(in opposition to the sun) will be seen in the zodiac at U, turned far
back through the whole arc TU in the zodiac; but in reality, following
always its uniform course, it has advanced not only in its own circle
but in the zodiac too, with respect to the center of the zodiac and to
the sun which is located there.
The earth and Jupiter then continuing their movements, when the earth is
at H and Jupiter is at H, It will be seen as having returned far back
through the zodiac by the whole arc UX; but the earth having arrived at
I and Jupiter at I, it will apparently have moved in the zodiac by only
the small space XY and will there appear stationary. Then when the earth
shall have progressed to K and Jupiter to K, Jupiter will have advanced
through the arc YN, in the zodiac; and, continuing its course, from L
the earth will see Jupiter at L in the point Z Finally, Jupiter at M
will be seen from the earth at M to have passed to A, still advancing.
And its whole apparent retrograde motion in the zodiac will be as much
as the arc TX, made by Jupiter while it is passing in its own circle
through the arc FH, the earth going through FH in its orbit.
Now what is said here of Jupiter is to be understood of Saturn and Mars
also. In Saturn these retrogressions are somewhat more frequent than in
Jupiter, because its motion is slower than Jupiter's, so that the earth
overtakes it in a shorter time. In Mars they are rarer, its motion being
faster than that of Jupiter, so that the earth spends more time in
catching up with it.
Next, as to Venus and Mercury, whose circles are included within that of
the earth, stoppings and retrograde motions appear in them also, due not
to anv motion that really exists in them, but to the annual motion of
the earth. This is acutely demonstrated by Copernicus, enlisting the aid
of Apollonius of Perga, in chapter 35 of Book
V in his Revolutions.
You see, gentlemen, with what ease and simplicity the annual motion--if
made by the earth--lends itself to supplying reasons for the apparent
anomalies which are observed in the movements of the five planets,
Saturn, Jupiter, Mars, Venus, and Mercury. It removes them all and
reduces these movements to equable and regular motions; and it was
Nicholas Copernicus who first clarified for us the reasons for this
But another effect, no less wonderful than this, and containing a knot
perhaps even more difficult to untie, forces the human intellect to
admit this annual rotation and to grant it to our terrestrial globe.
This is a new and unprecedented theory touching the sun itself For the
sun has shown itself unwilling to stand alone in evading the
confirmation of so important a conclusion, and instead wants to be the
greatest witness of all to this, beyond exception. So now hear this new
and mighty marvel.
[pp. 401-412. There ensues a theory of solar rotation on dual axes based upon the
movement of sun spots.]
...This, Simplicio, is all that occurred to my friend and to myself
regarding that which might be adduced in explanation of the appearances
in defense of their opinions by the Copernicans and by the Ptolemaics.
You may do with it whatever your own judgment persuades you to do.
SIMP. I recognize my own incapacity to take upon myself so important a
decision. As to my own ideas, I remain neutral, in the hope that a time
Will come when the mind will be freed by an illumination from higher
contemplations than these of our human reasoning, and all the mists
which keep it darkened will be swept away.
SAGR. Simplicio's counsel is excellent and pious, and worthy of being
accepted and followed
by everyone, since only that which is derived from the highest wisdom
and supreme authority may be embraced with complete security. But so far
as human reason is allowed to penetrate, confining myself within the
bounds of theory and of probable causes, I shall indeed say (with a
little more boldness than Simplicio exhibits) that I have not, among all
the many profundities that I have ever heard, met with anything which is
more wonderful to my intellect or has more decisively captured my mind
(outside of pure geometrical and arithmetical proofs) than these two
conjectures, one of which is taken from the stoppings and retrograde
motions of the five planets, and the other from the peculiarities of
movement of the sunspots. And it appears to me that they yield easily
and clearly the true cause of such strange phenomena, showing the reason
for such phenomena to be a simple motion which is mixed with many others
that are also simple but that differ among themselves. Moreover they
show this without introducing any difficulties; rather, they remove all
those which accompany other viewpoints. So much so that I am rapidly
coming to the conclusion that those who remain hostile toward this
doctrine must either not have heard it or must not have understood these
arguments, which are so numerous and so conclusive.
SALV. I do not give these arguments the status of either conclusiveness
or of inconclusiveness, since (as I have said before) my intention has
not been to solve anything about this momentous question, but merely to
set forth those physical and astronomical reasons which the two sides
can give me to set forth. I leave to others the decision, which
ultimately should not be ambiguous, since one of the arrangements must
be true and the other false. Hence it is not possible within the bounds
of human learning that the reasons adopted by the right side should be
anything but clearly conclusive, and those opposed to them, vain and
SAGR. Then it is now time for us to hear the
other side, from that booklet of theses or disquisitions which Simplicio
has brought back with him.
SIMP. Here is the book, and here is the place in which the author first
briefly describes the system of the world according to the position of
Copernicus, saying: Terram igitur una cum Luna lotoque hoc elementari
Copernicus etc. ("Therefore the earth, together with the moon and all
this elemental world, Copernicus" etc.)
SALV. Wait a bit, Simplicio; for it seems to me that this author at the
very outset declares himself to be very ill-informed about the position
he undertakes to refute, when he says that Copernicus makes the earth
together with the moon trace out the orbis magnnus in a year, moving
from east to west; a thing which, as it is false and impossible, has
accordingly never been uttered by Copernicus. Indeed, he makes it go in
the opposite direction (I mean from west to east; that is, in the ord6r
of the signs of the zodiac), so that it appears that the annual motion
belongs to the sun, which 'is placed immovably in the center of the
You see the excessive boldness of this man's self-confidence, setting
himself up to refute another's doctrine while remaining ignorant of the
basic foundations upon which the greatest and most important parts of
the whole structure are supported. This is a poor beginning for gaining the confidence of the reader, but let us proceed.
SIMP. The system of the universe explained, he begins to propose his
objections against the annual movement. The first of these he utters
ironically, in derision of Copernicus and his followers, writing that in
this fantastic arrangement of the world one must affirm the most sublime
inanities: That the sun, Venus, and Mercury are beneath the earth; that
heavy material naturally ascends and light stuff descends; that Christ,
our Saviour and Redeemer, rose to hell and descended into heaven when He
approached the sun. That when Joshua com
manded the sun to stand still, the earth stood still--or else the sun
moved opposite to the earth; that when the sun is in Cancer, the earth
is running through Capricorn, so that the winter signs make the summer
and the spring signs the autumn; that the stars do not rise and set for
the earth, but the earth for them; and that the east starts in the west
while the west begins in the east; in a word, that nearly the whole
course of the world is turned inside out.
