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| A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
The subject will be treated under the following heads:
Although at the time of Christ's birth Hellenic science had produced nearly all its masterpieces, it was still to give to the world Ptolemy's astronomy, the way for which had been paved for more than a century by the works of Hipparchus. The revelations of Greek thought on the nature of the exterior world ended with the "Almagest", which appeared about A.D. 145, and then began the decline of ancient learning. Those of its works that escaped the fires kindled by Mohammedan warriors were subjected to the barren interpretations of Mussulman commentators and like parched seed, awaited the time when Latin Christianity would furnish a favourable soil in which they could once more flourish and bring forth fruit. Hence it is that the time when Ptolemy put the finishing touches to his "Great Mathematical Syntax of Astronomy" seems the most opportune in which to study the field of ancient physics. An impassable frontier separated this field into two regions in which different laws prevailed. From the moon's orbit to the sphere enclosing the world, extended the region of beings exempt from generation, change, and death, of perfect, divine beings, and these were the star-sphere and the stars themselves. Inside the lunar orbit lay the region of generation and corruption, where the four elements and the mixed bodies generated by their mutual combinations were subject to perpetual change.
The science of the stars was dominated by a principle formulated by Plato and the Pythagoreans, according to which all the phenomena presented to us by the heavenly bodies must be accounted for by combinations of circular and uniform motions. Moreover, Plato declared that these circular motions were reducible to the rotation of solid globes all limited by spherical surfaces concentric with the World and the Earth, and some of these homocentric spheres carried fixed or wandering stars. Eudoxus of Cnidus, Calippus, and Aristotle vied with one another in striving to advance this theory of homocentric spheres, its fundamental hypothesis being incorporated in Aristotle's "Physics" and "Metaphysics". However, the astronomy of homocentric spheres could not explain all celestial phenomena, a considerable number of which showed that the wandering stars did not always remain at an equal distance from the Earth. Heraclides Ponticus in Plato's time, and Aristarchus of Samos about 280 B.C. endeavoured to account for all astronomical phenomena by a heliocentric system, which was an outline of the Copernican mechanics; but the arguments of physics and the precepts of theology proclaiming the Earth's immobility, readily obtained the ascendency over this doctrine which existed in a mere outline. Then the labours of Apollonius Pergæus (at Alexandria, 205 B.C.), of Hipparchus (who made observation at Rhodes in 128 and 127 B.C.), and finally of Ptolemy (Claudius Ptolemæus of Pelusium) constituted a new astronomical system that claimed the Earth to be immovable in the centre of the universe; a system that seemed, as it were, to reach its completion when, between A.D. 142 and 146, Ptolemy wrote a work called Megale mathematike syntaxis tes astronomias, its Arabian title being transliterated by the Christians of the Middle Ages, who named it "Almagest". The astronomy of the "Almagest" explained all astronomical phenomena with a precision which for a long time seemed satisfactory, accounting for them by combinations of circular motions; but, of the circles described, some were eccentric to the World, whilst others were epicyclic circles, the centres of which described deferent circles concentric with or eccentric to the World; moreover, the motion on the deferent was no longer uniform, seeming so only when viewed from the centre of the equant. Briefly, in order to construct a kinematical arrangement by means of which phenomena could be accurately represented, the astronomers whose work Ptolemy completed had to set at naught the properties ascribed to the celestial substance by Aristotle's "Physics", and between this "Physics" and the astronomy of eccentrics and epicycles there ensued a violent struggle which lasted until the middle of the sixteenth century.
In Ptolemy's time the physics of celestial motion was far more advanced than the physics of sublunary bodies, as, in this science of beings subject to generation and corruption, only two chapters had reached any degree of perfection, namely, those on optics (called perspective) and statics. The law of reflection was known as early as the time of Euclid, about 320 B.C., and to this geometrician was attributed, although probably erroneously, a "Treatise on Mirrors", in which the principles of catoptrics were correctly set forth. Dioptrics, being more difficult, was developed less rapidly. Ptolemy already knew that the angle of refraction is not proportional to the angle of incidence, and in order to determine the ratio between the two he undertook experiments the results of which were remarkably exact.
Statics reached a fuller development than optics. The "Mechanical Questions" ascribed to Aristotle were a first attempt to organize that science, and they contained a kind of outline of the principle of virtual velocities, destined to justify the law of the equilibrium of the lever; besides, they embod. the happy idea of referring to the lever theory the theory of all simple machines. An elaboration, in which Euclid seems to have had some part, brought statics to the stage of development in which it was found by Archimedes (about 287-212 B.C.), who was to raise it to a still higher degree of perfection. It will here suffice to mention the works of genius in which the great Syracusan treated the equilibrium of the weights suspended from the two arms of a lever, the search for the centre of gravity, and the equilibrium of liquids and floating bodies. The treatises of Archimedes were too scholarly to be widely read by the mechanicians who succeeded this geometrician; these men preferred easier and more practical writings as, for instance, those on the lines of Aristotle's "Mechanical Questions". Various treatises by Heron of Alexandria have preserved for us the type of these decadent works.
