The Systeme of the World: in Four Dialogues

1632 book by Galileo Galilei

The Systeme of the World: in Four Dialogues is the original 1661 English translation, by Thomas Salusbury, of Galileo Galilei's DIALOGO sopra i due MASSI SISTEMI DEL MONDO (1632). Galileo's publication is more generally recognized under the title of Stilman Drake's English translation, Dialogue Concerning the Two Chief World Systems, published in 1953. A revised and annotated edition of the Salusbury translation was also introduced in 1953 by Giorgio de Santillana under the title Dialogue on the Great World Systems.

The Systeme of the World, in Four Dialogues, title page 1661

The complete title of the Salusbury translation is "THE SYSTEME OF THE WORLD: IN FOUR DIALOGUES. Wherein the Two GRAND SYSTEMES Of PTOLOMY and COPERNICUS are largely discoursed of: And the REASONS, both Phylosophical and Physical, as well on the one side as the other, impartially and indefinitely propounded: By GALILEUS GALILEUS LINCEUS, A Gentleman of FLORENCE: Extraordinary Professor of the Mathematicks in the UNIVERSITY of PISA; and Chief Mathematician to the GRAND DUKE of TUSCANY."

Some alternative translations may be found under Galileo Galilei; Dialogue Concerning the Two Chief World Systems.



The Author's Preface

  • Judicious Reader, There was published some years since in Rome a salutiferous edict which... imposed a seaonable silence upon the Pythagorean opinion of the mobility of the earth. ...that decree was not the production of sober scrutiny but of ill-informed passion... consultors altogether ignorant of astronomical observations ought not to clip the wings of speculative wits with rash prohibitions.
  • I thought fit... to appear openly upon the theatre of the World as a witness of the naked truth.
  • It is my resolution... to give foreign nations to see of this matter... And, collecting all the speculations of mine that concern the Copernican system, to let them know that... there proceed from this climate not only doctrines for the health of the soul but also ingenious discoveries for the delight of the mind.
  • I have personated the Copernican... proceeding upon the hypothesis purely mathematical; striving by every artifice to represent it superior not to that of the immobility of the Earth absolutely but as it is defended by some who, claiming to profess the Peripatetic doctrine, retain of it no more than the name, and are content, foregoing the old ways, to adore shadows, not philosophizing with their own intelligence but with the sole remembrance of a few principles badly understood.
  • I will endeavour to show that all experiments that can be made upon the Earth are insufficient means to conclude for its mobility but are indifferently applicable to the Earth, movable or immovable...
  • We will examine the celestial phenomena that make for the Copernican hypothesis, as if it were to prove absolutely victorious, adding by the way certain new observations which yet serve only for astronomical facility, not for natural necessity.
  • I will propose an ingenious fancy. ...the unknown problem of the tides might receive some light, admitting of the Earth's motion. ...I have thought good to lay down those probabilities that would render it credible, admitting that the Earth did move.
  • I hope that by these considerations the world will come to know that, if other nations have navigated more than we, we have not studied less than they; and that our returning to assert the Earth's stability and to take the contrary only for a mathematical fantasy, proceeds not from lack of acquaintance with others' ideas thereof but... from those reasons that piety, religion, the knowledge of the Divine Omnipotence, and a consciousness of the incapacity of man's understanding dictate to us.
  • I chanced, many years ago, as I lived in the stupendous city of Venice, to converse frequently with the Signor Giovan Francesco Sagredo, a man of noble extraction and most acute intellect. There came thither from Florence, at the same time, Signor Filippo Salviati, whose least glory was the eminence of his blood and magnificence of his estate, a sublime intellect that knew no more exquisite pleasure than elevated speculations. In the company of these two I often discoursed of these matters before a certain Peripatetic philosopher, who seemed to have no greater obstacle in understanding the truth than the fame he had acquired by Aristotelian interpretations. Now, seeing that inexorable fate has deprived Venice and Florence of those two great lights in the early summer of their years, I did resolve... to perpetuate their lives to their honor in these leaves... Nor shall the honest Peripatetic want his place, to whom, for his excessive affection towards the commentaries of Simplicius, I thought fit, without mentioning his own name, to leave that of the author he so much respected. Let these two great souls, ever venerable to my heart, please to accept this public monument of my never dying love; and let the remembrance of their eloquence assist me in delivering to posterity the considerations that I have promised.
  • There had casually taken place... several discourses at times between these gentlemen which had rather inflamed than satisfied in their minds the thirst they had for learning; whereupon they took the wise resolution to meet together for certain days in which, all other business set aside, they might betake themselves with more ordered speculation to contemplate the wonders of God in heaven and on earth.