SALV. All of this is satisfactory to me except his having mixed passages
from the ever venerable and mighty Holy Scriptures among these apish
puerilities, and his having tried to utilize sacred things for wounding
anybody who might, without either affirming or denying anything,
philosophize Jokingly and in sport, having made certain assumptions and
desiring to argue about them among friends.
SIMP. Truly he scandalized me too, and not a little; especially later,
when he adds that if indeed the Copernicans answer these and the like
arguments in some distorted way, they still will not be able to answer
satisfactorily some things which come later.
SALV. Oh, that is worst of all, for he is pretending to have things
which are more effective and convincing than the authority of Holy Writ.
But let us, for our part, revere it, and pass on to physical and human
arguments. Yet if he does not adduce among his physical arguments
matters which make more sense than those set forth up to this point, we
may as well abandon him entirely. I am certainly not in favor of wasting
words answering such trifling tomfooleries. And as for his saying that
the Copernicans do reply to these objections, that is quite false. I
cannot believe that any man would put himself to such a pointless waste
SIMP. I, too, concur in this decision, let us, then, listen to his other
objections, which are more strongly supported. Now here, as you see, he
deduces with very precise calculations that if the orbit in which
Copernicus makes the earth travel
Around the sun in a year were scarcely perceptible with respect to the
immensity of the stellar sphere, as Copernicus says must be assumed,
then one would have to declare and maintain that the fixed stars were at
an inconceivable distance from us, and that the smallest of them would
be much larger than this whole orbit, while others would be larger than
the orbit of Saturn. Yet such bulks are truly too vast, and are
incomprehensible and unbelievable.
SALV. I have indeed seen something similar argued against Copernicus by
Tycho, so this is not the first time that I have revealed the fallacy--or
better, the fallacies--of this argument, built as it is upon completely
false hypotheses. It is based upon a dictum of Copernicus which is taken
by his adversaries with rigorous literalness, as do those quarrelsome
people who, being wrong about the principal issue of the case, seize
upon some single word accidentally uttered by their opponents and make a
great fuss about it without ever letting up.
For your better comprehension, know that Copernicus first explains the
remarkable consequences to the various planets deriving from the annual
movement of the earth; in particular the forward and retrograde
movements of the three outer planets. Then he adds that these apparent
mutations which are perceived to be greater in Mars than in Jupiter,
from Jupiter's being more distant, and still less in Saturn, from its
being farther away than Jupiter, remain imperceptible in the fixed stars
because of their immense distance from us in comparison with the
distance of Jupiter or of Saturn. Here the adversaries of this opinion
rise up, and take what Copernicus has called "imperceptible" as having
been assumed by him to be really and absolutely nonexistent. Remarking
that even the smallest of the fixed stars is still perceptible, since it
strikes our sense of sight, they set themselves to calculating (with the
Introduction of still more false assumptions), and deduce that in
Copernicus's doctrine one must admit that a fixed star
is much larger than the orbit of the earth.
Now in order to reveal the folly of their entire method, I shall show
that by assuming that a star of the sixth magnitude may be no larger
than the sun, one may deduce by means of correct demonstrations that the
distance of the fixed stars from us is sufficiently great to make quite
imperceptible in them the annual movement of the earth which in turn
causes such large and observable variations in the planets.
Simultaneously I shall clearly expose to you a gigantic fallacy in the
assumptions made by the adversaries of Copernicus.
To begin with, I assume along with Copernicus and in agreement with his
opponents that the radius of the earth's orbit, which is the distance
from the sun to the earth, contains 1,208 of the earth's radii.
Secondly, I assume with the same concurrence and in accordance with the
truth that the apparent diameter of the sun at its average distance is
about one-half a degree, or 30 minutes; this is 1,800 seconds, or
108,000 third-order divisions. And since the apparent diameter of a
fixed star of the first magnitude is no more than 5 seconds, or 300
thirds, and the diameter of one of the sixth magnitude measures 50
thirds (and here is the greatest error of Copernicus's adversaries),
then the diameter of the sun contains the diameter of a fixed star of
the sixth magnitude 2,160 times. Therefore if one assumes that a fixed
star of the sixth magnitude is really equal to the sun and not larger,
this amounts to saying that if the sun moved away until its diameter
looked to be 1/2160th of what it now appears to be, its distance would
have to be 2,160 times what it is In fact now.
This is the same as to say that the distance of a fixed star of the
sixth magnitude is 2,160 radii of the earth's orbit. And since the
distance from the earth to the sun is commonly granted to contain 1,208
radii of the earth, and the distance of the fixed star is, as we said,
2,160 radii of the orbit, then the radius of the earth in relation to
that of its orbit is much greater than (almost
double) the radius of that orbit in relation to the stellar sphere.
Therefore the difference in aspect of the fixed star caused by the
diameter of the earth's orbit would be little more noticeable than that
which is observed in the sun due to the radius of the earth.
SAGR. For a first step, this Is a bad fall.
SALV. It is indeed wrong, since according to this author a star of the
sixth magnitude would have to be as large as the earth's orbit in order
to justify the dictum of Copernicus. Yet assuming it to be equal only to
the sun, which in turn is rather less than one ten-millionth of that
orbit, makes the stellar sphere so large and distant that this alone is
sufficient to remove this objection against Copernicus.
SAGR. Please make this computation for me.
SALV. The calculation is very short and simple. The diameter of the sun
is 11 radii of the earth, and the diameter of the earth's orbit contains
2,416 of these radii, as both parties agree. So the diameter of the
orbit contains that of the sun approximately 220 times, and since
spheres are to each other as the cubes of their diameters, we take the
cube of 220 and we have the orbit 10,648,000 times as large as the sun.
The author would say that a star of the sixth magnitude would have to be
equal to this orbit.
SAGR. Then their error consists in their having been very much deceived
in taking the apparent diameter of the fixed stars.
SALV. That is the error, but not the only one. And truly I am quite
surprised at the number of astronomers, and famous ones too, who have
been quite mistaken in their determinations of the sizes of the fixed as
well as the moving stars, only the two great luminaries being excepted.