Shortly after the death of Ptolemy, Christian science took root at Alexandria with Origen (about 180-253), and a fragment of his "Commentaries on Genesis", preserved by Eusebius, shows us that the author was familiar with the latest astronomical discoveries, especially the precession of the equinoxes. However, the writings in which the Fathers of the Church comment upon the work of the six days of Creation, notably the commentaries of St. Basil and St. Ambrose, borrow but little from Hellenic physics; in fact, their tone would seem to indicate distrust in the teachings of Greek science, this distrust being engendered by two prejudices: in the first place, astronomy was becoming more and more the slave of astrology, the superstitions of which the Church diligently combatted; in the second place, between the essential propositions of peripatetic physics and what we believe to be the teaching of Holy Writ, contradictions appeared; thus Genesis was thought to teach the presence of water above the heaven of the fixed stars (the firmament) and this was incompatible with the Aristotelean theory concerning the natural place of the elements. The debates raised by this question gave St. Augustine an opportunity to lay down wise exegetical rules, and he recommended Christians not to put forth lightly, as articles of faith, propositions contradicted by physical science based upon careful experiments. St. Isidore of Seville (d. 636), a bishop, considered it legitimate for Christians to desire to know the teachings of profane science, and he laboured to satisfy this curiosity. His "Etymologies" and "De natura rerum" are merely compilations of fragments borrowed from all the pagan and Christian authors with whom he was acquainted. In the height of the Latin Middle Ages these works served as models for numerous encyclopædias, of which the "De natura rerum" by Bede (about 672-735) and the "De universo" by Rabanus Maurus (776-856) were the best known.
However, the sources from which the Christians of the West imbibed a knowledge of ancient physics became daily more numerous, and to Pliny the Elder's "Natural History", read by Bede, were added Chalcidius's commentary on Plato's "Timæus" and Martianus Capella's "De Nuptiis Philologiæ et Mercurii", these different works inspiring the physics of John Scotus Eriugena. Prior to A.D. 1000 a new Platonic work by Macrobius, a commentary on the "Somnium Scipionis", was in great favour in the schools. Influenced by the various treatises already mentioned, Guillaume of Conches (1080-1150 or 1154) and the unknown author of "De mundi constitutione liber", which, by the way, has been falsely attributed to Bede, set forth a planetary theory making Venus and Mercury satellites of the sun, but Eriugena went still further and made the sun also the centre of the orbits of Mars and Jupiter. Had he but extended this hypothesis to Saturn, he would have merited the title of precursor of Tycho Brahe.
The authors of whom we have heretofore spoken had only been acquainted with Greek science through the medium of Latin tradition, but the time came when it was to be much more completely revealed to the Christians of the West through the medium of Mussulman tradition.
There is no Arabian science. The wise men of Mohammedanism were always the more or less faithful disciples of the Greeks, but were themselves destitute of all originality. For instance, they compiled many abridgments of Ptolemy's "Almagest", made numerous observations, and constructed a great many astronomical tables, but added nothing essential to the theories of astronomical motion; their only innovation in this respect, and, by the way, quite an unfortunate one, was the doctrine of the oscillatory motion of the equinoctial points, which the Middle Ages ascribed to Thâbit ibn Kûrrah (836-901), but which was probably the idea of Al-Zarkali, who lived much later and made observations between 1060 and 1080. This motion was merely the adaptation of a mechanism conceived by Ptolemy for a totally different purpose.
In physics, Arabian scholars confined themselves to commentaries on the statements of Aristotle, their attitude being at times one of absolute servility. This intellectual servility to Peripatetic teaching reached its climax in Abul ibn Roshd, whom Latin scholastics called Averroës (about 1120-98) and who said: Aristotle "founded and completed logic, physics, and metaphysics . . . because none of those who have followed him up to our time, that is to say, for four hundred years, have been able to add anything to his writings or to detect therein an error of any importance". This unbounded respect for Aristotle's work impelled a great many Arabian philosophers to attack Ptolemy's "Astronomy" in the name of Peripatetic physics. The conflict between the hypotheses of eccentrics and epicycles was inaugurated by Ibn Bâdja, known to the scholastics as Avempace (d. 1138), and Abu Bekr ibn el-Tofeil, called Abubacer by the scholastics (d. 1185), and was vigorously conducted by Averroës, the protégé of Abubacer. Abu Ishâk ibn al-Bitrogi, known by the scholastics as Alpetragius, another disciple of Abubacer and a contemporary of Averroës, advanced a theory on planetary motion wherein he wished to account for the phenomena peculiar to the wandering stars, by compounding rotations of homocentric spheres; his treatise, which was more neo-Platonic than Peripatetic, seemed to be a Greek book altered, or else a simple plagiarism. Less inflexible in his Peripateticism than Averroës and Alpetragius, Moses ben Maimun, called Maimonides (1139-1204), accepted Ptolemy's astronomy despite its incompatibility with Aristotelean physics, although he regarded Aristotle's sublunary physics as absolutely true.