The First Dialogue

  • We have in our age new accidents and observations, and such, that I question not in the least, but if Aristotle were now alive, they would make him change his opinion; which may be easily collected from the very manner of his discoursing: For when he writeth that he e­steemeth the Heavens inalterable, &c. because no new thing was seen to be begot therein, or any old to be dissolved, he seems im­plicitely to hint unto us, that when he should see any such accident, he would hold the contrary; and confront, as indeed it is meet, sensible experiments to natural reason: for had he not made any reckoning of the senses, he would not then from the not seeing of any sensible mutation, have argued immutability.
    • Salviati, p. 37.
  • I do believe for certain, that he [Aristotle] first procured by help of the senses, such experiments and obser­vations as he could, to assure him as much as it was possible, of the conclusion, and that he afterwards sought out the means how to demonstrate it: For this, the usual course in demonstrative Sciences, and the reason thereof is, because when the conclusion is true, by help of resolutive Method, one may hit upon some pro­position before demonstrated, or come to some principle known per se; but if the conclusion be false, a man may proceed in in­finitum, and never meet with any truth already known; but ve­ry oft he shall meet with some impossibility or manifest absurdi­ty.
    • Salviati, p. 37-38.
  • Nor need you question but that Pythagoras a long time be­fore he found the demonstration for which he offered the Hecatomb, had been certain, that the square of the side subtending the right angle in a rectangle triangle, was equal to the square of the other two sides: and the certainty of the conclusion condu­ced not a little to the investigating of the demonstration, un­derstanding me alwayes to mean in demonstrative Sciences.
    • Salviati, p. 38.
  • What ever was the method of Aristotle, and whether his arguing à priori preceded sense à posteriori, or the contrary; it sufficeth that the same Aristotle preferreth (as hath been oft said) sensible ex­periments before all discourses...
    • Salviati, p. 38.
  • If this of which we dispute, were some point of Law, or other part of the Studies called Humanity, wherein there is neither truth nor falshood, if we will give sufficient credit to the acutenesse of the wit, readinesse of answers, and the general practice of Writers, then he who most aboundeth in these, makes his reason more probable and plausible; but in Natural Sciences, the conclusions of which are true and necessary, and wherewith the judgment of men hath nothing to do, one is to be more cautious how he goeth about to maintain anything that is false; for a man but of an ordinary wit, if it be his good for­ tune to be of the right side, may lay a thousand Demosthenes and a thousand Aristotles at his feet. Therefore reject those hopes and conceits, wherewith you flatter yourself, that there can be any men so much more learned, read, and versed in Authors, than we, that in despite of nature, they should be able to make that become true, which is false.
    • Salviati, p. 40.
  • If I was demanded what my first apprehension, and pure natural reason dictated to me concerning the production of things like or unlike there above, I would alwayes reply, that they are most different, and to us altogether unimaginable, for so me thinks the riches of Nature, and the omnipotence of our Creator and Governour, do require.
    • Salviati, p. 84.
  • I ever accounted extraordinary madnesse that of those, who would make humane comprehension the measure of what na­ture hath a power or knowledge to effect; whereas on the con­trary there is not any the least effect in Nature, which can be fully understood by the most speculative wits in the world. This their so vain presumption of knowing all, can take beginning from no­thing, unlesse from their never having known anything; for if one hath but once onely experienced the perfect knowledg of one onely thing, and but truly tasted what it is to know, he shall perceive that of infinite other conclusions, he understands not so much as one.
    • Sagredo, p. 84.
  • The having a perfect knowledg of nothing, maketh some believe they understand all things.
    • Commentator, p. 85.
  • Your discourse is very concluding; in confirmation of which we have the example of those who understand, or have known some thing, which the more knowing they are, the more they know, and freely confesse that they know little; nay, the wisest man in all Greece, and for such pronounced by the Oracle, openly professed to know that he knew nothing.
    • Salviati, p. 85.
  • It must be granted therefore, either that Socrates or that the Oracle itself was a lyar, that declaring him to be most wise, and he confessing that he knew himself to be most ig­norant.
    • Simplicio, p. 85.
  • Neither one nor the other doth follow, for that both the assertions may be true. The Oracle adjudged Socrates the wi­sest of all men, whose knowledg is limited; Socrates acknowledgeth that he knew nothing in relation to absolute wisdome, which is infinite; and because of infinite, much is the same part as is little, and as is nothing (for to arrive... to the infinite number, it is all one to accumulate thousands, tens, or ciphers,) therefore Socrates well perceived his wisdom to be nothing, in comparison of the infinite knowledg which he wanted. But yet, because there is some knowledg found amongst men, and this not equally shared to all, Socrates might have a greater share thereof than others, and therefore verified the answer of the Oracle.
    • Salviati, p. 85.