Among these men are al-Fergani, al-Battani, Thabit ben Korah, and more recently Tycho, Clavius, and all the predecessors of our Academician. For they did not take care of the
adventitious irradiation which deceptively makes the stars look a
hundred or more times as large as they are when seen without haloes. Nor
can these men be excused for their carelessness; it was within their
power to see the bare stars at their pleasure, for it suffices to look
at them when they first appear in the evening, or just before they
vanish at dawn. And Venus, if nothing else, should have warned them of
their mistake, being frequently seen in daytime so small that it takes
sharp eyesight to see it, though in the following night it appears like
a great torch. I Will not believe that they thought the true disc of a
torch was as It appears in profound darkness, rather than as it is when
perceived in lighted surroundings; for our lights seen from afar at
night look large, but from near at hand their true flames are seen to be
small and circumscribed. This alone might have sufficed to make them
To speak quite frankly, I thoroughly believe that none of them--not even
Tycho himself, accurate as he was in handling astronomical instruments
and despite his having built such large and accurate ones without a
thought for their enormous expense--ever set himself to determine and
measure the apparent diameter of any star except the sun and moon. I
think that arbitrarily and, so to speak, by rule of thumb some one among
the most ancient astronomers stated that such-and-such was the case, and
the later ones without any further experiment adhered to what this first
one had declared. For if any of them had applied himself to making any
test of the matter, he would doubtless have detected the error.
SAGR. But if they lacked the telescope (for you have already said that
our friend came to know the truth of the matter by means of that
instrument), they ought to be pardoned, not accused of negligence.
SALV. That would be true if they could not have obtained the result
without the telescope. It Is true that the telescope, by showing the
disc of the star bare and very many times enlarged, renders the
operations much easier, but one could carry them on without it, though
not with the same accuracy. I have done so, and this is the method I
have used. I hung up a light rope in the direction of a star (I made use
of Vega, which rises between the north and the northeast) and then by
approaching and retreating from this cord placed between me and the
star, I found the point where its width just hid the star from me. This
done, I found the distance of my eye from the cord, which amounts to the
same thing as one of the sides which includes the angle formed at my eye
and extending over the breadth of the cord.
[pp. 420-425. Salviati embarks upon a description of his method for measuring the
angular diameter of a star by attempting to remove the halo of light
surrounding it. By this method he claims to have discovered that stars
have a significantly smaller angular diameter than the eye normally
beholds. This leads to a brief excursion into optical properties, before
returning of the question of the star's distance.]
SALV. Simplicio, I wish you could for a moment put aside your affection
for the followers of your doctrines and tell me frankly whether you
believe that they comprehend in their own minds this magnitude which
they subsequently decide cannot be ascribed to the universe because of
its immensity. I myself believe that they do not. It seems to me that
here the situation is just as it is with the grasp of numbers when one
gets up into the thousands of millions, and the imagination becomes
confused and can form no concept. The same thing happens in
comprehending the magnitudes of immense distances; there comes into our
reasoning an effect similar to that which occurs to the senses on a
serene night, when I look at the stars and judge by sight that their
distance is but a few miles, or that the fixed stars are not a bit
farther off than Jupiter, Saturn, or even the moon.
But aside from all this, consider those previous disputes between the
astronomers and the Peripatetic philosophers about the reasoning as to
the distance of the new stars in Cassiopeia and Sagittarius, the
astronomers placing these among the fixed stars and the philosophers
believing them to be closer than the moon. How powerless are our senses
to distinguish large distances from extremely large ones, even when the
latter are in fact many thousands of times the larger!
And finally I ask you, 0 foolish man: Does your imagination first
comprehend some magnitude for the universe, which you then judge, to be
too vast? If it does, do you like imagining that your comprehension
extends beyond the Divine power? Would you like to imagine to yourself
things greater than God can accomplish? And if it does not comprehend
this, then why do you pass judgment upon things you do not understand?
SIMP. These arguments are very good, and no one denies that the size of
the heavens may exceed our imaginings, since God could have created it
even thousands of times larger than it is. But must we not admit that
nothing has been created in vain, or is idle, in the universe? Now when
we see this beautiful order among the planets, they being arranged
around the earth at distances commensurate with their producing upon it
their effects for our benefit, to what end would there then be
interposed between the highest of their orbits (namely, Saturn's), and
the stellar sphere, a vast space without anything in it, superfluous,
and vain? For the use and convenience of whom?
SALV. It seems to me that we take too much upon ourselves, Simplicio,
when we will have it that merely taking care of us is the adequate work
of Divine wisdom and power, and the limit beyond which it creates and
disposes of nothing.
I should not like to have us tie its hand so. We should be quite content
in the knowledge that God and Nature are so occupied with the government
of human affairs that they could not apply themselves more to us even if
they had no other cares to attend to than those of the human race alone.
I believe that I can explain what I mean by a very appropriate and most
noble example, derived from the action of the light of the sun. For when
the sun draws up some vapors here, or warms a plant there, it draws
these and warms this as if it had nothing else to do. Even in ripening a
bunch of grapes, or perhaps just a single grape, it applies itself so
effectively that it could not do more even if the goal of all its
affairs were just the ripening of this one grape. Now if this grape
receives from the sun everything it can receive, and is not deprived of
the least thing by the sun simultaneously producing thousands and
thousands of other results, then that grape would be guilty of pride or
envy if it believed or demanded that the action of the sun's rays should
be employed upon itself alone.
I am certain that Divine Providence omits none of the things which look
to the government of human affairs, but I cannot bring myself to believe
that there may not be other things in the universe dependent upon the
infinity of its wisdom, at least so far as my reason informs me; yet if
the facts were otherwise, I should not resist believing in reasoning
which I had borrowed from a higher understanding. Meanwhile, when I am
told that an immense space interposed between the planetary orbits and
the starry sphere would be useless and vain, being idle and devoid of
stars, and that any immensity going beyond our comprehension would be
superfluous for holding the fixed stars, I say that it is brash for our
feebleness to attempt to judge the reason for God's actions, and to call
everything in the universe vain and superfluous which does not serve us.
SAGR. Say rather, and I think you will be
speaking more accurately, "which we do not know to serve us." I believe
that one of the greatest pieces of arrogance. or rather madness, that
can be thought of is to say, "Since I do not know how Jupiter or Saturn
is of service to me, they are superfluous, and even do not exist."