It cannot be said exactly when the first translations of Arabic writings began to be received by the Christians of the West, but it was certainly previously to the time of Gerbert (Sylvester II; about 930-1003). Gerbert used treatises translated from the Arabic, and containing instructions on the use of astronomical instruments, notably the astrolabe, to which instrument Hermann the Lame (1013-54) devoted part of his researches. In the beginning of the twelfth century the contributions of Mohammedan science and philosophy to Latin Christendom became more and more frequent and important. About 1120 or 1130 Adelard of Bath translated the "Elements" of Euclid, and various astronomical treatises; in 1141 Peter the Venerable, Abbot of Cluny, found two translators, Hermann the Second (or the Dalmatian) and Robert of Rétines, established in Spain; he engaged them to translate the Koran into Latin, and in 1143 these same translators made Christendom acquainted with Ptolemy's planisphere. Under the direction of Raimond (Archbishop of Toledo, 1130; d. 1150), Domengo Gondisalvi (Gonsalvi; Gundissalinus), Archdeacon of Segovia, began to collaborate with the converted Jew, John of Luna, erroneously called John of Seville (Johannes Hispalensis). While John of Luna applied himself to works in mathematics, he also assisted Gondisalvi in translating into Latin a part of Aristotle's physics, the "De Cælo" and the "Metaphysics", besides treatises by Avicenna, Al-Gazâli, Al-Fârâbi, and perhaps Salomon ibn Gebirol (Avicebron). About 1134 John of Luna translated Al-Fergâni's treatise "Astronomy", which was an abridgement of the "Almagest", thereby introducing Christians to the Ptolemaic system, while at the same time his translations, made in collaboration with Gondisalvi, familiarized the Latins with the physical and metaphysical doctrines of Aristotle. Indeed the influence of Aristotle's "Physics" was already apparent in the writings of the most celebrated masters of the school of Chartres (from 1121 until before 1155), and of Gilbert de la Porrée (1070-1154).
The abridgement of Al-Fergâni's "Astronomy", translated by John of Luna, does not seem to have been the first work in which the Latins were enabled to read the exposition of Ptolemy's system; it was undoubtedly preceded by a more complete treatise, the "De Scientia stellarum" of Albategnius (Al-Battâni), latinized by Plato of Tivoli about 1120. However, the "Almagest" itself was still unknown. Moved by a desire to read and translate Ptolemy's immortal work, Gerard of Cremona (d. 1187) left Italy and went to Toledo, eventually making the translation which he finished in 1175. Besides the "Almagest", Gerard rendered into Latin other works, of which we have a list comprising seventy-four different treatises. Some of these were writings of Greek origin, and included a large portion of the works of Aristotle, a treatise by Archimedes, Euclid's "Elements" (completed by Hypsicles), and books by Hippocrates. Others were Arabic writings, such as the celebrated "Book of Three Brothers", composed by the Beni Mûsa, "Optics" by Ibn Al-Haitam (the Alhazen of the Scholastics), "Astronomy" by Geber, and "De motu octavæ sphæræ" by Thâbit ibn Kûrrah. Moreover, in order to spread the study of Ptolemaic astronomy, Gerard composed at Toledo his "Theoricæ planetarum", which during the Middle Ages became one of the classics of astronomical instruction. Beginners who obtained their first cosmographic information through the study of the "Sphæra", written about 1230 by Joannes de Sacrobosco, could acquire a knowledge of eccentrics and epicycles by reading the "Theoricæ planetarum" of Gerard of Cremona. In fact, until the sixteenth century, most astronomical treatises assumed the form of commentaries, either on the "Sphæra", or the "Theoricæ planetarum".
"Aristotle's philosophy", wrote Roger Bacon in 1267, "reached a great development among the Latins when Michael Scot appeared about 1230, bringing with him certain parts of the mathematical and physical treatises of Aristotle and his learned commentators". Among the Arabic writings made known to Christians by Michael Scot (before 1291; astrologer to Frederick II) were the treatises of Aristotle and the "Theory of Planets", which Alpetragius had composed in accordance with the hypothesis of homocentric spheres. The translation of this last work was completed in 1217. By propagating among the Latins the commentaries on Averroës and on Alpetragius's theory of the planets, as well as a knowledge of the treatises of Aristotle, Michael Scot developed in them an intellectual disposition which might be termed Averroism, and which consisted in a superstitious respect for the word of Aristotle and his commentator.
There was a metaphysical Averroism which, because professing the doctrine of the substantial unity of all human intellects, was in open conflict with Christian orthodoxy; but there was likewise a physical Averroism which, in its blind confidence in Peripatetic physics, held as absolutely certain all that the latter taught on the subject of the celestial substance, rejecting in particular the system of epicycles and eccentrics in order to commend Alpetragius's astronomy of homocentric spheres.
