History of science

"Five geometers—Clairaut, Euler, D'Alembert, Lagrange and Laplace—shared among them the world of which Newton had revealed the existence. They explored it in all directions, penetrated into regions believed inaccessible, pointed out countless phenomena in those regions which observation had not yet detected, and finally—and herein lies the imperishable glory—they brought within the domain of a single principle, a unique law, all that is most subtle and mysterious in the motions of the celestial bodies. Geometry also had the boldness to dispose of the future; when the centuries unroll themselves they will scrupulously ratify the decisions of science."

"Studies serve for delight, for ornament, and for ability. Their chief use for delight, is in privateness and retiring; for ornament, is in discourse; and for ability, is in the judgment and disposition of business. For expert men can execute, and perhaps judge of particulars, one by one; but the general counsels, and the plots and marshalling of affairs, come best from those that are learned. To spend too much time in studies, is sloth; to use them too much for ornament, is affectation; to make judgment wholly by their rules, is the humour of a scholar scholastic]. They perfect nature, and are perfected by experience. For natural abilities are like natural plants, that need proyning by study; and studies themselves do give forth directions too much at large, except they be bounded in by experience. Crafty men contemn studies; simple men admire them; and wise men use them. For they teach not their own use; but that is a wisdom without [outside of] them, and above them, won by observation. Read not to contradict and confute, nor to believe and take for granted, nor to find talk and discourse, but to weigh and consider. Some books are to be tasted, others to be swallowed, and some few to be chewed digested. That is, some books are to be read only parts; others to be read, but not curiously; and some few to be read wholly, and with diligence and attention. Some books also may be read by deputy, and extracts made of them by others; but that would be only in less important arguments, and the meaner sort of books: else distilled books are, like common distilled waters, flashy things. Reading maketh a full man; conference a ready man; and writing an exact man. And, therefore, if a man write little, he had need have a great memory; if he confer little, he had need have a present wit; and if he read little, he had need have much cunning, to seem to know that he doth not."

"The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws."

"Let such a history be once provided and well set forth, and let there be added to it such auxiliary and light-giving experiments... and the investigation of nature and of all sciences will be the work of a few years. ...In this way, and in this way only, can the foundations of a true and active philosophy be established; and then will men wake as from deep sleep."

"This history I call Primary History, or the Mother History."

"Atomism began life as a philosophical idea that would fail virtually every contemporary test of what should be regarded as 'scientific'; yet, eventually, it became the cornerstone of physical science."

"Scanning the past millennia of human achievement reveals just how much has been achieved during the last three hundred years since Newton set in motion the effective mathematization of Nature. We found that the world is curiously adapted to a simple mathematical description. It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within and enigma."

"Maxwell in particular noted that the phenomena of electromagnetism did not fit into the scheme of Newtonian mechanics. Whereas it had been thought that only the distance between two objects determined the force one exerted on the other, electric charges in motion, such as are met with in electric currents, were found to produce effects not encountered when charges are at rest. Celestial bodies will only attract each other; electric charges at rest will either attract or repel... they will exert forces only in the direction of the connecting straight line. Oersted discovered that an electric current (...charges in motion) will exert a force on a magnetic needle at right angles to the connecting straight line. Previous observations in astronomy had tended to show that the force between two bodies depended only on their instantaneous configuration, but Hertz showed by experiment that electromagnetic disturbances propagate as waves, at a finite rate of speed. Hence the force experienced by one body can be understood and explained only in terms of the history of the other."

"Maxwell succeeded in casting all known electromagnetic effects into a mathematical form that has endured to this day... known as Maxwell's field equations. Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space ('). Faraday and Maxwell regarded the effect on an electrically charged body as giving rise to stresses in its immediate surroundings. These in turn produce stresses in ever widening circles, gradually diminishing... These stresses... thought of as capable of existence in otherwise empty space, are called fields... intermediaries between material particles and which assume the burden of Newton's action at a distance."