Because, 0 deluded man, neither do I know how my arteries are of service
to me, nor my cartilages, spleen, or gall, I should not even know that I
had gall, or a spleen, or kidneys, if they had not been shown to me in
many dissected corpses. Even then I could understand what my spleen does
for me only if it were removed. In order to understand how some
celestial body acted upon me (since you want ail their actions to be
directed at me), it would be necessary to remove that body for a while,
and say that whatever effect I might then feel to be missing in me
depended upon that star.
Besides, what does it mean to say that the space between Saturn and the
fixed stars, which these men call too vast and useless, is empty of
world bodies? That we do not see them, perhaps? Then did the four
satellites of Jupiter and the companions of Saturn come into the heavens
when we began seeing them, and not before? Were there not innumerable
other fixed stars before men began to see them"The nebulae were once
only little white patches; have we with our telescopes made them become
clusters of many bright and beautiful stars? Oh, the presumptuous, rash
ignorance of mankind!
SALV. There is no need, Sagredo, to probe any farther into their
fruitless exaggerations. Let us continue our plan, which is to examine
the validity of the arguments brought forward by each side without
deciding anything, leaving the decision to those who know more about it
Returning to our natural and human reason, I say that these terms
"large," "small" "immense," "minute," etc. are not absolute, but
relative; the same thing in comparison with various others may be called
at one time
"immense" and at another "Imperceptible," let alone "small." Such being
the case, I ask: In relation to what can the stellar sphere of
Copernicus be called too vast? So far as I can see, it cannot be
compared or said to be too vast except in relation to some other thing
of the same kind. Now let us take the smallest thing of the same kind,
which will be the orbit of the moon. If the stellar orb must be
considered too vast in relation to that of the moon, then every other
magnitude which exceeds some other of its kind by a similar or greater
ratio ought also to be said to be too vast; and likewise, by the same
reasoning, it should be said not to exist in the universe. Then the
elephant and the whale will be mere chimeras and poetical fictions,
because the former are too vast in comparison with ants (being land
animals), and the latter in relation to gudgeons (being fish). And if
actually found in nature, they would be immeasurably large; for the
elephant and whale certainly exceed the ant and gudgeon in a much
greater ratio than the stellar sphere does that of the moon, taking the
stellar sphere to he as large as is required by the Copernican system.
Besides, how large is the sphere of Jupiter, and how great is that
assigned to Saturn as the receptacle of a single star, though the planet
itself is small in comparison with a fixed star! Surely if to each fixed
star such a large portion of the space in the universe should be
assigned as its container, that orb which contains an innumerable
quantity of these would have to he made many thousands of times larger
than suffices for the needs of Copernicus. Moreover, do you not call a
fixed star very small--I mean even one of the most conspicuous ones, let
alone those which escape our sight? And we call it so in comparison with
the surrounding space. Now if the whole stellar sphere were one single
blazing body, who is there that does not understand that in an infinite
space there could be assigned a distance so great that, from there, such
a brilliant sphere would appear as small as or even smaller than
a fixed star now appears to us from the earth? So from such a point we
should judge as small the very things which we now call immeasurably
SAGR. To me, a great ineptitude exists on the part of those who would
have it that God made the universe more in proportion to the small
capacity of their reason than to Ms immense, His infinite, power.
SIMP. All this that you are saying is good, but what the other side
objects to is having to grant that a fixed star must be not only equal
to, but much greater than, the sun; for both are still individual bodies
located within the stellar orb. And it seems to me much to the purpose
that this author inquires, "To what end and use are such vast frames?
Produced for the earth, perhaps? That is, for a trifling little dot? And
why so remote as to appear very small and be absolutely unable to act in
any way upon the earth? To what purpose such a disproportionately large
abyss between these and Saturn? All these things are baffling, for they
cannot be maintained by probable reasons."
SALV. From the questions this fellow asks, it seems to me that one may
deduce that if only the sky, the stars, and their distances were
permitted to keep the sizes and magnitudes which he has believed in up
to this point (though he has surely never imagined for them any
comprehensible magnitudes), then he would completely understand and be
satisfied about the benefits which would proceed from them to the earth,
which itself would no longer be such a trifling thing. Nor would these
stars any longer be so remote as to seem quite minute, but large enough
to be able to act upon the earth. And the distance between them and
Saturn would be in good proportion, and he would have Very probable
reasons for everything, which I should very much like to have heard. But
seeing how confused and contradictory he is in these few words leads me
to believe that he is very thrifty with or else hard up for these
probable reasons, and that what he
calls reasons are more likely fallacies, even shadows of foolish
fantasies. Therefore I ask him whether these celestial bodies really act
upon the earth, and whether it was for that purpose that they were made
of such-and-such sizes and arranged at such-and-such distances, or
whether they have nothing to do with terrestrial affairs? If they have
nothing to do with the earth, then it is a great folly for us
Terrestrials to want to be arbiters of their sizes and regulators of
their local dispositions, we being quite ignorant of all their affairs
and interests. But if he says that they do act, and that it is to this
end that they are directed, then this amounts to admitting what he
denies in another place, and praising what he has just finished
condemning when he said that celestial bodies located at such distances
from the earth as to appear minuscule could not act upon it in any way.
Now, my good man, in the starry sphere, which is already established at
whatever distance it is, and which you have just decided is well
proportioned for an influence upon terrestrial matters, a multitude of
stars do appear quite small, and a hundred times as many are entirely
invisible to us--which is to appear smaller than small. Therefore you
must now (contradicting yourself) deny their action upon the earth, or
else (still contradicting yourself) admit that their appearing small
does not detract from their power to act. Or else (and this would be a
frank and honest confession) you must grant and freely admit that your
judgment about their sizes and distances was folly, not to say
presumption or brashness.
SIMP. As a matter of fact, I also saw immediately, upon reading this
passage, the obvious contradiction in his saying that the stars of
Copernicus, so to speak, could not act upon the earth because they
appeared so small, and his not noticing that he had granted action upon
the earth to the stars of Ptolemy and his own, these not merely
appearing small but being for the most part invisible.
SALV. But now I come to another point. Upon
what basis does he say that the stars appear so smaII? Is it perhaps
because that is the way they look to us? Does he not know that this
comes about from the instrument which we use in looking at them--that is,
our eyes? Or for that matter that by changing instruments we may see
them larger and larger, as much as we please? Who knows; perhaps to the
earth, which beholds them without eyes, they may appear quite huge and
as they really are?