Scientific Averroism found partisans even among those whose purity of faith constrained them to struggle against metaphysical Averroism, and who were very often Peripatetics in so far as was possible without formally contradicting the teaching of the Church. For instance, William of Auvergne (d. 1249), who was the first to combat "Aristotle and his sectarians" on metaphysical grounds, was somewhat misled by Alpetragius's astronomy, which, moreover, he understood but imperfectly. Albertus Magnus (1193 or 1205-1280) followed to a great extent the doctrine of Ptolemy, although he was sometimes influenced by the objections of Averroës or affected by Alpetragius's principles. Vincent of Beauvais in his "Speculum quadruplex", a vast encyclopædic compilation published about 1250, seemed to attach great importance to the system of Alpetragius, borrowing the exposition of it from Albertus Magnus. Finally, even St. Thomas Aquinas gave evidence of being extremely perplexed by the theory (1227-74) of eccentrics and epicycles which justified celestial phenomena by contradicting the principles of Peripatetic physics, and the theory of Alpetragius which honoured these principles but did not go so far as to represent their phenomena in detail.
This hesitation, so marked in the Dominican school, was hardly less remarkable in the Franciscan. Robert Grosseteste or Greathead (1175-1253), whose influence on Franciscan studies was so great, followed the Ptolemaic system in his astronomical writings, his physics being imbued with Alpetragius's ideas. St. Bonaventure (1221-74) wavered between doctrines which he did not thoroughly understand, and Roger Bacon (1214-92) in several of his writings weighed with great care the arguments that could be made to count for or against each of these two astronomical theories, without eventually making a choice. Bacon, however, was familiar with a method of figuration in the system of eccentrics and epicycles which Alhazen had derived from the Greeks; and in this figuration all the motions acknowledged by Ptolemy were traced back to the rotation of solid orbs accurately fitted one into the other. This representation, which refuted most of the objections raised by Averroës against Ptolemaic astronomy, contributed largely to propagate the knowledge of this astronomy, and it seems that the first of the Latins to adopt it and expatiate on its merits was the Franciscan Bernard of Verdun (end of thirteenth century), who had read Bacon's writings. In sublunary physics the authors whom we have just mentioned did not show the hesitation that rendered astronomical doctrines so perplexing, but on almost all points adhered closely to Peripatetic opinions .
Averroism had rendered scientific progress impossible, but fortunately in Latin Christendom it was to meet with two powerful enemies: the unhampered curiosity of human reason, and the authority of the Church. Encouraged by the certainty resulting from experiments, astronomers rudely shook off the yoke which Peripatetic physics had imposed upon them. The School of Paris in particular was remarkable for its critical views and its freedom of attitude towards the argument of authority. In 1290 William of Saint-Cloud determined with wonderful accuracy the obliquity of the ecliptic and the time of the vernal equinox, and his observations led him to recognize the inaccuracies that marred the "Tables of Toledo", drawn up by Al-Zarkali. The theory of the precession of the equinoxes, conceived by the astronomers of Alfonso X of Castile, and the "Alphonsine Tables" set up in accordance with this theory, gave rise in the first half of the fourteenth century to the observations, calculations, and critical discussions of Parisian astronomers, especially of Jean des Linières and his pupil John of Saxonia or Connaught.
At the end of the thirteenth century and the beginning of the fourteenth, sublunary physics owed great advancement to the simultaneous efforts of geometricians and experimenters -- their method and discoveries being duly boasted of by Roger Bacon who, however, took no important part in their labours. Jordanus de Nemore, a talented mathematician who, not later than about the beginning of the thirteenth century, wrote treatises on arithmetic and geometry, left a very short treatise on statics in which, side by side with erroneous propositions, we find the law of the equilibrium of the straight lever very correctly established with the aid of the principle of virtual displacements. The treatise, "De ponderibus", by Jordanus provoked research on the part of various commentators, and one of these, whose name is unknown and who must have written before the end of the thirteenth century, drew, from the same principle of virtual displacements, demonstrations, admirable in exactness and elegance, of the law of the equilibrium of the bent lever, and of the apparent weight (gravitas secundum situm) of a body on an inclined plane.
Alhazen's "Treatise on Perspective" was read thoroughly by Roger Bacon and his contemporaries, John Peckham (1228-91), the English Franciscan, giving a summary of it. About 1270 Witelo (or Witek; the Thuringopolonus), composed an exhaustive ten-volume treatise on optics, which remained a classic until the time of Kepler, who wrote a commentary on it.
Albertus Magnus, Roger Bacon, John Peckham, and Witelo were deeply interested in the theory of the rainbow, and, like the ancient meteorologists, they all took the rainbow to be the image of the sun reflected in a sort of a concave mirror formed by a cloud resolved into rain. In 1300 Thierry of Freiberg proved by means of carefully-conducted experiments in which he used glass balls filled with water, that the rays which render the bow visible have been reflected on the inside of the spherical drops of water, and he traced with great accuracy the course of the rays which produce the rainbows respectively.
