"I have always read that the world, both land and water, was spherical, as the authority and researches of Ptolemy and all the others who have written on this subject demonstrate and prove, as do the eclipses of the moon and other experiments that are made from east to west, and the elevation of the North Star from north to south." (Christopher Columbus, [Letter to the Sovereigns on the Third Voyage], 1498)
"Yet the widespread planetary theories, advanced by Ptolemy and most other astronomers, although consistent with the numerical data, seemed likewise to present no small difficulty. For these theories were not adequate unless they also conceived certain equalizing circles, which made the planet appear to move at all times with uniform velocity neither on its deferent sphere nor about its own epicycle's center." (Nicolaus Copernicus, "De revolutionibus orbium coelestium" ["On the Revolutions of the Heavenly Spheres"], 1543)
"If Nicolaus Copernicus, the distinguished and incomparable master, in this work had not been deprived of exquisite and faultless instruments, he would have left us this science far more well-established. For he, if anybody, was outstanding and had the most perfect understanding of the geometrical and arithmetical requisites for building up this discipline. Nor was he in any respect inferior to Ptolemy; on the contrary, he surpassed him greatly in certain fields, particularly as far as the device of fi t ness and compendious harmony in hypotheses is concerned. And his apparently absurd opinion that the Earth revolves does not obstruct this estimate, because a circular motion designed to go on uniformly about another point than the very center of the circle, as actually found in the Ptolemaic hypotheses of all the planets except that of the Sun, offends against the very basic principles of our discipline in a far more absurd and intolerable way than does the attributing to the Earth one motion or another which, being a natural motion, turns out to be imperceptible. There does not at all arise from this assumption so many unsuitable consequences as most people think." (Tycho Brahe, [letter to Christopher Rothman] 1587)
"In astronomy the scenery is continually shifting, and the modes of language vary in proportion as this inexhaustible science makes progress in improvement, and supplies us with new theories. Ptolemy spake the language ot the people: to Copernicus we are indebted for the language of astronomy; which Tycho Brahe in some measure confounded: Kepler and Newton rectified his faults, and gave to astronomical language a superior degree of elegance and perfection. The discoveries of the present and future times will introduce in this respect farther changes. All these different modes of language will, nevertheless, continue to be always intelligible; and may always be preserved in a certain degree, and within certain limitations." (Johann H Lambert, "The System of the World", 1800)
"If the Greeks had not cultivated Conic Sections, Kepler could not have superseded Ptolemy; if the Greeks had cultivated Dynamics, Kepler might have anticipated Newton." (William Whewell, "History of the Inductive Sciences, from the Earliest to the Present Time", 1857)
"Newton's theory [of gravitation] is the circle of generalization which includes all the others [as Kepler's laws, Ptolemy's theory, etc.]; - the highest point of the inductive ascent; - the catastrophe of the philosophic drama to which Plato had prologized; - the point to which men's minds had been journeying for two thousand years." (William Whewell, "History of the Inductive Sciences, from the Earliest to the Present Time", 1857)
"All the men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned in what had been before them. There is not one exception. I do not say that every man has made direct acquaintance with the whole of his mental ancestry [...] But [...]it is remarkable how many of the greatest names in all departments of knowledge have been real antiquaries in their several subjects. [...] I may cite among those [...] in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, Newton, Locke." (Augustus De Morgan, "A Budget of Paradoxes", 1872)
"Euclid, Archimedes, and Apollonius brought geometry to as high a state of perfection as it perhaps could be brought without first introducing some more general and more powerful method than the old method of exhaustion. A briefer symbolism, a Cartesian geometry, an infinitesimal calculus, were needed. The Greek mind was not adapted to the invention of general methods. Instead of a climb to still loftier heights we observe, therefore, on the part of later Greek geometers, a descent during which they paused here and there to look around for details which had been passed by in the hasty ascent." (Florian Cajori, "A History of Mathematics", 1893)
"Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates." (David E Smith, "History of Mathematics", 1923)
"Ptolemy [...] against the champions of this or that cosmology of the heavens [...] had dared to claim that it is legitimate to interpret the facts of astronomy by the simplest geometrical scheme which will 'save the phenomena', no matter whose metaphysics might be upset. His conception of the physical structure of the earth, however, prevented him from carrying through in earnest this principle of relativity, as his objections to the hypothesis that the earth moves amply show." (Edwin A Burtt, "The Metaphysical Foundations of Modern Physical Science", 1925)
"Great scientific minds, from Claudius Ptolemy of the second century to Isaac Newton of the seventeenth, invested their formidable intellects in attempts to deduce the nature of the universe from the statements and philosophies contained in religious writings. [...] Had any of these efforts worked, science and religion today might be one and the same. But they are not." (Neil deGrasse Tyson, "The Sky Is Not the Limit: Adventures of an Urban Astrophysicist", 2000)
"It is difficult to falsify the hypothesis of dark matter, because, as with Ptolemy's epicycles, true believers can always add additional arbitrary features and free parameters to overcome any conceivable difficulties that occur with the dark matter models." (John Moffat, "Reinventing Gravity", 2008)
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