"The old contrast, often amounting to hostility, between scientific and humane subjects needs to be broken down and replaced by a scientific humanism. At the same time, the teaching of science proper requires to be humanized. The dry and factual presentation requires to be transformed... by emphasizing the living and dramatic character of scientific advance... Here the teaching of the history of science, not isolated as at present, but in close relation to general history teaching, would serve to correct the existing atmosphere of scientific dogmatism. It would show at the same time how secure are the conquests of science in the control they give over natural processes and how insecure and provisional, however necessary, are the rational interpretations, the theories and hypotheses put forward at each stage. Past history by itself is not enough, the latest developments of science should not be excluded because they have not yet passed the test of time. It is absolutely necessary to emphasize the fact that science not only has changed but is continually changing, that it is an activity and not merely a body of facts. Throughout, the social implications of science, the powers that it puts into men’s hands, the uses... should be brought out and made real by a reference to immediate experience of ordinary life. ...[I]t should be possible to introduce the teaching of practical scientific methods by making students find out for themselves new relationships in things that already concern them and not in artificially simplified and unnecessarily abstract experiment."

"In every age there is a turning point, a new way of seeing and asserting the coherence of the world. It is frozen in the statues of Easter Island that put a stop to time—and in the medieval clocks of Europe that once also seemed to say the last word about the heavens for ever. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or of man. But in retrospect, what commands our attention as much are the continuities—the thoughts that run or recur from one civilization to another."

"If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston.""

"An invention acts rather like a trigger, because, once it's there, it changes the way things are, and that change stimulates the production of another invention, which in turn, causes change, and so on. Why those inventions happened, between 6,000 years ago and now, where they happened and when they happened, is a fascinating blend of accident, genius, craftsmanship, geography, religion, war, money, ambition... Above all, at some point, everybody is involved in the business of change, not just the so-called "great men." Given what they knew at the time, and a moderate amount of what's up here [pointing to head], I hope to show you that you or I could have done just what they did, or come close to it, because at no time did an invention come out of thin air into somebody's head, [snaps fingers] like that. You just had to put a number of bits and pieces, that were already there, together in the right way."

"How curious, after all, is the way in which we moderns think about our world! And it is all so novel, too. The cosmology underlying our mental processes is but three centuries old—a mere infant in the history of thought—and yet we cling to it with the same embarrassed zeal with which a young father fondles his new-born baby."

"Considering the part played by the sciences in the story of our Western civilization, it is hardly possible to doubt the importance which the history of science will sooner or later acquire both in its own right and as the bridge which has been so long needed in between the Arts and the Sciences."

"In spite of all the allegations of self-love, the facts at first associated with the name of a particular man end by being anonymous, lost forever in the ocean of Universal Science. Thus the monograph imbued with individual human quality becomes incorporated, stripped of sentamentalisms, in the abstract doctrine of the general treatise. To the hot sun of actuality will succeed—if they do succeed—the cold beams of the history of learning."

"A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed."

"This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem."

"The book, as far as I am aware, is the first attempt to connect the natural sciences into a history of creation."

"The progress of knowledge is very irregular, somewhat resembling the movements of an army, of which some battalions are in vigorous health, while others are sickly or overburdened with baggage. The experimental marches on at a good pace; the observational proceeds but slowly; the speculative is left far in the rear."

"History of science played a very important role for me. Before I knew well how to do an experiment, I knew why Joliot has missed the neutron, why his wife missed the fission, why they succeeded in having artificial radioactivity, and even why they almost missed the other things, by doing very nice experiments, but didn't come to the conclusion. That is science. Science is doubt, is research. It is not something which is—and that is the danger of teaching—which is too academic and which the people explain [to] you... it is like the logic thing that comes out of the computer, which is not true. You have intuition, you have passion."