But it is time for us to leave these trifles and get to more important
matters. I have already demonstrated two things: first, at what distance
the firmament may be placed so that the diameter of the earth's orbit
would make no greater variation in it than that which the terrestrial
diameter makes with respect to the sun at its distance therefrom, and I
then showed that in order to make a fixed star appear to us as of the
size we see, it is not necessary to assume it to be larger than the sun.
Now I should like to know whether Tycho or any of his disciples has ever
tried to investigate in any way whether any phenomenon is perceived in
the stellar sphere by which one might boldly affirm or deny the annual
motion of the earth.
SAGR. I should answer "no" for them, they having had no need to do so,
since Copernicus himself says that there is no such variation there; and
they, arguing ad hominem, grant this to him. Then on this assumption
they show the improbability which follows from it; namely, it would be
required to make the sphere so immense that in order for a fixed star to
look as large as it does, it would actually have to be so immense in
bulk as to exceed the earth's orbit--a thing which is, as they say,
SALV. So it seems to me, and I believe that they
argue against the man more in the defense of another man than out of any
great desire to get at the truth. And not only do I believe that none of
them ever applied himself to making such observations, but I am not even
sure that any of them knew what variation ought to be produced
in the fixed stars by the annual movement of the earth, if the stellar
sphere were not at such a distance that any variation in them would
vanish on account of its smallness. For to stop short of such researches
and fall back upon the mere dictum of Copernicus may suffice to refute
the man, but certainly not to clear up the fact.
Now it might be that there is a variation, but that it Is not looked
for; or that because of its smallness, or through lack of accurate
instruments, it was not known by Copernicus. This would not be the first thing that he
failed to know, either for lack of instruments or from some other
deficiency. Yet, grounded upon most solid theories, he affirmed what
seemed to be contradicted by things he did not understand. For as
already said, without a telescope it cannot be comprehended that Mars
does increase sixty times and Venus forty times in one position as
against another, and their differences appeared to be much less than the
true ones. Yet since that time it has become certain that such
variations are, to a hair, Just what the Copernican system required.
Hence it would be a good thing to investigate with the greatest possible
precision whether one could really observe such a variation as ought to
be perceived in the fixed stars, assuming an annual motion of the earth.
[pp. 433-448. There follows a discussion about just what sorts of movements would or
would not be perceptible among the stars, given the earth's annual
rotation on a fixed axis, and Salviati's assertion that the stars are not
all equidistant from the (supposed) center of the universe.]
SIMP. Really, to be quite frank, I do feel a great repugnance against
having to concede the distance of the fixed stars to be so great that
the alterations just explained would have to remain entirely imperceptible in them.
SALV. Do not completely despair, Simplicio; perhaps there is yet some
way of tempering your difficulties. First of all, that the apparent size
of the stars is not seen to alter visibly need not appear entirely
improbable to you when you see that men's estimates in such a matter may
be so grossly in error, particularly when looking at brilliant objects.
Looking, for example, at a burning torch from a distance of two hundred
paces, and then coming closer by three or four yards, do you believe
that you yourself would perceive it as larger? For my part, I should
certainly not discover this even if I approached by twenty or thirty
paces; sometimes I have even happened to see such a light at a distance,
and been unable to decide whether it was coming toward me or going away,
when in fact it was approaching. Now what of this? If the same approach
and retreat of Saturn (I mean double the distance from the sun to us) is
almost entirely imperceptible, and if it is scarcely noticeable in
Jupiter, what could it amount to in the fixed stars, which I believe you
would not hesitate to place twice as far away as Saturn? In Mars, which
while approaching us. . .
SIMP. Please do not labor this point, for I am indeed convinced that
what you have said about the unaltered appearance of the apparent sizes
of the fixed stars may very well be the case. But what shall we say to
that other difficulty which arises from no variation at all being seen
in their changing aspects?
SALV. Let us say something which will perhaps satisfy you also on this
point. Briefly, would you be content if those alterations really were
perceived in the stars which seem to you so necessary if the annual
motion belongs to the earth?
SIMP. I should indeed be, so far as this particular is concerned.
SALV. I wish you had said that if such a variation were perceived,
nothing would remain that could cast doubt upon the earth's mobility,
since no counter could be found to such an event. But even though this
may not make itself visible to us, the earth's mobility Is not thereby
excluded, nor its immobility necessarily proved. It is possible,
Copernicus declares, that the immense distance of the starry sphere
makes such small phenomena unobservable. And as has already been
remarked, it may be that up to the present they have not even been
looked for, or, if looked for, not sought out in such a way as they need
to be; that is, with all necessary precision and minute accuracy. It is
hard to achieve this precision, both on account of the imperfection of
astronomical instruments, which are subject to much variation, and
because of the shortcomings of those who handle them with less care than
is required. A cogent reason for putting little faith in such
observations is the disagreement we find among astronomers in assigning
the places, I shall say not merely of novas and of comets, but of the
fixed stars themselves, and even of polar altitudes, about which they
disagree most of the time by many minutes.
As a matter of fact, how would you expect anyone to be sure, with a
quadrant or sextant that customarily has an arm three or four yards
long, that he is not out by two or three minutes in the setting of the
perpendicular or the alignment of the alidade? For on such a circumference this will be no more
than the thickness of a millet seed. Besides which, it is almost
impossible for the instrument to be constructed absolutely accurate and
then maintained so. Ptolemy distrusted an armillary instrument
constructed by Archimedes himself for determining the entry of the sun
into the equinox.
SIMP. But if the instruments are thus suspect, and the observations are
so dubious, how can we ever safely accept them and free them from error?
I have heard great vauntings of Tycho's instruments, which were made at
enormous expense, and of his remarkable skill in making observations.
SALV. I grant you all this, but neither the one fact nor the other
suffices to make us certain in affairs of such importance. I want to
have us use instruments far larger than those of Tycho's; quite precise
ones, and made at minimum cost, whose sides will be four, six, twenty,
thirty, or fifty miles, so that a degree is a mile wide, a minute is
fifty yards, and a second is little less than a yard. In a word, we may
have them as large as we please, without their costing us a thing.
Being at a villa of mine near Florence, I plainly observed the arrival
of the sun at the summer solstice and its subsequent departure. For one
evening at its setting it hid itself behind a cliff in the Pietrapana
Mountains, about sixty miles away, leaving only a small shred of itself
revealed to the north, the breadth of which was not the hundredth part
of its diameter. But the following evening, at the same position of
setting, it left a like part of itself showing which was noticeably
thinner. This is a conclusive proof that it had commenced to move away
from the tropic; yet the sun's return between the first and second
observations surely did not amount to one second of arc along the
horizon. Making the observation later with a fine telescope which would
multiply the disc of the sun more than a thousandfold turned out to be
pleasant and easy.