  • I think I very well understand this particular amongst men, Simplicius, there is a power of operating, but not equally dispensed to all; and it is without question that the power of an Emperor is far greater than that of a private person; but, both this and that are nothing in comparison of the Divine Omnipotence. Amongst men, there are some that better understand Agriculture than many others; but the knowledg of planting a Vine in a trench, what hath it to do with the knowledg of ma­king it to sprout forth, to attract nourishment, to select this good part from that other, for to make thereof leaves, another to make sprouts, another to make grapes, another to make raisins, ano­ther to make the huskes of them, which are the works of most wise Nature? This is one only particular act of the innumerable, which Nature doth, and in it alone is discovered an infinite wisdom, so that Divine Wisdom may be concluded to be infinitely infinite.
    • Sagredo, p. 85.
  • Do we not say that the judicious discovering of a most lovely Statua in a piece of Marble, hath sublimated the wit of Buonarruotti far above the vulgar wits of other men? And yet this work is onely the imitation of a meer aptitude and disposition of exteriour and superficial mem­bers of an immoveable man; but what is it in comparison of a man made by nature, composed of as many exteriour and inte­riour members, of so many muscles, tendons, nerves, bones, which serve to so many and sundry motions? but what shall we say of the senses, and of the powers of the soul, and lastly, of the understanding? May we not say, and that with reason, that the structure of a Statue falls far short of the formation of a living man, yea more of a contemptible worm?
    • Salviati, p. 85-86.
  • I must have recourse to a Philosophical distinction, and say that the understanding is to be taken two ways, that is intensivè, or extensivè; and that extensive, that is, as to the multitude of intel­ligibles, which are infinite, the understanding of man is as nothing, though he should understand a thousand propositions; for that a thousand, in respect of infinity is but as a cypher: but taking the understanding intensive, (in as much as that term imports) intensively, that is, perfectly some propositions, I say, that humane wis­dom understandeth some propositions so perfectly, and is as abso­lutely certain thereof, as Nature herself; and such are the pure Mathematical sciences, to wit, Geometry and Arithmetick: in which Divine Wisdom knows infinite more propositions, because it knows them all; but I believe that the knowledge of those few compre­hended by humane understanding, equalleth the divine, as to the certainty objectivè, for that it arriveth to comprehend the neces­sity thereof, than which there can be no greater certainty.
    • Salviati, p. 86.
  • As to the truth, of which Mathematical demonstrations give us the knowledge, it is the same, which the divine wisdom knoweth; but this I must grant you, that the manner whereby God knoweth the infinite propo­sitions, of which we understand some few... his is done at one single thought or intuition; and whereas we... beginning from one of the most simple, and taking that for its definition, do proceed with argumentation to another...
    • Salviati, p. 86.
  • What other, is that proposition, that the square of the side subtending the right angle in any triangle, is equal to the squares of the other two, which include it, but onely the Paralellograms being upon common bases, and between parallels equal amongst themselves?
    • Salviati, p. 87.
  • These inferences, which our intellect apprehendeth with time and a gradual motion, the Divine Wisdom, like light, penetrateth in an instant, which is the same as to say, hath them alwayes pre­sent...
    • Salviati, p. 87.
  • Our understanding, both as to the manner and the multitude of the things comprehended by us, is infinitely surpast by the Divine Wisdom; but yet I do not so vilifie it, as to repute it absolutely nothing; yea rather, when I consider how many and how great misteries men have understood, discovered, and contrived, I very plainly know and understand the mind of man to be one of the works, yea one of the most ex­cellent works of God.
    • Salviati, p. 87.
  • If I behold a statue of some excellent master, I say with my self: "When wilt thou know how to chizzle away the refuse of a piece of Marble, and discover so lovely a figure as lyeth hid therein? When wilt thou mix and spread so many colors upon a Cloth, or Wall, and represent therewith all visible objects, like a Michael Angelo, a Raphaello, or a Tizvano? If I behold what invention men have had in comparting Musical intervals, in establishing Precepts and Rules for the management thereof with admirable delight to the ear, when shall I cease my astonishment? What shall I say of such and so various instruments of that Art? The reading of excellent Poets, with what admiration doth it swell anyone who attentively considereth the invention of concepts and their explanation? What shall we say of Architecture? What of Navigation? But, above all other stupendous inventions, what sublimity of mind was that in him, that imagined to himself to find out a way to communicate his most secret thoughts to any other person, though very far distant from him either in time or place, speaking with those that are in the Indies, speaking to those who are not yet born, nor shall be this thousand, or ten thousand years? And with how much facility? but by the various collection of twenty-four little letters upon a paper? Let this be the Seal of all the admirable inventions of man and the close of our Discourse for this day. For the warmer hours being past, I suppose that Salviatus hath a desire to go and take the cool air in his Gondelo...
    • Sagredus, p. 88.