"Every science may be exhibited under two methods or procedures, the Historical and the Dogmatic. ...The more discoveries are made, the greater becomes the labour of the historical method of study, and the more effectual the dogmatic, because the new conceptions bring forward the earlier ones in a fresh light. ...By the dogmatic method, therefore, must every advanced science be attained, with so much of the historical combined with it as is rendered necessary ..."

"The most important ploy that nineteenth-century European scholars devised to avoid acknowledging that the roots of civilization are Afroasiatic was to minimize the importance of Egyptian, Sumerian, and Semitic contributions and to focus instead almost entirely on the Greeks. According to this idea, the Egyptians, Sumerians, and Semites established rather static and uninteresting cultures, while the really worthwhile developments in the rise of civilization were the work of the dynamic and sophisticated Greeks, who were considered to be of Aryan stock because their language is part of the Indo-European family. ...It was claimed that the Greeks developed their culture all on their own, with virtually no contribution from the earlier civilizations."

"In the nineteenth century C.E., a small but influential group of German scholars led by Karl Otfried Müller decided that the ancient Greek authors did not know what they were talking about—that their traditions of external influences were simply "myths." …They were convinced that the principle of historical explanation was race, and they believed they had discovered the "scientific laws of race." …only the white race ...had the natural ability to create advanced civilizations. ...This "racial science" …served as a useful ideology to explain the "natural right" of white Europeans to dominate the darker peoples of the world."

"Modern science will continue to be blindly destructive as long as its operations are determined by the anarchism of market economic forces. The problem to be solved is whether science, technology, and industry can be brought under genuinely democratic control in the context of a global planned economy, so that all of us can collectively put our hard-won scientific knowledge to mutually beneficial use. I am confident it can be accomplished, but will it? If so, there is reason for optimism. If not... well, to paraphrase Keynes, "in the not-so-long run we're all dead.""

"The strategic act by which Grosseteste and his thirteenth- and fourteenth-century successors created modern experimental science was to unite the experimental habit of the practical arts with the rationalism of twelfth-century philosophy."

"Before the eighth century [B.C.] no scientific astronomy was possible owing to the absence of one indispensable condition, namely, the possession of an exact system of chronology. The old calendar already in use about the year 2500, and perhaps earlier, was composed of twelve s. But as twelve lunar periods make only 354 days, a thirteenth month was from time to time inserted to bring the date at which the festivals recurred each year, into harmony with the seasons. It was only little by little that greater precision was attained by observing at what date the heliac rising of certain fixed stars took place. ...By degrees, direct observation of celestial phenomena, intended either to enable soothsayers to make predictions or to fix the calendar, led to the establishment of the fact that certain... phenomena recurred at regular intervals, and the attempt was then made to base predictions on the calculation of this recurrence or periodicity. This necessitated a strict chronology, at which the Babylonians did not arrive till the middle of the eighth century B.C.: in 747 they adopted the so-called "era of ." ...the moment when, doubtless owing to the establishment of a lunisolar cycle, they kept properly constructed chronological tables. Farther back there was no certainty in regard to the calculation of time. It is from that moment that the records of eclipses begin which Ptolemy used, and which are still sometimes employed by men of science for the purpose of testing their lunar theories."

"When we realize the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton's day. ...any speaker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. As for Newton, not only did he not know nothing of the non-mechanical negative experiments, but in addition, the equations of electrodynamics had not been discovered... even if he had conceived of space-time through some divine inspiration, he could never have utilised it for the purpose of establishing the relativity of all motion. His ignorance of non-Euclidean geometry would have rendered the task impossible. In fact, space-time, in the seventeenth century, would have been a hindrance, and the sole result of its premature introduction into science would have been to muddle everything up and render the discovery of Newton's law of gravitation well-nigh impossible. And this brings us to another point which is often true in physical science. Premature discoveries are apt to do more harm than good. ...had the astronomers of the seventeenth century possessed more perfect telescopes, had they recognized that the planets (Mercury, in particular) did not obey Kepler's laws rigorously, Newton's law might never have been discovered. At all events, its correctness would have been questioned seriously and mathematicians might have lost courage and doubted their ability to discover natural laws. Leverrier, for example, might have lacked the necessary assurance to carry out his lengthy calculations leading to the discovery of Neptune. In short, physical science proceeds by successive approximations, and too rapid jumps in the accretion of knowledge are liable to be disastrous."

