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The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
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I therefore concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury about the Sun; which at length was established as clear as daylight by numerous other observations.
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I would beg the wise and learned fathers [of the church] to consider with all diligence the difference which exists between matters of mere opinion and matters of demonstration.
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I have been judged vehemently suspect of heresy, that is, of having held and believed that the sun in the centre of the universe and immoveable, and that the earth is not at the center of same, and that it does move. Wishing however, to remove from the minds of your Eminences and all faithful Christians this vehement suspicion reasonably conceived against me, I abjure with a sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error, heresy, and sect contrary to the Holy Catholic Church. (Quoted in Shea and Artigas 194)
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Nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages...
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Wine is sunlight, held together by water.
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To excite in us tastes, odors, and sounds I believe that nothing is required in external bodies except shapes, numbers, and slow or rapid movements. ... if ears, tongues, and noses were removed, shapes and numbers and motions would remain, but not odors or tastes or sounds.
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Nothing can be taught to a man, only it's possibly to help him to discover it inside.
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The number of people that can reason well is much smaller than those that can reason badly. If reasoning were like hauling rocks, then several reasoners might be better than one. But reasoning isn't like hauling rocks, it's like, it's like racing, where a single, galloping Barbary steed easily outruns a hundred wagon-pulling horses.
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Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written.
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In regard to the philosophers, if they be true philosophers, i.e., lovers of truth, they should not be irritated that the earth moves. Rather, if they realize that they have held a false belief, they should thank those have shown them the truth; and if their opinion stands firm that the earth doesn't move, they will have reason to boast than be angered.
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They seemed to forget that the increase of known truths stimulates the investigation, establishment and growth of the arts; not their dimination or destruction.
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In my studies of astronomy and philosophy I hold this opinion about the universe, that the Sun remains fixed in the centre of the circle of heavenly bodies, without changing its place; and the Earth, turning upon itself, moves round the Sun.
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It is a beautiful and delightful sight to behold the body of the Moon.
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The book of nature is written in the language of mathematics.
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Knowing thyself, that is the greatest wisdom.
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Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position-eventually, I say, at such a time as it might be physically or logically proved that the earth moves and the sun stands still.
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See now the power of truth.
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E pur si muove. "Albeit It does move". (That's what Galileo purportedly muttered after torturers forced him to recant his theory that the earth orbits the sun.)
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Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
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I do not know what to say in a case so surprising, so unlooked for and so novel.
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One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.
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Mathematics is the language with which God has written the universe.