The system of Thierry of Freiberg, at least that part relating to the primary rainbow, was reproduced about 1360 by Themon, "Son of the Jew" (Themo ju d i), and, from his commentary on "Meteors", it passed on down to the days of the Renaissance when, having been somewhat distorted, it reappeared in the writings of Alessandro Piccolomini, Simon Porta, and Marco and Antonio de Dominis, being thus propagated until the time of Descartes.
The study of the magnet had also made great progress in the course of the thirteenth century; the permanent magnetization of iron, the properties of the magnetic poles, the direction of the Earth's action exerted on these poles or of their action on one another, are all found very accurately described in a treatise written in 1269 by Pierre of Maricourt (Petrus Peregrinus). Like the work of Thierry of Freiberg on the rainbow, the "Epistola de magnete" by Maricourt was a model of the art of logical sequence between experiment and deduction.
The University of Paris was very uneasy because of the antagonism existing between Christian dogmas and certain Peripatetic doctrines, and on several occasions it combatted Aristotelean influence. In 1277 Etienne Tempier, Bishop of Paris, acting on the advice of the theologians of the Sorbonne, condemned a great number of errors, some of which emanated from the astrology, and others from the philosophy of the Peripatetics. Among these errors considered dangerous to faith were several which might have impeded the progress of physical science, and hence it was that the theologians of Paris declared erroneous the opinion maintaining that God Himself could not give the entire universe a rectilinear motion, as the universe would then leave a vacuum behind it, and also declared false the notion that God could not create several worlds. These condemnations destroyed certain essential foundations of Peripatetic physics; because, although, in Aristotle's system, such propositions were ridiculously untenable, belief in Divine Omnipotence sanctioned them as possible, whilst waiting for science to confirm them as true. For instance, Aristotle's physics treated the existence of an empty space as a pure absurdity; in virtue of the "Articles of Paris" Richard of Middletown (about 1280) and, after him, many masters at Paris and Oxford admitted that the laws of nature are certainly opposed to the production of empty space, but that the realization of such a space is not, in itself, contrary to reason; thus, without any absurdity, one could argue on vacuum and on motion in a vacuum. Next, in order that such arguments might be legitimatized, it was necessary to create that branch of mechanical science known as dynamics.
The "Articles of Paris" were of about the same value in supporting the question of the Earth's motion as in furthering the progress of dynamics by regarding vacuum as something conceivable.
Aristotle maintained that the first heaven (the firmament) moved with a uniform rotary motion, and that the Earth was absolutely stationary, and as these two propositions necessarily resulted from the first principles relative to time and place, it would have been absurd to deny them. However, by declaring that God could endow the World with a rectilinear motion, the theologians of the Sorbonne acknowledged that these two Aristotelean propositions could not be imposed as a logical necessity and thenceforth, whilst continuing to admit that, as a fact, the Earth was immovable and that the heavens moved with a rotary diurnal motion, Richard of Middletown and Duns Scotus (about 1275-1308) began to formulate hypotheses to the effect that these bodies were animated by other motions, and the entire school of Paris adopted the same opinion. Soon, however, the Earth's motion was taught in the School of Paris, not as a possibility, but as a reality. In fact, in the specific setting forth of certain information given by Aristotle and Simplicius, a principle was formulated which for three centuries was to play a great rôle in statics, viz. that every heavy body tends to unite its centre of gravity with the centre of the Earth.
When writing his "Questions" on Aristotle's "De Cælo" in 1368, Albert of Helmstadt (or of Saxony) admitted this principle, which he applied to the entire mass of the terrestrial element. The centre of gravity of this mass is constantly inclined to place itself in the centre of the universe, but, within the terrestrial mass, the position of the centre of gravity is incessantly changing. The principal cause of this variation is the erosion brought about by the streams and rivers that continually wear away the land surface, deepening its valleys and carrying off all loose matter to the bed of the sea, thereby producing a displacement of weight which entails a ceaseless change in the position of the centre of gravity. Now, in order to replace this centre of gravity in the centre of the universe, the Earth moves without ceasing; and meanwhile a slow but perpetual exchange is being effected between the continents and the oceans. Albert of Saxony ventured so far as to think that these small and incessant motions of the Earth could explain the phenomena of the precession of the equinoxes. The same author declared that one of his masters, whose name he did not disclose, announced himself in favour of the daily rotation of the Earth, inasmuch as he refuted the arguments that were opposed to this motion. This anonymous master had a thoroughly convinced disciple in Nicole Oresme who, in 1377, being then Canon of Rouen and later Bishop of Lisieux, wrote a French commentary on Aristotle's treatise "De Cælo", maintaining with quite as much force as clearness that neither experiment nor argument could determine whether the daily motion belonged to the firmament of the fixed stars or to the Earth. He also showed how to interpret the difficulties encountered in "the Sacred Scriptures wherein it is stated that the sun turns, etc. It might be supposed that here Holy Writ adapts itself to the common mode of human speech, as also in several places, for instance, where lt is written that God repented Himself, and was angry and calmed Himself and so on, all of which is, however, not to be taken in a strictly literal sense". Finally, Oresme offered several considerations favourable to the hypothesis of the Earth's daily motion. In order to refute one of the objections raised by the Peripatetics against this point, Oresme was led to explain how, in spite of this motion, heavy bodies seemed to fall in a vertical line; he admitted their real motion to be composed of a fall in a vertical line and a diurnal rotation identical with that which they would have if bound to the Earth. This is precisely the principle to which Galileo was afterwards to turn.
