Though the imperfections of the Ptolemaic system were not immediately perceived, especially during the confusion which attended the decline and destruction of the Roman empire, their effects did not fail, in process of time, to become fully evident. In the ninth century, on the revival of science in the east, under the encouragement of the caliphs, surnamed Abassides, Ptolemy's astronomical tables were found to deviate so widely from the actual situations of the celestial bodies, as to be no longer useful in calculations: and it became necessary for the Saracen astronomers at Bagdat to form tables entirely new. The Saracens carried their astronomical knowledge with them into Spain; and, in the thirteenth century again, the new tables were found unfit to represent the celestial motions; and, to supply their place, the tables, called Alphonsine, were constructed, by the direction of Alphonso the 10th, king of Castile. The errors even of the Alphonsine tables became, in the fifteenth century, equally sensible with the former. But though it was hence evident, that the revolutions of the celestial bodies were not precisely what the excentric circles and epicycles of the ancients represented, such was the veneration of astronomers for Hipparchus and Ptolemy, from whom they derived all that was valuable in their science; and, indeed, so great was the merit of subjecting motions, so intricate as the apparent celestial revolutions, to any settled rules; that no suspicions concerning the principles of the theory appear to have been entertained. All that was proposed even by eminent astronomers, such as Purbach and Muller, surnamed Regiomontanus, was only to correct the theory by more accurate observations: and none of the amendments, which they introduced, was inconsistent with its principles. It was the celebrated Copernicus, a native of Thorn in Polish Prussia, who first called in question the principles themselves, and to whom the exclusive honour belongs, of substituting for the Ptolemaic a new and more beautiful system, representing the celestial motions with much more simplicity, and, after its principles were fully understood, with incomparably greater accuracy.

It does not appear that Copernicus originally meditated such a total revolt from the authority of Ptolemy, as that to which, in the course of forming his theory, he was eventually led. Though equally sensible with others of the deviation of the Ptolemaic tables from the actual state of the heavens, the chief cause of his dissatisfaction with Ptolemy's theory related to his explications of the first planetary inequalities, and was his departure in these explications from the principle of uniform motion in perfect circles, which all astronomers considered as sacred and inviolable. When Hipparchus introduced an excentric orbit into the solar theory, no trespass against this principle was committed; because the sun was supposed to move uniformly round its centre: but when Ptolemy extended the application of excentrics to the planetary orbits, and supposed every epicycle to move uniformly round a point, not in the centre of the deferent, the principle was undeniably abandoned: for the uniformity attained was in a foreign orbit, called an equant; and there was a real and evident inequality in its own. It was this part of the theory of Ptolemy which, Copernicus tells us, he chiefly disapproved; and, as he found the explication of the first inequality, by means of an excentric with an equant, irreconcileable with his favourite principle, he seems to have had at first no higher purpose in view, than to substitute an explication of a different kind, and more consonant to that principle.

The theory which he proposed to substitute, for explaining the first inequalities in a manner more consistent with the principle of uniformity, was the ancient concentric one: and it was in restoring this from its neglected state, that the distinguishing and essential part of his system, in which he ventured to depart, not only from the authority of Ptolemy, but from all the established opinions of mankind, seems first to have presented itself to his thoughts. When both inequalities were represented by means of concentric circles with epicycles, the necessary multiplicity of epicycles confounded the imagination; and the chief recommendation of the excentric theory, and even the original cause of framing it, was the banishing several of the epicycles by which the imagination had been perplexed. The same desire therefore of simplicity, which led Ptolemy to substitute an excentric orbit, in the explication of the first inequality, for the concentric with its epicycle, seems to have had equal influence, in suggesting to Copernicus a like substitution for the epicycles used in the explication of the second. He discovered in the annual orbit of the sun, or earth, an universal epicycle, which explained the second inequalities more advantageously than all the various separate ones with which the planetary orbits had been encumbered: and in fact the solar orbit had been already employed in this explication, at least in some degree; for while the ancients formed the argument of the equation of the second inequality, by taking the difference between the places of the sun and the planet (47), they were actually converting the sun's orbit into an epicycle. These seem to have been the motives by which Copernicus was led to conceive the bold design of attributing motion to the earth; and, by the application which he made of her annual orbit, he found the simplicity which he sought; not like Ptolemy, at the expence of the sacred principle of uniformity, but in some sense perfectly consistent with it. This attachment indeed to the doctrines of uniform circular motion, which made him reject the excentric of Ptolemy, was merely a prejudice connected with the imperfect state of physical knowledge; for the motions of the planets are in reality neither circular, nor uniform: but, in the present instance, it produced the happiest and most important effects, and proved the introduction of all that is true and valuable in astronomy.