The Second Dialogue

  • The sum of yesterdayes conferences were an examination of the Principles of Ptolomy and Copernicus, and which of their opinions is the more probable and rational; that, which affirmeth the sub­stance of the Cœlestial bodies to be ingenerable, incorruptible, un­alterable, impassible, and in a word, exempt from all kind of change, save that of local, and therefore to be a fifth essence, quite different from this of our Elementary bodies, which are generable, corrup­tible, alterable, &c. or else the other, which taking away such deformity from the parts of the World, holdeth the Earth to en­joy the same perfections as the other integral bodies of the universe; and esteemeth it a moveable and erratick Globe, no lesse than the Moon, Jupiter, Venus, or any other Planet.
    • Sagredo, p. 89-91.
  • Do you question whether Aristotle, had he but seen the novelties discovered in Hea­ven, would not have changed his opinion, amended his Books, and embraced the more sensible Doctrine; rejecting those silly Gulls, which too scrupulously, go about to defend what ever he hath said; not considering, that if Aristotle were such a one as they fancy him to themselves, he would be a man of an untracta­ble wit, an obstinate mind, a barbarous soul, a stubborn will, that accounting all men else but as silly sheep, would have his Oracles preferred before the Senses, Experience, and Nature herself?
    • Salviati, p. 93-94.
  • Because it is more easie for a man to sculk under anothers shield than to shew himself openly, they tremble, and are affraid to stir one step from him; and rather than they will admit some alterations in the Heaven of Aristotle, they will impertinently de­ny those they behold in the Heaven of Nature.
    • Salviati, p. 94.
  • We need a Guid in unknown and uncouth wayes, but in champion places, and open plains, the blind only stand in need of a Leader; and for such, it is better that they stay at home. But he that hath eyes in his head, and in his mind, him should a man choose for his Guid. Yet mistake me not, thinking that I speak this, for that I am against hearing of Aristotle; for on the contrary, I commend the reading, and diligently studying of him; and onely blame the servile giving ones self up a slave unto him, so, as blindly to subscribe to what ever he delivers, and without search of any farther reason thereof, to receive the same for an inviolable decree. Which is an abuse, that carrieth with it ano­ther great inconvenience, to wit, that others will no longer take pains to understand the validity of his Demonstrations. And what is more shameful, than in the middest of publique disputes, whilest one person is treating of demonstrable conclusions, to hear another interpose with a passage of Aristotle, and not sel­dome writ to quite another purpose, and with that to stop the mouth of his opponent? But if you will continue to study in this manner, I would have you lay aside the name of Philosophers; and call your selves either Historians or Doctors of Memory, for it is not sit, that those who never philosophate, should usurp the honourable title of Philosophers.
    • Salviati, p. 95-96.
  • Therefore Simplicius, come either with arguments and demonstrations of your own, or of Aristotle, and bring us no more Texts and na­ked authorities, for our disputes are about the Sensible World, and not one of Paper.
    • Salviati, p. 96.
  • Whatsoever motion may be ascribed to the Earth, it is necessary that it be to us, (as inhabitants upon it, and conse­quently partakers of the same) altogether imperceptible, and as if it were not at all, so long as we have regard onely to terrestrial things...
    • Salviati, p. 97.
  • If we consider onely the immense magnitude of the Starry Sphere, compared to the smalness of the Terrestrial Globe, contained therein so many mil­lions of times; and moreover weigh the velocity of the motion which must in a day and night make an entire revolution thereof, I cannot perswade my self, that there is any man who believes it more reasonable and credible, that the Cœlestial Sphere turneth round, and the Terrestrial Globe stands still.
    • Salviati, p. 98.
  • He which should hold it more ra­tional to make the whole Universe move, and thereby to salve the Earths mobility, is more unreasonable than he that being got to the top of your Turret, should desire, to the end onely that he might behold the City, and the Fields about it, that the whole Country might turn round, that so he might not be put to the trouble to stir his head.
    • Sagredo, p. 98.
  • Motion is so far Motion, and as Motion operateth, by how far it hath relation to things which want Motion: but in those things which all equally partake thereof it hath nothing to do, and is as if it never were. And thus the Merchandises with which a ship is laden, so far move, by how far leaving London, they pass by France, Spain, Italy, and sail to Aleppo, which London, France, Spain &c. stand still, not moving with the ship: but as to the Chests, Bales and other Parcels, wherewith the ship is stow'd and and laden, and in respect of the ship it self, the Motion from Lon­don to Syria is as much as nothing; and nothing altereth the re­lation which is between them: and this, because it is common to all, and is participated by all alike: and of the Cargo which is in the ship, if a Bale were romag'd from a Chest but one inch onely, this alone would be in that Cargo, a greater Motion in respect of the Chest, than the whole Voyage of above three thousand miles, made by them as they were stived together.
    • Salviati, p. 98.
  • I hold it [the concept or relative motion] to be much more antient: and suspect that Aristotle in receiving it from some good School, did not fully under­stand it, and that therefore, having delivered it with some altera­tion, it hath been an occasion of confusion amongst those, who would defend whatever he saith. And when he writ, that what­ soever moveth, doth move upon something immoveable, I suppose that he equivocated, and meant, that whatever moveth, moveth in respect to something immoveable; which proposition admitteth no doubt, and the other many.