Aristotle maintained the simultaneous existence of several worlds to be an absurdity, his principal argument being drawn from his theory of gravity, whence he concluded that two distinct worlds could not coexist and be each surrounded by its elements; therefore it would be ridiculous to compare each of the planets to an earth similar to ours. In 1277 the theologians of Paris condemned this doctrine as a denial of the creative omnipotence of God; Richard of Middletown and Henry of Ghent (who wrote about 1280), Guillaume Varon (who wrote a commentary on the "Sentences" about 1300), and, towards 1320, Jean de Bassols, William of Occam (d. after 1347), and Walter Burley (d. about 1348) did not hesitate to declare that God could create other worlds similar to ours. This doctrine, adopted by several Parisian masters, exacted that the theory of gravity and natural place developed by Aristotle be thoroughly changed; in fact, the following theory was substituted for it. If some part of the elements forming a world be detached from it and driven far away, its tendency will be to move towards the world to which it belongs and from which it was separated; the elements of each world are inclined so to arrange themselves that the heaviest will be in the centre and the lightest on the surface. This theory of gravity appeared in the writings of Jean Buridan of Béthune, who became rector of the University of Paris in 1327, teaching at that institution until about 1360; and in 1377 this same theory was formally proposed by Oresme. It was also destined to be adopted by Copernicus and his first followers, and to be maintained by Galileo, William Gilbert, and Otto von Guericke.
If the School of Paris completely transformed the Peripatetic theory of gravity, it was equally responsible for the overthrow of Aristotelean dynamics. Convinced that, in all motion, the mover should be directly contiguous to the body moved, Aristotle had proposed a strange theory of the motion of projectiles. He held that the projectile was moved by the fluid medium, whether air or water, through which it passed and this, by virtue of the vibration brought about in the fluid at the moment of throwing, and spread through it. In the sixth century of our era this explanation was strenuously opposed by the Christian Stoic, Joannes Philoponus, according to whom the projectile was moved by a certain power communicated to it at the instant of throwing; however, despite the objections raised by Philoponus, Aristotle's various commentators, particularly Averroës, continued to attribute the motion of the projectile to the disturbance of the air, and Albertus Magnus, St. Thomas Aquinas, Roger Bacon, Gilles of Rome, and Walter Burley persevered in maintaining this error. By means of most spirited argumentation, William of Occam made known the complete absurdity of the Peripatetic theory of the motion of projectiles. Going back to Philoponus's thesis, Buridan gave the name impetus to the virtue or power communicated to the projectile by the hand or instrument throwing it; he declared that in any given body in motion, this impetus was proportional to the velocity, and that, in different bodies in motion propelled by the same velocity, the quantities of impetus were proportional to the mass or quantity of matter defined as it was afterwards defined by Newton.
In a projectile; impetus is gradually destroyed by the resistance of air or other medium and is also destroyed by the natural gravity of the body in motion, which gravity is opposed to the impetus if the projectile be thrown upward; this struggle explains the different peculiarities of the motion of projectiles. In a falling body, gravity comes to the assistance of impetus which it increases at every instant, hence the velocity of the fall is increasing incessantly.