Now my idea is for us to make our observations of the fixed stars with
similar instruments, utilizing some star in which the changes would be
conspicuous. These are, as I have already explained, the ones which are
farthest from the ecliptic. Among them Vega, a very large star close to
the pole of the ecliptic, would be the most convenient when operating in
the manner I am about to describe to you, so far as the more northern
countries are concerned, though I am going to make use of another star.
I have already been looking by myself for a place well adapted for such
observations. The place Is an open plain,
above which there rises to the north a very prominent mountain, at the
summit of which is built a little chapel facing west and east, so that
the ridgepole of its roof may cut at right angles the meridian over some
house situated in the plain. I wish to affix a beam parallel to that
ridgepole and about a yard above it. This done, I shall seek in the
plain that place from which one of the stars of the Big Dipper is hidden
by this beam which I have placed, just when the star crosses the
meridian. Or else, if the beam is not large enough to hide the star, I
shall find the place from which the disc of the star is seen to be cut
in half by the beam--an effect which can be discerned perfectly by means
of a fine telescope. It will be very convenient if there happens to be
some house at the place from which this event can be perceived, but if
not, then I shall drive a stick firmly into the ground and affix a mark
to indicate where the eye is to be placed whenever the observation is to
be repeated. I shall make the first of these observations at the summer
solstice, in order to continue them from month to month, or whenever I
please, until the other solstice.
By means of such observations, the star's rising or lowering can be
perceived no matter how small it may be. And if in the course of these
operations any such variation shall happen to become known, how great an
achievement will be made in astronomy' For by this means, besides
ascertaining the annual motion, we shall be able to gain a knowledge of
the size and distance of that same star.
SAGR. I thoroughly understand the whole procedure, and the operations
seem to me to be so easy and so well adapted to what is wanted, that it
may very reasonably be believed that Copernicus himself, or some other
astronomer, has actually performed them.
SALV. It seems the other way around to me, for it is improbable that if
anyone had tried this he would not have mentioned the result, whichever
opinion it turned out to favor. But no one is
known to have availed himself of this method, for the above or for any
other purpose; and without a fine telescope it could not very well be
put into effect.
SAGR. What you say completely satisfies me. Now, since quite a while
remains until the night, if you want me to find any rest then, I hope it
will not be too much trouble for you to explain to us those problems
which a little while ago you asked us to put off until tomorrow. Please
give us back the reprieve which we extended to you, and abandoning all
other arguments explain to us how (assuming the motions which Copernicus
attributes to the earth, and keeping immovable the sun and the fixed
stars) such events may follow as pertain to the elevation and lowering
of the sun, the changing of the seasons, and the inequalities of nights
and days, in Just the way that is so easily understood to take place in
the Ptolemaic system.
SALV. I must not and cannot refuse anything which Sagredo pleads for.
The delay that I requested was only to give me time to rearrange in my
mind the premises which are useful for a clear and comprehensive
explanation of the manner in which these events take place in the
Copernican as well as in the Ptolemaic system. Indeed, more easily and
simply in the former than in the latter, so that it may be clearly seen
that the former hypothesis is as easy for nature to put into effect as
it is hard for the intellect to comprehend. Nevertheless I hope, by
utilizing explanations other than those resorted to by Copernicus, to
make even the learning of it very much less obscure. In order to do
this, I shall set forth some assumptions as known and self-evident, as
First. I assume that the earth is a spherical body which rotates about
its own axis and poles, and that every point on its surface traces out
the circumference of a circle, greater or lesser according as the
designated point is more or less distant from the poles. Of these
circles, that one is greatest which is traced out by a point equidistant
from the poles. All these circles are parallel to one another, and we
shall refer to them as parallels.
Second. The earth being spherical in shape and its material being
opaque, half its surface is continually lighted and the rest is dark.
The boundary which separates the lighted part from the dark being a
great circle, we shall call this the boundary circle of light.
Third. When the boundary circle of light passes through the earth's
poles It will cut all the parallels into equal sections, it being a
great circle; but, not passing through the poles, it will cut them all
into unequal parts except the central circle; this, being also a great
circle, will be cut into equal parts in any case.
Fourth. Since the earth turns about its own poles, the length of day and
night is determined by the arcs of the parallels cut by the boundary
circle of light. The arc which remains in the illuminated hemisphere
determines the length of the day, and the remainder that of the night.
These things being set forth, we may wish to draw a diagram for a
clearer understanding of what comes next. (Fig. 6)
First let us indicate
the circumference of a circle, to represent for us the orbit of the
earth, described in the plane of the ecliptic. This we may divide by two
diameters into four equal parts; Capricorn, Cancer, Libra, and Aries,
which shall here represent at the same time the four cardinal points;
that is, the two solstices and the two equinoxes. And in the center of
this circle, let us denote the sun, O, fixed and immovable.
Now with the four points Capricorn, Cancer, Libra, and Aries as centers,
we shall draw four equal circles which to us will represent the earth at
these four different seasons. The center of the earth travels in the
space of a year around the whole circumference Capricorn-Aries-Cancer
moving from west to east in the order of the signs of the zodiac. It is already
evident that when the earth is in Capricorn the sun Will appear in
Cancer, the earth moving along the arc from
Capricorn to Aries, the sun will appear to be moving along the arc from
Cancer to Libra. In a word, it will run through the signs of the zodiac
in their order during the space of a year. So with this first
assumption, the apparent annual motion of the sun around the ecliptic is
satisfied beyond any argument.
Coming now to the other movement-that is, the diurnal motion of the
earth about itself--its poles and axis must be established. These must be
understood to be not perpendicularly erect to the plane of the ecliptic;
that is, not parallel to the axis of the earth's orbit, but inclined
from right angles about twenty-three and one-half degrees, with the
North Pole toward the axis of the earth's orbit when the center of the
earth is at the solstitial point in Capricorn Assuming, then, that the
center of the terrestrial globe Is at that point, let us indicate the
poles and the axis AB, tilted twenty-three and one-half degrees from the
perpendicular on the Capricorn-Cancer diameter, so that the angle
A-Capricorn-Cancer amounts to the complement, or sixty-six and one-half
degrees, and this inclination must be assumed to be immutable. We shall
take the upper pole, A, to be the north, and the other, B, the south.