    • Salviati, p. 99.
  • We having divided the Universe into two parts, one of which is necessarily moveable, and the other immoveable; for the obtaining of whatsoever may depend upon, or be required from such a motion, it may as well be done by making the Earth alone, as by making all the rest of the World to move: for that the operation of such a motion consists in nothing else, save in the relation or habitude which is between the Cœlestial Bodies, and the Earth, the which relation [with an exchange in the two terms] is all that is changed. Now if for the obtaining of the same effect ad unguem [to a nail's thickness], it be all one whe­ther the Earth alone moveth, the rest of the Universe standing still; or that, the Earth onely standing still, the whole Universe moveth with one and the same motion; who would believe, that Nature (which by common consent, doth not that by many things, which may be done by few) hath chosen to make an innumerable number of most vast bodies move, and that with an unconceivable velocity, to perform that, which might be done by the moderate motion of one alone about its own Centre? ...which self same effect falls out exactly in the same manner, if, without troubling so great a part of the Universe.
    • Salviati, p. 99-100.
  • Nature never doth that by many things, which may be done by a few.
    • Commentator, p. 100.
  • If you will ascribe this Great Motion to Heaven, you must of necessity make it contrary to the particular motion of all the Orbs of the Planets, each of which without controversie hath its peculiar motion from the West towards the East, and this but very easie and moderate: and then you make them to be hurried to the contrary part, i. e. from East to West, by this most furious diurnal motion: whereas, on the contrary, making the Earth to move in it self, the contrariety of motions is taken away, and the onely motion from West to East is accom­modated to all appearances, and exactly satisfieth every Phœno­menon.
    • Salviati, p. 100.
  • The Ptolomaique Hypothesis... most unreasonably confoundeth the order, which we assuredly see to be amongst those Cœlestial Bodies, the circumgyration of which is not questionable, but most certain. And that Order is, that according as an Orb is greater, it finisheth its revolution in a longer time, and the lesser, in shorter. ...but if you would have the Earth immoveable, it is necessary, that when you have past from the short period of the Moon, to the others successively bigger, until you come to that of Mars in two years, and from thence to that of the bigger Sphere of Jupiter in twelve years, and from this to the other yet bigger of Saturn, whose period is of thirty years, it is necessary, I say, that you passe to another Sphere incomparably greater still than that, and make this to ac­complish an entire revolution in twenty four hours. ...But the motion of the Earth being granted, the order of the pe­riods will be exactly observed, and from the very slow Sphere of Saturn, we come to the fixed Stars, which are wholly immovea­ble.
    • Salviati, p. 101-102.
  • If the Starry Sphere be supposed moveable [there is an] immense disparity between the motions of those stars themselves; of which some would come to move most swiftly in most vast cir­cles, others most slowly in circles very small, according as those or these should be found nearer, or more remote from the Poles. ... And not onely the magnitudes of the circles, and conse­quently the velocity of the motions of these Stars, shall be most different from the circles and motions of those others, but... the self-same Stars shall successively vary its circles and velocities: For that those, which two thousand years since were in the Equinoctial, and consequently did with their motion describe very vast cir­cles, being in our dayes many degrees distant from thence, must of necessity become more slow of motion, and be reduced to move in lesser circles, and it is not altogether impossible but that a time may come, in which some of them which in aforetime had continually moved, shall be reduced by uniting with the Pole, to a state of rest, and then after some time of cessation, shall return to their motion again.
    • Salviati, p. 102.
  • No thought can comprehend what ought to be the solidity of that immense Sphere, whose depth so stedfastly holdeth fast such a multitude of Stars... Or else, supposing the Heavens to be fluid, as we are with more reason to believe, so as that every Star wandereth to and fro in it, by wayes of its own, what rules shall regulate their motions, and to what pur­pose, so, as that being beheld from the Earth, they appear as if they were made by one onely Sphere? ...nor can I see how the Earth, a pendent body, and equilibrated upon its centre, exposed indif­ferently to either motion or rest, and environed with a liquid am­bient, should not yield also as the rest, and be carried about.
    • Salviati, p. 102-103.
  • It sufficeth not to know that it [the nature of a body falling downwards] is streight, but its requi­site to know whether it be uniform, or irregular; that is, whe­ther it maintain alwayes one and the same velocity, or else goeth retarding or accelerating. ...Neither doth this suffice, but its requisite to know ac­cording to what proportion such accelleration is made; a Pro­blem, that I believe was never hitherto understood by any Phi­losopher or Mathematician; although Philosophers, and particu­larly the Peripateticks, have writ great and entire Volumes, touching motion.
    • Salviati, p. 143-144.