"The present century has witnessed the emergence of two grand theories of mathematical physics: the Theory of Relativity and the Quantum Theory. Both theories were conceived for coordinating certain bodies of facts which the classical theories were unable to interpret; and neither theory would have seen the day had it not been for the increased refinement of experimental measurements which rendered the disclosure of these facts possible. But although the two theories were born under similar circumstances, they soon branched in opposite directions. The theory of relativity has developed into a doctrine whose principle field of application is found in the world of large-scale phenomena, whereas the quantum theory has become identified with the atomic and subatomic worlds. To this extent the theories are complimentary."

"Inasmuch as both Rayleigh's and Wien's laws of radiation, though incorrect, appear to express facts correctly at opposite limits of temperature and frequency, we may presume that the correct law must have an intermediary form, passing over into Rayleigh's when [temperature] T is large and [frequency] ν small, and into Wein's when the reverse situation... Planck, guided by these considerations, devised a new theory of radiation which he called the "Quantum Theory." From this theory Planck was able to derive a radiation law which satisfied Wien's relation, ...the displacement law [when the temperature is increased, intensities of all the frequencies increase, while the radiation of maximum intensity is directly proportional to the absolute temperature] and Stefan's law, and which was in excellent agreement with experimental measurements at all temperatures."

"1. Small particles called atoms exist and compose all matter; 2. They are indivisible and indestructible; 3. Atoms of the same chemical element have the same chemical properties and do not transmute or change into different elements."

"The genesis of all science can be traced to the contemplation of... occult influences. Astrology preceded astronomy, chemistry grew out of alchemy, and the theory of numbers had its precursor in a sort of numerology which to this day persists in otherwise unaccountable omens and superstitions."

"While we cannot place Pythagoras among the great or event near-great mathematicians, his position in the history of scientific thought remains unchallenged. ...dictum "Number rules the universe" ...in the broad modern sense ...is there anything in the dictum to which a modern scientist could not or would not subscribe? The theories of relativity and quanta have shaken the physical sciences to the very foundation, forcing the physicist to cast overboard such principles as conservation of energy or economy of action, and to revise the very concepts of space, time, matter, cause and effect. Still, number reigns as firmly in the new physics as it did in the old."

"Great is the power of steady misrepresentation; but the history of science shows that fortunately this power does not long endure."

"The rise of the scientific spirit was a notable feature of the Renaissance: men no longer accepted without question the opinions of the ancients about the universe and the laws governing the natural world; dogma was subjected to experiment, and when it failed to survive the test it was rejected and new theories were formulated. Thus science in the modern sense was born, and rapid progress was made in mathematics, physics, chemistry, and biology. But the immediate consequences for technology were confined to a few specialized fields; in the main, technological progress still depended upon the empirical methods by practical men. On the whole, up to 1750 science probably gained more from technology than vice versa. Among the notable exceptions... were the navigational instruments that played so important a part in the great voyages of exploration and in surveying and cartography; the application of the principle of the pendulum to time-measurement; and, particularly, the growing exploitation of chemistry. However, the new outlook on natural phenomena was only one manifestation of a healthy scepticism: technological processes which often had changed very little for centuries were carefully scrutinized to see what improvements could usefully be made. The Royal Society, founded in 1660 to further the investigation of natural phenomena by observation and experiment, in its early days directed at least as much of its attention to the improvement of existing arts and industries as to the advancement of fundamental scientific knowledge. Among the Society's early activities was the founding of Greenwich Observatory in 1675 for the strictly practical purpose of 'finding out the longitude for perfecting navigation'."

