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It is a right, yes a duty, to search in cautious manner for the numbers, sizes, and weights, the norms for everything [God] has created. For He himself has let man take part in the knowledge of these things ... For these secrets are not of the kind whose research should be forbidden; rather they are set before our eyes like a mirror so that by examining them we observe to some extent the goodness and wisdom of the Creator.
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We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.
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Astronomy would not provide me with bread if men did not entertain hopes of reading the future in the heavens.
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I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
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Thus God himself was too kind to remain idle and began to play the game of signatures signing his likeness unto the world: therefore I chance to think that all nature and the graceful sky are symbolized in the art of Geometria.
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Quantity is the fundamental feature of things, the 'primarium accidens substantiae,' ...prior to the other categories.
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I believe the geometric proportion served the creator as an idea when He introduced the continuous generation of similar objects from similar objects.
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After the birth of printing books became widespread. Hence everyone throughout Europe devoted himself to the study of literature... Every year, especially since 1563, the number of writings published in every field is greater than all those produced in the past thousand years. Through them there has today been created a new theology and a new jurisprudence; the Paracelsians have created medicine anew and the Copernicans have created astronomy anew. I really believe that at last the world is alive, indeed seething, and that the stimuli of these remarkable conjunctions did not act in vain.
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On how the motion of a planet defines its sphere: ... and thus it comes about gradually by the linking and accumulation of a great many revolutions that a kind of concave sphere is displayed, having the same center as the Sun, just as by a great many circles of silken thread, linked with each other and wound together, the dwelling of a silkworm is made.
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A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.
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The heavenly motions... are nothing but a continuous song for several voices, perceived not by the ear but by the intellect, a figured music which sets landmarks in the immeasurable flow of time.
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Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.
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Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.
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The roads by which men arrive at their insights into celestial matters seem to me almost as worthy of wonder as those matters in themselves.
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I used to measure the heavens, now I measure the shadows of Earth. Although my mind was heaven-bound, the shadow of my body lies here.
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Wherever there are qualities there are likewise quantities, but not always vice versa.
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Nature uses as little as possible of anything.
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Of a number of variant hypotheses about the same facts, that one is true which shows why facts, which in the other hypotheses remain unrelated, are as they are, i.e., which demonstrates their orderly and rational mathematical connexion.
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I believe only and alone in the service of Jesus Christ. In him is all refuge and solace.
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The soul of the newly born baby is marked for life by the pattern of the stars at the moment it comes into the world, unconsciously remembers it, and remains sensitive to the return of configurations of a similar kind.
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My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honour due to its maker) and that in it almost all the variety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight.
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Since we astronomers are priests of the highest God in regard to the book of nature, it befits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God.
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The heavenly bodies are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which... sets landmarks in the immeasurable flow of time. It is therefore, no longer surprising that man, in imitation of his creator, has at last discovered the art of figured song, which was unknown to the ancients. Man wanted to reproduce the continuity of cosmic time... to obtain a sample test of the delight of the Divine Creator in His works, and to partake of his joy by making music in the imitation of God.
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Where there is matter, there is geometry.