  • We speak of the peice of Ordinance mounted per­pendicular to the Horizon, that is, of a shot towards our vertical point, and to conclude, of the return of the ball by the same line unto the same peice, though that in the long time which it is se­parated from the peice, the earth hath transported it many miles towards the East; now it seemeth, that the ball ought to fall a like distance from the peice towards the West; the which doth not happen: therefore the peice without having been moved did stay expecting the same. The answer is the same with that of the stone falling from the Tower; and all the fallacy, and equivocati­on consisteth in supposing still for true, that which is in question; for the Opponent hath it still fixed in his conceit that the ball departs from its rest, being discharged by the fire from the piece; and the departing from the state of rest, cannot be, unlesse the immobility of the Terrestrial Globe be presupposed, which is the conclusion of that was in dispute; Therefore, I reply, that those who make the Earth moveable, answer, that the piece, and the ball that is in it, partake of the same motion with the Earth; nay that they have this together with her from nature; and that therefore the ball departs in no other manner from its quiescence, but conjoyned with its motion about the cen­tre, the which by its projection upwards, is neither taken away, nor hindered; and in this manner following, the universal motion of the Earth towards the East, it alwayes keepeth perpendicular over the said piece, as well in its rise as in its return. And the same you see to ensue, in making the experiment in a ship with a bullet shot upwards perpendicularly with a Crosse-bow, which returneth to the same place whether the ship doth move, or stand still.
    • Salviati, p. 153-154.
  • I would not do so much wrong to Plato, but yet I may truly say with Aristotle, that he too much lost himself in, and too much doted upon that, his Geometry: for that in conclusion these Mathematical subtilties, Salviatus, are true in abstract, but applied to sensible and Physical matter, they hold not good. For the Mathematicians will very well demonstrate for example, that Sphæra tangit planum in puncto [the sphere touches the plane at the point]; a position like to that in dispute, but when one cometh to the matter, things succeed quite another way. And so I may say of these angles of contact, and these proportions; which all evaporate into Air, when they are applied to things material and sensible.
    • Simplicius, p. 181.
  • I would be loth to leave you in that other which you hold, namely, that a material Sphere doth not touch a plain in one sole point: and I could wish some few hours conversation with some persons conversant in Geometry, might make you a little more intelligent amongst those who know nothing thereof.
    • Salviati, p. 181-182.
  • The truth sometimes gaines strength by con­tradiction.
    • Commentator, p. 182.
  • Things are ex­actly the same in abstract as in con­crete.
    • Commentator, p. 185.
  • Contact in a sin­gle point is not pe­culiar to the per­fect Spheres onely, but belongeth to all curved figures.
    • Commentator, p. 186.
  • It is more diffi­cult to find Figures that touch with a part of their sur­face, than in one sole point.
    • Commentator, p. 186.
  • If any figure can be given to a Solid, the Spherical is the easi­est of all others, as it is likewise the most simple, and holdeth the same place amongst solid figures, as the Circle holdeth amongst the superficial. The description of which Circle, as being more ea­sie than all the rest, hath alone been judged by Mathematicians worthy to be put amongst the postulata belonging to the descri­ption of all other figures.
    • Salviati, p. 186.
  • The formation of the Sphere is so very easie, that if in a plain plate of hard metal you take an empty or hollow circle, within which any Solid goeth casually re­volving that was before but grosly rounded, it shall, without any other artifice be reduced to a Spherical figure, as perfect as is pos­sible for it to be; provided, that that same Solid be not lesse than the Sphere that would passe thorow that Circle. And that which is yet more worthy of our consideration is, that within the self-same incavity one may form Spheres of several magnitudes.
    • Salviati, p. 186-187.
  • The circular Fi­gure only is placed amongst the postu­lata of Mathema­ticians.
    • Commentator, p. 187.
  • The Sphericall Figure is easier to be made than any other. ...Sphericall Fi­gures of sundry magnitudes may be made with one onely instrument.
    • Commentator, p. 187.
  • Above all things it must be considered, that the motion of descending grave bodies is not uniform, but departing from rest they go continually accelerating.. But this general notion is of no avail, if it be not known according to what proportion this increase of velocity is made; a conclusion that hath been until our times unknown to all Philoso­phers; and was first found out & demonstrated by the Academick [Galileo], our common friend, who in some of his writings not yet publish­ed... he proveth, how that the acceleration of the right mo­tion of grave bodies, is made according to the numbers uneven beginning ab unitate [from unity], that is, any number of equal times being assigned, if in the first time the moveable departing from rest shall have passed such a certain space, as for example, an ell, in the se­cond time it shall have passed three ells, in the third five, in the fourth seven, and so progressively, according to the following odd numbers; which in short is the same, as if... the [sums of] spaces passed are to each other, as the squares of their times.
    • Salviati, p. 198.