"Growing skill in the working of metals is... exemplified by the development of the instrument-maker's craft. To many... we make reference elsewhere—for example, clocks, navigational instruments and balances. ...Brass, ivory, and closed-grained woods, such as box and pear, were the principal materials of the instrument-makers, with brass becoming increasingly favoured because of its rigidity and permanence. For the shaping of metal the lathe was a valuable tool, and the clock-makers in particular developed it greatly for precision work. The engraving of scales was, of course, a most important part of the work: until the advent of mechanical devices, this was done with simple engraving tools and punches, the design being first set out by geometrical methods. The earliest products of the instrument-makers were made mainly for astronomical purposes or to apply astronomical methods in navigation: they included astrolabes, cross-staffs, quadrants, sundials, and orreries, as well as basic geometrical instruments such as compasses and rules. From the seventeenth century, however, a variety of new instruments, or much improved versions of old ones, began to appear. The needs of surveyors led to the elaboration of the hodometer... enabling distances to be measured... Improvements in artillary called for more accurate sighting of cannon, and by the beginning of the seventeenth century the gunner's level had been highly developed. The invention of the telescope and microscope introduced new problems both in the making of lenses and of the instruments in which they were mounted: the new instruments were a regular part of the instrument-maker's trade from about 1660. From 1700 the revolution in science was making still further demands on the craft, and air-pumps, thermometers, barometers, electrical machines, and other instruments were called for in constantly increasing quantities."

"Greek and medieval knowledge accepted the world in its qualitative variety, and regarded nature's processes as having ends, or in technical phrase as teleological. New science was expounded so as to deny the reality of all qualities in real, or objective, existence. Sounds, colors, ends, as well as goods and bads, were regarded as purely subjective — as mere impressions in the mind. Objective existence was then treated as having only quantitative aspects — as so much mass in motion, its only differences being that at one point in space there was a larger aggregate mass than at another, and that in some spots there were greater rates of motion than at others. Lacking qualitative distinctions, nature lacked significant variety. Uniformities were emphasized, not diversities; the ideal was supposed to be the discovery of a single mathematical formula applying to the whole universe at once from which all the seeming variety of phenomena could be derived. This is what a mechanical philosophy means."

"Les hypothèses ne sont point le produit d'une création soudaine, mais le résultat d'une évolution progressive. [Hypotheses are not the product of sudden creation, but the result of progressive évolution.]"

"Science and religion are two human enterprises sharing many common features. They share these features also with other enterprises such as art, literature and music. The most salient features of all these enterprises are discipline and diversity. Discipline to submerge the individual fantasy in a greater whole. Diversity to give scope to the infinite variety of human souls and temperaments. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual—these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion."

"Science as subversion has a long history. ...Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. ...We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice."

"The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ...A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ...Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ...Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant."

"Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague."

"According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought... scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes... science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature's secrets by itself, but both together have been amazingly successful. For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday and Darwin and Rutherford were Baconians; Pascal and Laplace and Poincaré were Cartesians. Newton was at heart a Cartesian, using pure thought... to demolish the Cartesian dogma of vortices. Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms."

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science."

"...The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought."

"If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz."

"Scientific thought is a development of pre-scientific thought."

"I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth."

"What Luther's burning of the Papal Bull was in the religious field, in the field of natural science was the great work of Copernicus, in which he, although timidly... threw down a challenge to ecclesiastical superstition. From then on natural science was in essence emancipated from religion, although the complete settlement of accounts in all details has gone on to the present day and in many minds is still far from being complete. But from then on the development of science went forward with giant strides, increasing, so to speak, proportionately to the square of the distance in time from its point of departure, as if it wanted to show the world that for the motion of the highest product of organic matter, the human mind, the law that holds good is the reverse of that for the motion of inorganic matter."

"Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them."