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two articles of the order, to wit, the order "not to teach," and "in any manner," you argued that we ought to believe that, in the lapse of fourteen or sixteen years, they had escaped your memory, and that this was also the reason why you were so silent as to the order, when you sought permission to publish your book, and that this is said by you not to excuse your error, but that it may be attributed to vainglorious ambition, rather than to malice. But this very certificate, produced on your behalf, has greatly aggravated your offense, since it is therein declared that the said opinion is contrary to the Holy Scripture; and yet you have dared to treat of it, to defend it, and to argue that it is probable; nor is there any extenuation in the licence artfully and cunningly extorted by you, since you did not intimate the command imposed upon you.

But whereas it appeared to us that you had not disclosed the whole truth in regard to your intentions, We thought it necessary to proceed to the rigorous examination of you, in which (without any prejudice to what you had confessed, and which is above detailed against you, with regard to your said intention) you answered like a good Catholic. Therefore, having seen and maturely considered the merits of your cause, with your said confessions and excuses, and everything else which ought to be seen and considered, We have come to the underwritten final sentence against you.

Invoking, therefore, the Most Holy name of Our Lord Jesus Christ, and of His Most Glorious Virgin Mother Mary, by this our final sentence, which, sitting in council and judgment for the tribunal of the Reverend Masters of Sacred Theology, and Doctors of Both Laws, Our Assessors, We put forth in this writing touching the matters and controversies before us, between the Magnificent Charles Sincerus, Doctor of Both Laws, Fiscal Proctor of this Holy Office, of the one part, and you, Galileo Galilei, an examined and confessed criminal from this present writing as above, of the other part. We pronounce, judge and declare, that you, the said Galileo, by reason of these things which have been detailed in the course of this writing, and which, as above, you have confessed, have rendered yourself vehemently suspected by this Holy Office of heresy; that is to say, that you believe and hold the false doctrine, and contrary to the Holy and Divine Scriptures, namely, that the sun is the centre of the world, and that it does not move from the east to west, that the earth does move and is not the centre of the world; also that an opinion can be held

and supported as probable after it has been declared and finally decreed contrary to the Holy Scripture, and consequently that you have incurred all the censures and penalties enjoined and promulgated in the sacred canons, and other general and particular constitutions, against delinquents of this description. From which it is Our pleasure that you be absolved, provided that, first, with a sincere heart and unfeigned faith, in Our presence, you abjure, curse, and detest the said errors and heresies and every other error and heresy contrary to the Catholic and Apostolic Church of Rome, in the form now shown to you.

But, that your grievous and pernicious error and transgression may not go altogether unpunished, and that you may be made more cautious in the future, and may be a warning to others to abstain from delinquencies of this sort, We decree that the book of the Dialogues of Galileo Galilei be prohibited by a public edict.

We condemn you to the formal prison of this Holy Office for a period determinable at Our pleasure; and by way of salutary penance, We order you, during the next three years, to recite once a week the seven Penitential Psalms.

Reserving to ourselves the power of moderating, commuting, or taking off the whole or part of the said punishment or penance.

And so We say, pronounce, and by Our sentence declare, decree, and reserve, in this and every other better form and manner, which lawfully we may and can use.

So we, the undersigned Cardinals, pronounce.

FELICE, Cardinal di Ascoli,
GUIDO, Cardinal Bentivoglio,
DESIDERIO, Cardinal di Cremona,
ANTONIO, Cardinal S. Onofrio,

BERLINGERO, Cardinal Gessi,

FABRICIO, Cardinal Verospi,
MARTINO, Cardinal Ginetti.

II. HIS RECANTATION

I Galileo Galilei, son of the late Vincenzo Galilei of Florence, aged seventy years, being brought personally to judgment, and kneeling before you, Most Eminent and Most Reverend Lords Cardinals, General Inquisitors of the Universal Christian Republic against heret

ical depravity, having before my eyes the Holy Gospels, which I touch with my own hands, swear, that I have always believed, and now believe, and with the help of God will in future believe, every article which the Holy Catholic and Apostolic Church of Rome holds, teaches and preaches. But because I had been enjoined by this Holy Office altogether to abandon the false opinion which maintains that the sun is the centre and immovable, and forbidden to hold, defend, or teach the said false doctrine in any manner, and after it had been signified to me that the said doctrine is repugnant with the Holy Scripture, I have written and printed a book, in which I treat of the same doctrine now condemned, and adduce reasons with great force in support of the same, without giving any solution, and therefore, have been judged grievously suspected of heresy; that is to say, that I have held and believed that the sun is the centre of the world and immovable, and that the earth is not the centre and movable.

Wishing, therefore, to remove from the mind of Your Eminences, and of every Catholic Christian, this vehement suspicion rightfully entertained towards me, with a sincere heart and unfeigned faith, I abjure, curse and detest the said errors and heresies, and generally every other error and sect contrary to the said Holy Church; and I swear that I will nevermore in future say or assert anything verbally, or in writing, which may give rise to a similar suspicion of me; but if I shall know any heretic, or anyone suspected of heresy, that I will denounce him to this Holy Office, or to the Inquisitor and Ordinary of the place in which I may be.

I swear, moreover, and promise, that I will fulfill, and observe fully, all the penances which have been or shall be laid to me by this Holy Office. But if it shall happen that I violate any of my said promises, oaths and protestations (which God avert!), I subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons, and other general and particular constitutions, against delinquents of this description. So may God help me, and His Holy Gospels, which I touch with my own hands.

I, the above-named Galileo Galilei, have abjured, sworn, promised and bound myself, as above, and in witness thereof with my own hand have subscribed this present writing of my abjuration, which I have

recited word for word. At Rome in the Convent of Minerva, 22nd June, 1633.

I, Galileo Galilei, have abjured as above with my own hand.

From ROUTLEDGE. History of Science. See also K. VON GEBLER. Galileo Galilei and the Roman Curia. London, 1879.

F. PREFACE TO THE

PHILOSOPHIE NATURALIS PRINCIPIA MATHEMATICA (1686)

BY ISAAC NEWTON

Since the ancients (as we are told by Pappus) made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavored to subject the phenomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy. The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art but in the artificers. He that works with less ac

curacy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, fetched from without, it is able to produce so many things. Therefore geometry is founded in mechanical practice and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts are

chiefly conversant in the moving of bodies, it comes to pass that geometry is commonly referred to their magnitudes, and mechanics to their motion. In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motion, accurately proposed and demonstrated. This part of mechanics was cultivated by the ancients in the five powers which relate to manual arts, who considered gravity (it not being a manual power) no otherwise than as it moved weights by those powers. Our design, not respecting arts, but philosophy, and our subject, not manual, but natural, powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the system of the World; for by the propositions mathematically demonstrated in the first book, we there derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.

In the publication of this work, the most acute and universally learned Mr. Edmund Halley not only assisted me with his pains in correcting the press and taking care of the schemes, but it was to his solicitations that its becoming public is owing; for when he had obtained of me my demonstrations of the figures of the celestial orbits, he continually pressed me to communicate the same to the Royal

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