With the assistance of these principles concerning impetus, Buridan accounts for the swinging of the pendulum. He likewise analyses the mechanism of impact and rebound and, in this connexion, puts forth very correct views on the deformations and elastic reactions that arise in the contiguous parts of two bodies coming into collision. Nearly all this doctrine of impetus is transformed into a very correct mechanical theory if one is careful to substitute the expression vis viva for impetus. The dynamics expounded by Buridan were adopted in their entirety by Albert of Saxony, Oresme, Marsile of Inghem, and the entire School of Paris. Albert of Saxony appended thereto the statement that the velocity of a falling body must be proportional either to the time elapsed from the beginning of the fall or to the distance traversed during this time. In a projectile, the impetus is gradually destroyed either by the resistance of the medium or by the contrary tendency of the gravity natural to the body. Where these causes of destruction do not exist, the impetus remains perpetually the same, as in the case of a millstone exactly centred and not rubbing on its axis; once set in motion it will turn indefinitely with the same swiftness. It was under this form that the law of inertia at first became evident to Buridan and Albert of Saxony. The conditions manifested in this hypothetic millstone are realized in the celestial orbs, as in these neither friction nor gravity impedes motion; hence it may be admitted that each celestial orb moves indefinitely by virtue of a suitable impetus communicated to it by God at the moment of creation. It is useless to imitate Aristotle and his commentators by attributing the motion of each orb to a presiding spirit. This was the opinion proposed by Buridan and adopted by Albert of Saxony; and whilst formulating a doctrine from which modern dynamics was to spring, these masters understood that the same dynamics governs both celestial and sublunary bodies. Such an idea was directly opposed to the essential distinction established by ancient physics between these two kinds of bodies. Moreover, following William of Occam, the masters of Paris rejected this distinction; they acknowledged that the matter constituting celestial bodies was of the same nature as that constituting sublunary bodies and that, if the former remained perpetually the same, it was not because they were, by nature, incapable of change and destruction, but simply because the place in which they were contained no agent capable of corrupting them. A century elapsed between the condemnations pronounced by Etienne Tempier (1277) and the editing of the "Traité du Ciel et du Monde" by Oresme (1377) and, within that time, all the essential principles of Aristotle's physics were undermined, and the great controlling ideas of modern science formulated. This revolution was mainly the work of Oxford Franciscans like Richard of Middletown, Duns Scotus, and William of Occam, and of masters in the School of Paris, heirs to the tradition inaugurated by these Franciscans; among the Parisian masters Buridan, Albert of Saxony, and Oresme were in the foremost rank.
The great Western Schism involved the University of Paris in politico-religious quarrels of extreme violence; the misfortunes brought about by the conflict between the Armagnacs and Burgundians and by the Hundred Years' War, completed what these quarrels had begun, and the wonderful progress made by science during the fourteenth century in the University of Paris suddenly ceased. However, the schism contributed to the diffusion of Parisian doctrines by driving out of Paris a large number of brilliant men who had taught there with marked success. In 1386 Marsile of Inghem (d. 1396), who had been one of the most gifted professors of the University of Paris, became rector of the infant University of Heidelberg, where he introduced the dynamic theories of Buridan and Albert of Saxony.
About the same time, another master, reputedly of Paris, Heinrich Heimbuch of Langenstein, or of Hesse, was chiefly instrumental in founding the University of Vienna and, besides his theological knowledge, brought thither the astronomical tradition of Jean des Linières and John of Saxony. This tradition was carefully preserved in Vienna, being magnificently developed there throughout the fifteenth century, and paving the way for Georg Purbach (1423-61) and his disciple Johann Müller of Königsberg, surnamed Regiomontanus (1436-76). It was to the writing of theories calculated to make the Ptolemaic system known, to the designing and constructing of exact instruments, to the multiplying of observations, and the preparing of tables and almanacs (ephemerides), more accurate than those used by astronomers up to that time, that Purbach and Regiomontanus devoted their prodigious energy. By perfecting all the details of Ptolemy's theories, which they never called in question, they were most helpful in bringing to light the defects of these theories and in preparing the materials by means of which Copernicus was to build up his new astronomy.
Averroism flourished in the Italian Universities of Padua and Bologna, which were noted for their adherence to Peripatetic doctrines. Still from the beginning of the fifteenth century the opinions of the School of Paris began to find their way into these institutions, thanks to the teaching of Paolo Nicoletti of Venice (flourished about 1420). It was there developed by his pupil Gaetan of Tiene (d. 1465). These masters devoted special attention to propagating the dynamics of impetus in Italy.
About the time that Paola of Venice was teaching at Padua, Nicholas of Cusa came there to take his doctorate in law. Whether it was then that the latter became initiated in the physics of the School of Paris matters little, as in any event it was from Parisian physics that he adopted those doctrines that smacked least of Peripateticism. He became thoroughly conversant with the dynamics of impetus and, like Buridan and Albert of Saxony, attributed the motion of the celestial spheres to the impetus which God had communicated to them in creating them, and which was perpetuated because, in these spheres, there was no element of destruction. He admitted that the Earth moved incessantly, and that its motion might be the cause of the precession of the equinoxes. In a note discovered long after his death, he went so far as to attribute to the Earth a daily rotation. He imagined that the sun, the moon, and the planets were so many systems, each of which contained an earth and elements analogous to our Earth and elements, and to account for the action of gravity in each of these systems he followed closely the theory of gravity advanced by Oresme.