If the earth is assumed to revolve about its axis AB in twenty-four
hours, also from west to east, circles parallel to one another will be
described by all points noted on its surface. In this first position of
the earth, we shall designate the great circle CD and the two which are
twenty-three and one-half degrees from it--EF above, and GN below--and
these others at the two extremes, 1K and LM, at a similar distance from
the poles A and B; and we could have drawn countless other circles
parallel to these five, traced by innumerable points on the earth. Let
us now assume that the earth is transported by the annual motion of its
center to the other positions already marked, passing to them according
to the following laws: That its own axis AB not only does not change its
inclination to the plane of the ecliptic, but that it does not vary its
direction, either; remaining thus always parallel to itself, it points
continually toward the same parts of the universe, or let us say of the
firmament. This means that if we imagine the axis to be prolonged, it
would describe with its upper end a circle parallel and equal to the
earth' s orbit through Libra, Capricorn, Aries, and Cancer, as the upper
base of a cylinder described by itself in its annual motion upon the
base, Libra-Capricorn-Aries-Cancer. Hence, because of this unchanging
tilt, let us draw these other three figures around the centers of Aries,
Cancer, and Libra, exactly similar to the one drawn around the center of
Next let us consider the first diagram of the earth. Because of the axis
AB being inclined at twenty-three and one-half degrees toward the sun,
and since the arc Al is also twenty-three and one-half degrees, the
light of the sun illumines the hemisphere of the terrestrial globe
exposed to the sun (of which only half is seen here), divided from the
dark part by the boundary of light, IM The parallel CD, being a great
circle, will be divided into equal parts by this, but all others will be
cut into unequal parts because the boundary of light W does not pass
through the poles A and B. The parallel IK together with all others
described between it and the pole A, will be entirely within the
illuminated part, just as on the other hand the opposite ones toward the
pole B and contained within the parallel LM will remain in the dark.
Besides this, since the arc Al is equal to the arc FD, and the arc AF is
common to IKF and AFD, the latter two are equal, each being one
quadrant; and since the whole arc IFM is a semicircle, the arc MF will
also be a quadrant and equal to FKI. Hence the sun, 0, in this position
of the earth, will be vertical to anyone. at the point F. But through
the diurnal revolution around the fixed axis AB, all points on the
parallel EF pass through this same point F, and therefore on such a day
the sun at midday will be overhead to all inhabitants of the parallel
EF; and to them it will seem to describe by its motion that circle which
we call the tropic of Cancer.
But to the inhabitants of all parallels above the parallel EF toward the
North Pole, A, the sun is below their zenith toward the south. On the
other hand, to all inhabitants of the parallels below EF toward the
equator CID and the South Pole B, the midday sun is elevated above the
zenith toward the North Pole, A.
Next you may see how of all parallels, only the great circle CD is cut
into equal parts by the boundary of light IM, the others above and below
this all being cut into unequal parts. Of the upper ones, the
semidiurnal arcs (which are those in the part of the earth lighted by
the sun) are greater than the seminocturnal ones, which remain in the
dark. The contrary happens for the remainder which are beneath the great
circle CD toward the pole B; of these, the semidiurnal arcs are smaller
than the seminocturnal. Also you may see quite plainly that the
differences of these arcs go on increasing as the parallels become
closer to the poles, until the parallel IK stays entirely in the lighted
part, and its inhabitants have a twenty-four-hour day without night. In
contrast to this the parallel LM, remaining all in the dark, has a night
of twenty-four hours without day.
Next let us proceed to the third diagram of the earth, here placed with
its center at the Cancer point, from which the sun would appear to be at
the first point of Capricorn. It Is indeed easy to see that as the axis
AB has not changed its tilt, but has remained parallel to itself, the
appearance and situation of the earth are precisely the same as in the
first diagram, except that the hemisphere which in the first was lighted
by the sun remains in shadow here, and the one which was previously dark
now becomes illuminated. Hence what occurred in the first diagram is now
reversed with respect to the differences of days and nights and their
relative length or shortness.
The first thing noticed is that where in the first figure, the circle 1K
was entirely in the light it is now all in the dark; and LM, which
opposite, is now entirely in the light, where it was previously
completely in shadow. Of the parallels between the great circle CD and
the pole A, the semidiurnal arcs are now smaller than the seminocturnal,
which is the opposite of the first; and of the others toward the pole B,
the semidiurnal arcs are now longer than the seminocturnal, likewise the
opposite of What took
place in the other position of the earth. You may now see the sun made
vertical to the inhabitants of the tropic GN, and for those of the
parallel EF it is depressed southward through the entire arc ECG; that
is, forty-seven degrees. It has, in short, gone from one tropic to the
other, passing through the equator, being raised and then dropped along
the meridian through the said interval of forty-seven degrees. This
entire change has its origin not in any dropping or rising of the earth;
on the contrary, in its never dropping nor rising, but in generally
keeping itself always in the same location with respect to the universe
and merely going around the sun, which is situated at the center of this
same plane in which the earth moves around it in the annual motion.