The Third Dialogue

  • You, Simplicius, as I believe, have gone by boat many times to Padoua, and if you will confess the truth, you never felt in your self the participation of that motion, unless when the boat running a-ground, or encoun­tring some obstacle, did stop, and that you with the other Passen­gers being taken on a sudden, were with danger over-set. It would be necessary that the Terrestrial Globe should meet with some rub that might arrest it, for I assure you, that then you would discern the impulse residing in you, when it should toss you up towards the Stars.
    • Salviati, p. 229.
  • It may be collected how easily one may be deceived by the bare appearance, or, if you will, representation of the sense. And the accident is, the Moons seeming to follow those that walk the streets in the night, with a pace equal to theirs, whilst they see it go gli­ding along the Roofs of houses, upon which it sheweth just like a cat, that really running along the ridges of houses, leaveth them behind. An appearance that, did not reason interpose, would but too manifestly delude the sight.
    • Sagredo, p. 230.
  • I have twice or thrice observed in the discourses of this Authour, that to prove that a thing is so, or so, he still alledgeth, that in that manner it is conformable with our understanding; or that otherwise we should never be able to conceive of it; or that the Criterium of Philosophy would be overthrown. As if that na­ture had first made mens brains, and then disposed all things in conformity to the capacity of their intellects. But I incline rather to think that Nature first made the things themselves, as she best liked, and afterwards framed the reason of men capable of con­ceiving (though not without great pains) some part of her se­crets.
    • Sagredo, p. 238.
  • Nature first made things as she pleased, and after­wards capacitated mens understand­ings for conceiving of them.
    • Commentator, p. 238.
  • Although I might very rationally put it in dispute, whe­ther there be any such centre in nature, or no; being that neither you nor any one else hath ever proved, whether the World be fi­nite and figurate, or else infinite and interminate; yet nevertheless granting you, for the present, that it is finite, and of a terminate Spherical Figure, and that thereupon it hath its centre; it will be requisite to see how credible it is that the Earth, and not rather some other body, doth possesse the said centre.
    • Salviati, p. 293.
  • If I deny his [Aristotle's] assumption, to wit, that the Universe is moveable, all his demonstrations come to nothing, for he onely proveth the Universe to be finite and terminate, for [by assuming] that it is moveable.
    • Salviati, p. 294.
  • I do not ask the Peripateticks... they, as observant and humble vassals of Aristotle, would deny all the ex­periments and all the observations in the World, nay, would also refuse to see them, that they might not be forced to acknowledg them, and would say that the World stands as Aristotle writeth, and not as nature will have it, for depriving them of the shield of his Authority, with what do you think they would appear in the field?
    • Salviati, p. 294.
  • Now if it were true that the centre of the World is the same about which... the Planets, move, it is most certain that it is not the Earth, but the Sun rather that is fixed in the centre of the World. So that as to this first simple and general apprehension, the middle place belongeth to the Sun, and the Earth is as far remote from the centre, as it is from that same Sun.
    • Salviati, p. 295.
  • The seeing all the Planets one while neerer and ano­ther while farther off from the Earth with so great differences, that for example, Venus when it is at the farthest, is six times more remote from us, than when it is neerest, and Mars riseth almost eight times as high at one time as at another.
    • Salviati, p. 295.
  • It is argued in the three superiour planets Mars, Jupi­ter, and Saturn, in that we find them alwayes neerest to the Earth when they are in opposition to the Sun, and farthest off when they are towards the conjunction, and this approximatian and recession importeth thus much that Mars neer at hand, ap­peareth very neer 60 times greater than when it is remote. As to Venus in the next place, and to Mercury, we are certain that they revolve about the Sun, in that they never move far from him, and in that we see them one while above and another while below it, as the mutations of figure in Venus necessarily argueth.
    • Salviati, p. 295.
  • The annual mo­tion of the Earth mixing with the motions of the o­ther Planets pro­duce extravagant appearances.
    • Commentator, p. 296.
  • As to the operation of the diurnal motion upon the Celestial bodies, it neither was, nor can be other, than to make the Universe seem to run precipitately the contrary way; but this annual motion intermixing with the particular motions of all the planets, produceth very many ex­travagancies, which have disarmed and non-plust all the greatest Scholars in the World.
    • Salviati, p. 296.
  • The centre of the Celestial conversions of the five planets Saturn, Jupiter, Mars, Venus and Mercury, is the Sun; and shall be likewise the centre of the motion of the Earth, if we do but succeed in our attempt of placing it in Hea­ven.
    • Salviati, p. 296.