When the design was thus conceived of ascribing motion to the earth, and displacing her from the centre of the planetary system, Copernicus found that, bold as it was, it was not destitute of support from many powerful arguments, and even from several striking astronomical phenomena. In particular, he found that an acknowledgment of its propriety was made, however undesignedly, in the whole theory of the epicycles, which, by the annual orbit of the earth, he proposed to abolish. The ratio of the semi-diameter of the epicycle of Mars, to the semi-diameter of his orbit, exceeded that of 6 to 10; and, in the theory of Venus it was still greater; for it exceeded that of 7 to 10; and therefore, when the distance of the former planet from the earth varied from 4 to 16, and of the latter from 3 to 17, it was undeniably absurd to consider the earth as the centre of their motions: and the absurdity was the same, though not so evident, of supposing the earth to be the centre of the motions of the other planets. Copernicus found also that the Ptolemaic arrangement of the inferior planets had not always been generally received; for Plato, and his followers, placed them beyond the sun; and he saw that the reasons for inverting this order, and including their orbits between those of the sun and moon, were unsatisfactory and inconclusive. The distance of the sun from the earth, Ptolemy reckoned at 1160 of the earth's semi-diameters, and that of the moon in apogee, at 64. The interjacent space between these two orbits he filled up, first, with the epicycle of Mercury of 177 in diameter, and next with that of Venus of 910; thus bringing Mercury's epicycle almost in contact with the lunar orbit, and the epicycle of Venus almost in contact with the solar orbit: and the principal reason which he assigns for crowding them in these positions, is the improbability of supposing a space so vast to have been left wholly empty; forgetting that, by this very arrangement, he had allotted, to the single epicycle of Venus, a space more than four times, or according to a more probable deduction, more than six times as extensive in breadth, as the space allotted to the earth, the moon, and Mercury, all together. The other reason alleged for this arrangement, viz. the propriety of the sun's holding the middle station, between the planets whose digressions permitted them to come into opposition with him, and those whose digressions were more limited, was both false and frivolous: for the moon's digressions were unlimited, though her orbit was arranged on the same side of the sun with those of Venus and Mercury. No reason also appeared from this arrangement, why the digressions of Venus and Mercury should be limited, why their revolutions should be so intimately connected with those of the sun, or why any one of all the planets, the superior ones not excepted, should be placed nearer to the earth than any other. On these accounts Copernicus could not fail to consider the theory of the inferior planets, attributed to the ancient Egyptians, and held by several Latin astronomers, and particularly by Martianus Capella in the fifth century, as much more worthy of attention than the Ptolemaic, and as giving a much more consistent explication of their phenomena. In this, the sun was the centre about which Venus and Mercury performed their revolutions: and, as the earth was not included within their orbits, it was impossible that they should be seen from the earth, to make any greater digressions from the sun than the limits of these orbits would allow: and the reason was also manifest, both of the relative positions assigned them with respect to the sun, and of the intimate connection of their apparent annual circuit round the earth with the apparent solar revolution. This theory Copernicus applied to the superior planets, and found the application attended with like success; for, though their oppositions shewed that the earth was included within their orbits, their near approaches to the earth in their oppositions, and the vast distances to which they removed in their conjunctions, made it impossible that the earth could be the centre of their motions. This variation of distance was especially remarkable in the planet Mars; who, in oppositions, appears equal in size to Jupiter, but towards his conjunctions no larger than a star of the second or third magnitude; and afforded an unquestionable proof that none of the superior orbits approaches so near the earth. It was from this extension of the Egyptian theory concerning the inferior planets to the superior, and making the sun the centre of all the planetary orbits, that the transition seems to have been more immediately made to the doctrine of the motion, or revolution, of the earth, like any other planet, round the sun. For, as the variations of distance shewed the earth to be nearest to the orbits of Mars and Venus, and as she was evidently within the former, and without the latter, no reason appeared why she should not partake of the revolutions round the sun, in which so many other bodies, and some of them thought to be of greater magnitude, on both sides of her, were supposed to be involved: nay, on the contrary, strong probability appeared that she did partake in those revolutions; for, on this principle, all the varieties of the distances of the planets, and all the circumstances of their second inequalities were at once and easily explained: and they could not be explained otherwise, without the improbable supposition of the annual revolution of the whole planetary orbits, round her centre. The only celestial body, which could not be subjected to the general law of describing an orbit round the sun as a centre, was the moon: for, though her oppositions, like those of Mars, proved that the earth was included within her orbit, her parallaxes shewed her distances to be much less than the least distance of Venus; and the variations of her distance were so inconsiderable as not to require, or even to admit, of any other centre of her motions than the earth. In the interjacent space, therefore, between the orbits of Mars and Venus, and where the former system made the sun to move, Copernicus placed the orbit of the moon with the earth in its centre; and supposed both together, like some great planet, to revolve round the sun, in the precise time of an apparent solar revolution. The sun was now considered as the only immoveable body in the system: for Copernicus was not influenced by the objection of his apparent progress through the zodiac; being convinced, from innumerable examples, how unavoidably we ascribe to surrounding objects all the real motions of which we are not sensible: and, by the immoveable position of the sun in the centre, and the continual revolutions of the earth and planets round it, at different distances, and in different times, not only were the second inequalities explained in general, without the embarrassment of epicycles, but the causes also of the different times of the revolutions in these imaginary epicycles, and of their different magnitudes, became fully evident. In particular, the cause became evident, why both the direct and retrograde arches of Jupiter were greater, and required longer time than those of Saturn, and less than those of Mars; and the like arches of Venus greater than those of Mercury: and why those vicissitudes returned more frequently in Saturn than in Jupiter and Mars; and more frequently in Mercury than in Mars and Venus. It is true that no reciprocations of this kind had been observed in any of the fixed stars: but this Copernicus boldly, though justly ascribed to their immense distance, in comparison with which the diameter of the whole terrestrial orbit, though bearing a sensible ratio to the distance even of the remotest planet, entirely vanished. When he had thus ascribed a periodical revolution to the earth, the transition was more easy to the doctrine of her diurnal rotation, by which his theory was completed; for, if it was improbable that the sun, carrying along with him the whole planetary orbits, should revolve annually round the earth; it was much more improbable that all these, together with the immense sphere of the fixed stars, should revolve round her every 24 hours, with a rapidity incomparably greater, and almost indeed inconceivable.