Here a remarkable phenomenon must be noticed, which is that just as the
preservation of the axis of the earth in the same direction with respect
to the universe (or let us say toward the highest fixed stars) makes the
sun appear to us to rise and fall by as much as forty-seven degrees
without any rise or drop in the fixed stars at all, so if on the
contrary the earth's axis were continually kept at a given inclination
toward the sun (or we might say toward the axis of the zodiac), no
alteration of ascent or descent would appear to be made by the sun. Thus
the inhabitants of a given place would always have the same periods of
night and day, and the same kind or season; that is, some people would
always have Writer, some always summer, some spring, etc. But on the
other hand, the changes in the fixed stars with regard to rising and
falling would then appear enormous to us, amounting to this same
forty-seven degrees. For an understanding of this let us go back to a
consideration of the position of the earth in the first diagram, where
the axis AB is seen with its upper pole A tilted toward the sun. In the
third figure the same axis has kept the same direction toward the
highest sphere by remaining parallel to itself, so the upper pole A no
longer tilts toward the sun but tilts away from it, and lies
forty-seven degrees from its first position. Thus, in order to reproduce
the same inclination of the pole A toward the sun, it would be required
(by turning the globe along its circumference ACBD) to take it
forty-seven degrees toward E; and any Fixed star observed on the
meridian would be raised or lowered by that many degrees. Now let us
proceed with an explanation of the rest, and consider the earth placed
in the fourth diagram with its center at the first point of Libra, the
sun appearing in the beginning of Aries. Thus the earth's axis, which in
the first diagram was assumed to be inclined to the Capricorn-Cancer
diameter and hence to be in the same plane as that which cuts the
earth's orbit perpendicularly in the Capricorn-Cancer line, when
transferred to the fourth figure (being kept always parallel to itself,
as we have said), comes to be in a plane which is likewise vertical to
the plane of the earth's orbit, and parallel to the one which cuts the
latter at right angles along the Capricorn-Cancer diameter. Hence the
line from the center of the sun to the center of the earth (from 0 to
Libra) Will be perpendicular to the axis BA. But this same line from the
center of the sun to the center of the earth is always perpendicular
also to the boundary circle of light; therefore this same circle will
pass through the poles A and B in the fourth figure, and the axis AB
will lie in its plane. But the great circle, passing through the poles
of the parallels, will divide them all into equal parts, therefore the
arcs IK EF, CD, GN, and LM will all be semicircles, and the lighted
hemisphere will be this one which faces us and the sun, and the boundary
circle of light will be this very circumference ACBD. And when the earth
is at this place, the equinox will occur for all its inhabitants.
The same Will happen in the second diagram, where the earth having its
lighted hemisphere toward the sun shows to us its dark side with the
nocturnal arcs. These are also all semicircles, and consequently also
make an equinox. Finally, since the line produced from the center of the
to the center of the earth is perpendicular to the axis AB, to which
likewise the great circle CD among the parallels is perpendicular, the
same line O--Libra necessarily passes through the same plane as the
parallel CD, cutting its circumference in the center of the daytime arc
CD; therefore the sun will be vertical to anyone located in that cut.
But all inhabitants of that parallel pass by there, carried by the
earth's rotation, and have the midday sun directly overhead; therefore
the sun will appear to all inhabitants of the earth to be tracing out
the greatest parallel, called the equatorial circle.
Moreover, the earth being at either of the solstitial points, one of the
polar circles IK or LM is entirely in the light and the other in the
shadow; but when the earth is at the equinoctial points, half of each of
these polar circles is in the light and the balance in the dark. It
should not be hard to see how the earth in passing, for example, from
Cancer (where the parallel IK is entirely dark) to Leo, a part of the
parallel IK toward the point I will commence to enter the light, and the
boundary of light IM will begin to retreat toward the poles A and B,
cutting the circle ACBD no longer at I and M, but in two other points
failing between the endpoints I, A, M, and B, of the arcs IA and MB.
Thus the inhabitants of the circle IK begin to enjoy the light, and
those of the circle LM to experience the darkness.
See, then, how two simple noncontradictory motions assigned to the
earth, performed in periods well suited to their sizes, and also
conducted from west to east as in the case of all movable world bodies,
supply adequate causes for all the visible phenomena. These phenomena
can be reconciled with a fixed earth only by renouncing all the symmetry
that is seen among the speeds and sizes of moving bodies, and
attributing an inconceivable velocity to an enormous sphere beyond all
the others, while lesser spheres move very slowly. Besides, one must
make the motion of the former contrary to
that of the latter, and to increase the improbability, must have the
highest sphere transport all the lower ones opposite to their own
inclination. I leave it to your judgment which has the more likelihood
SAGR. For my part, so far as my senses are concerned, there is a great
difference between the simplicity and ease of effecting results by the
means given in this new arrangement and the multiplicity, confusion, and
difficulty found in the ancient and generally accepted one. For if the
universe were ordered according to such a multiplicity, one would have
to remove from philosophy many axioms commonly adopted by all
philosophers. Thus it is said that Nature does not multiply things
unnecessarily; that she makes use of the easiest and simplest means for
producing her effects; that she does nothing in vain, and the like.
I must confess that I have not heard anything more admirable than this,
nor can I believe that the human mind has ever penetrated into subtler
speculations. I do not know how it looks to Simplicio.
SIMP. If I must tell you frankly how it looks to me, these appear to me
to me some of those geometrical subtleties which Aristotle reprehended
in Plato when he accused him of departing from sound philosophy by too
much study of geometry. I have known some very great Peripatetic
philosophers, and heard them advise their pupils against the study of
mathematics as something which makes the intellect sophistical and inept
for true philosophizing; a doctrine diametrically opposed to that of
Plato, who would admit no one into philosophy who had not first mastered
SALV. I endorse the policy of these Peripatetics of yours in dissuading
their disciples from the study of geometry, since there is no art better
suited for the disclosure of their fallacies. You see how different they
are from the mathematical philosophers, who much prefer dealing with
those who are well informed about the general Peripatetic philosophy than with those who lack such information and because of that deficiency are unable to make comparisons between one
doctrine and the other.
But setting all this aside, please tell me what absurdities or excessive
subtleties make this Copernican arrangement the less plausible so far as
you are concerned.
SIMP. As a matter of fact, I did not completely understand it, perhaps
because I am not very well versed either in the way the same effects are
produced by Ptolemy--I mean these planetary stoppings, retrograde
movements, approaches and retreats, lengthenings and shortenings of the
day, alterations of the seasons, etc. But passing over the consequences
which stem from the basic assumptions, I feel no small difficulties to
exist in these assumptions themselves, and if the assumptions fall to
the ground then they bring the whole structure into ruin. Now since the
whole framework of Copernicus seems to me to be built upon a weak
foundation (being supported upon the mobility of the earth), then if
this were removed, there would be no room for further argument. And to
remove it, Aristotle's axiom that to a simple body only one simple
motion can be natural appears to be sufficient. Here three movements, if
not four, are assigned to the earth, a simple body; and all of them are
quite different from one another. For besides the straight motion toward
the center, which cannot be denied to it as a heavy body, there are
ascribed to it a circular motion in a great circle around the sun in one
year, and a whirling upon itself every twenty-four hours, and (what is
most extreme, and possibly for that reason you have remained silent
about this) another whirling about its own center, completed in a year,
and opposite to the previously mentioned twenty-four-hour motion. My
mind feels a great repugnance to this.
[pp. 462-481. The three characters again enter the realm of physics, from which
they proceed to a discussion of William Gilbert's De Magnete (1600), his
theories of magnetism and the possibility of the Earth being a
End of the Third Day
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