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The laws of nature are written by the hand of God in the language of mathematics.
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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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The surface of the Moon is not smooth, uniform, and precisely spherical as a great number of philosophers believe it to be, but is uneven, rough, and full of cavities and prominences, being not unlike the face of the Earth, relieved by chains of mountains and deep valleys.
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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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When the moon is ninety degrees away from the sun it sees but half the earth illuminated (the western half). For the other (the eastern half) is enveloped in night. Hence the moon itself is illuminated less brightly from the earth, and as a result its secondary light appears fainter to us.
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The book of nature is written in the language of mathematics.
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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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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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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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Knowing thyself, that is the greatest wisdom.
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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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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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Nothing can be taught to a man, only it's possibly to help him to discover it inside.
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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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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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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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Mathematics is the language with which God has written the universe.
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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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It is a beautiful and delightful sight to behold the body of the Moon.
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See now the power of truth.
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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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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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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.