There were also some ancient authorities which seemed to encourage Copernicus in the opinions he was thus led to conceive, or at least tended to introduce them to the world with less appearance of absolute innovation. He first found, as he tells us, in Cicero's writings, a tradition, transmitted by Theophrastus, of the opinion of Nicetas of Syracuse, which made the sun, the moon, and the whole starry heavens immoveable, and ascribed their constant apparent diurnal revolutions to the sole rotation of the earth on an axis. Next, he found in Plutarch, not only a similar tradition, that the same doctrine of the diurnal rotation of the earth was asserted by Heraclides of Pontus, and Zephantus the Pythagorean; but also, what he thought had a reference to her annual revolution, and that this was said by Philolaus of Crotona, another disciple of Pythagoras, to be performed about the central fire, or sun. We have also seen the favourable opinion which he entertained, and the more extensive use which he made, of what is called the ancient Egyptian system; where Venus and Mercury are considered as satellites to the sun: and this opinion could not fail to be confirmed, when he saw that Ptolemy, though not in words, had in effect adopted it, by making the mean place of the sun the centre of both their epicycles; and that the framers of the Alphonsine tables had, at least with respect to Venus, expressly adopted it, by considering the solar orbit not only as her equant, but even as the deferent of her epicycle. But the reasons which were decisive with Copernicus, and far outweighed all authorities, in the formation of his system, were certainly the satisfactory explication which it gave of all the circumstances of the second inequalities, and the symmetry and proportion, which he calls admirable, of all its parts. It was not a mere assemblage, like the Ptolemaic, of unconnected parts in arbitrary positions: but, as the ratio of his general epicycle to every particular orbit was given, the ratios were also given of the orbits to one another; and the position of every one was determinate, and not arbitrarily assumed.

In the Copernican system, the sun is placed in the centre of the universe, and Copernicus expresses a peculiar satisfaction at contemplating him in this situation, the most commodious for diffusing light and heat to the whole celestial bodies: for he supposed that the fixed stars, equally with the planets, derived their splendour from him. The planets perform round him their periodical revolutions, in the following order determined by the ratio of every orbit to that of the earth; Mercury, Venus, the Earth attended by her satellite the moon, Mars, Jupiter, and Saturn; and after these may now be added the planet discovered by Herschel. The earth, instead of continuing to be the centre of the motions of the sun and planets, is degraded to become herself a planet, and is the centre only of the motions of the moon. It has been since discovered, that Jupiter has four moons, and Saturn five, which they carry along with them, as our moon is carried along by the earth, in accomplishing their revolutions about the sun. To the five moons, or satellites, of Saturn, Herschel has also discovered that two more ought to be added, and that his own planet is accompanied by two. Beyond these, and at an immense distance, is placed the sphere of the fixed stars; and its diurnal revolution, together with that of all the moveable celestial bodies referred to it, is considered in this system merely as apparent, and produced by the diurnal rotation of the terrestrial globe.

Notwithstanding the simplicity and symmetry of this system, and all the advantages by which it was recommended, Copernicus was so much aware of the objections that would be made to it, and the prejudices which it would have to encounter, that he was deterred from publishing it to the world, and forbore, for thirty years, to communicate it, except to some confidential friends. Many of the astronomical phenomena, by which it is supported, were then undiscovered: the rotation, for example, of other celestial bodies on their axes, had not been observed: none of the changes had been seen, in the phases especially of Venus and Mercury, which this system rendered necessary: the principle of gravitation and its important consequences were almost wholly unknown: and, till the aberration of the fixed stars was discovered, it seemed altogether incredible, that the translation of the earth, in her annual revolution, from one extremity of her immense orbit to another, should produce no change on the apparent magnitudes, or the relative positions, of the fixed stars. It was not, therefore, till near the close of life, nor even then without the importunities of his friends, particularly of Schomberg cardinal of Capua, and Gisius bishop of Culm, that his consent to the publication was obtained: and, when the first edition of his work was completed, under the inspection of the eminent George Joachim Rheticus, at Nurenberg, on the 24th of May, 1543, the illustrious author, a few days after receiving a copy, died in his 72d year at Frawenberg.