  • My admiration, Sagredus, is very different from yours, you wonder that so few are followers of the Pythagorean Opinion; and I am amazed how there could be any yet left till now that do em­brace and follow it: Nor can I sufficiently admire the eminencie of those mens wits that have received and held it to be true, and with the sprightlinesse of their judgements offered such violence to their own sences, as that they have been able to prefer that which their reason dictated to them, to that which sensible experiments re­presented most manifestly on the contrary. That the reasons against the Diurnal virtiginous revolution of the Earth by you already ex­amined, do carry great probability with them, we have already seen; as also that the Ptolomaicks, and Aristotelicks, with all their Sectators did receive them for true, is indeed a very great argument of their efficacie; but those experiments which apertly contradict the annual motion, are of yet so much more manifestly repugnant, that (I say it again) I cannot find any bounds for my admiration, how that reason was able in Aristarchus and Copernicus, to com­mìt such a rape upon their Sences, as in despight thereof, to make her self mistress of their credulity.
    • Salviati, p. 301.
  • Although Astronomy in the courses of many ages hath made a great progress in discovering the constitution and motions of the Celestial bodies, yet is it not hitherto arrived at that height, but that very many things remain undecided, and haply many others also undiscovered.
    • Salviati, p. 415.
  • To say... that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing [of the seas], is an absolute vanity, not onely be­cause it is not exprest, nor seen how it should so happen, but the falsity is obvious, for that the Revolution of the Earth is not con­trary to the motion of the Moon, but is towards the same way. So that all that hath been hitherto said, and imagined by others, is, in my judgment, altogether invalid. But amongst all the famous men that have philosophated upon this admirable effect of Nature, I more wonder at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascri­bed to the Earth, before him, hath for all that given his ear and assent to the Moons predominancy over the Water, and to oc­cult properties, and such like trifles.
    • Salviati, p. 421-422.
  • We have now, from these four dayes Dis­course, great attestations, in favour of the Copernican Systeme, amongst which these three taken: the first, from the Stations and Retrogradations of the Planets, and from their approaches and recessions from the Earth; the second, from the Suns revolving in it self, and from what is observed in its spots; the third, from the Ebbing and Flowing of the Sea do shew very rational and concluding.
    • Sagredo, p. 422.
  • If, at more leasure go­ing over the things again that have been alledged you meet with any doubts, or scruples not well resolved, you will excuse my oversight, as well for the novelty of the Notion, as for the weaknesse of my wit, as also for the grandure of the Subject, as also finally, because I do not, nor have pretended to that as­sent from others, which I my self do not give to this conceit, which I could very easily grant to be a Chymæra, and a meer paradox...
    • Salviati, p. 423.
  • And you Sagredus, although in the Discourses past you have many times, with great applause, declared, that you were pleased with some of my conjectures, yet do I believe, that that was in part more occasioned by the novelty than by the cer­tainty of them, but much more by your courtesie, which did think and desire, by its assent, to procure me that content which we naturally use to take in the approbation and applause of our own matters... your civility hath obliged me to you...
    • Salviati, p. 423.
  • So am I also pleased with the ingenuity of Simplicius. Nay, his constancy in maintaining the Doctrine of his Master, with so much strength & undauntedness, hath made me much to love him. ...I ask pardon, if I have sometimes moved him with my too bold and resolute speaking: and let him be assured that I have not done the same out of any inducement of sinister affection, but onely to give him occasion to set before us more lofty fancies that might make me the more knowing.
    • Salviati, p. 423.
  • As for the past Discourses, and particulatly in this last, of the reason of the Ebbing and Flowing of the Sea, I do not, to speak the truth, very well apprehend the same, but by that slight Idea, what e­ver it be, that I have formed thereof to my self, I confesse that your conceit seemeth to me far more ingenuous than any of all those that I ever heard besides, but yet neverthelesse I esteem it not true and concluding: but keeping alwayes before the eyes of my mind a solid Doctrine... I know that both you being asked, Whether God, by his infinite Power and Wisdome might confer upon the Element of Water the reciprocal motion which we observe in the same in any other way, than by making the containing Vessel to move; I know, I say, that you will answer, that he might, and knew how to have done the same many wayes, and those unimaginable to our shallow understanding: upon which I forthwith conclude, that this being granted, it would be an extravagant boldnesse for any one to goe about to limit and confine the Divine Power and Wisdome to some one particular conjecture of his own.
    • Simplicius, p. 423-424.
  • This of yours is admirable, and truly Angelical Do­ctrine, to which very exactly that other accords, in like manner divine, which whilst it giveth us leave to dispute, touching the constitution of the World, addeth withall (perhaps to the end, that the exercise of the minds of men might neither be discou­raged, nor made bold) that we cannot find out the works made by his hands. Let therefore the Disquisition permitted and or­dain'd us by God, assist us in the knowing, and so much more admiring his greatnesse, by how much lesse we finde our selves too dull to penetrate the profound Abysses of his infinite Wis­dome.
    • Salviati, p. 424.
  • Above all, I shall very impatiently wait to hear the Elements of the new Science of our Academick about the natural and violent local Motions. And in the mean time, we may, according to our custome, spend an hour in taking the Air in the Gondola that waiteth for us. FINIS.
    • Sagredo, p. 424.