Leonardo da Vinci (1452-1519) was perhaps more thoroughly convinced of the merits of the Parisian physics than any other Italian master. A keen observer, and endowed with insatiable curiosity, he had studied a great number of works, amongst which we may mention the various treatises of the School of Jordanus, various books by Albert of Saxony, and in all likelihood the works of Nicholas of Cusa; then, profiting by the learning of these scholars, he formally enunciated or else simply intimated many new ideas. The statics of the School of Jordanus led him to discover the law of the composition of concurrent forces stated as follows: the two component forces have equal moments as regards the direction of the resultant, and the resultant and one of the components have equal moments as regards the direction of the other component. The statics derived from the properties which Albert of Saxony attributed to the centre of gravity caused Vinci to recognize the law of the polygon of support and to determine the centre of gravity of a tetrahedron. He also presented the law of the equilibrium of two liquids of different density in communicating tubes, and the principle of virtual displacements seems to have occasioned his acknowledgement of the hydrostatic law known as Pascal's. Vinci continued to meditate on the properties of impetus, which he called impeto or forza, and the propositions that he formulated on the subject of this power very often showed a fairly clear discernment of the law of the conservation of energy. These propositions conducted him to remarkably correct and accurate conclusions concerning the impossibility of perpetual motion. Unfortunately he misunderstood the pregnant explanation, afforded by the theory of impetus, regarding the acceleration of falling bodies, and like the Peripatetics attributed this acceleration to the impulsion of the encompassing air. However, by way of compensation, he distinctly asserted that the velocity of a body that falls freely is proportional to the time occupied in the fall, and he understood in what way this law extends to a fall on an inclined plane. When he wished to determine how the path traversed by a falling body is connected with the time occupied in the fall, he was confronted by a difficulty which, in the seventeenth century, was likewise to baffle Baliani and Gassendi.
Vinci was much engrossed in the analysis of the deformations and elastic reactions which cause a body to rebound after it has struck another, and this doctrine, formulated by Buridan, Albert of Saxony, and Marsile of Inghem he applied in such a way as to draw from it the explanation of the flight of birds. This flight is an alternation of falls during which the bird compresses the air beneath it, and of rebounds due to the elastic force of this air. Until the great painter discovered this explanation, the question of the flight of birds was always looked upon as a problem in statics, and was likened to the swimming of a fish in water. Vinci attached great importance to the views developed by Albert of Saxony in regard to the Earth's equilibrium. Like the Parisian master, he held that the centre of gravity within the terrestrial mass is constantly changing under the influence of erosion and that the Earth is continually moving so as to bring this centre of gravity to the centre of the World. These small, incessant motions eventually bring to the surface of the continents those portions of earth that once occupied the bed of the ocean and, to place this assertion of Albert of Saxony beyond the range of doubt, Vinci devoted himself to the study of fossils and to extremely cautious observations which made him the creator of Stratigraphy. In many passages in his notes Vinci asserts, like Nicholas of Cusa that the moon and the other wandering stars are worlds analogous to ours, that they carry seas upon their surfaces, and are surrounded by air; and the development of this opinion led him to talk of the gravity binding to each of these stars the elements that belonged to it. On the subject of this gravity he professed a theory similar to Oresme's. Hence it would seem that, in almost every particular, Vinci was a faithful disciple of the great Parisian masters of the fourteenth century, of Buridan, Albert of Saxony, and Oresme.
Whilst, through the anti-Peripatetic influence of the School of Paris, Vinci reaped a rich harvest of discoveries, innumerable Italians devoted themselves to the sterile worship of defunct ideas with a servility that was truly astonishing. The Averroists did not wish to acknowledge as true anything out of conformity with the ideas of Aristotle as interpreted by Averroës; with Pompanazzi (1462-1526), the Alexandrists, seeking their inspiration further back in the past, refused to understand Aristotle otherwise than he had been understood by Alexander of Aphrodisias; and the Humanists, solicitous only for purity of form, would not consent to use any technical language whatever and rejected all ideas that were not sufficiently vague to be attractive to orators and poets; thus Averroists, Alexandrists, and Humanists proclaimed a truce to their vehement discussions so as to combine against the "language of Paris", the "logic of Paris", and the "physics of Paris". It is difficult to conceive the absurdities to which these minds were led by their slavish surrender to routine. A great number of physicists, rejecting the Parisian theory of impetus, returned to the untenable dynamics of Aristotle, and maintained that the projectile was moved by the ambient air. In 1499 Nicolò Vernias of Chieti, an Averroist professor at Padua, taught that if a heavy body fell it was in consequence of the motion of the air surrounding it.
A servile adoration of Peripateticism prompted many so-called philosophers to reject the Ptolemaic system, the only one which, at that time, could satisfy the legitimate exigencies of astronomers, and to readopt the hypothesis of homocentric spheres. They held as null and void the innumerable observations that showed changes in the distance of each planet from the Earth. Alessandro Achillini of Bologna (1463-1512), an uncompromising Averroist and a strong opponent of the theory of impetus and of all Parisian doctrines, inaugurated, in his treatise "De orbibus" (1498), a strange reaction against Ptolemaic astronomy; Agostino Nifo (1473-1538) laboured for the same end in a work that has not come down to us; Girolamo Fracastorio (1483-1553) gave us, in 1535, his book "De homocentricis", and Gianbattista Amico (1536), and Giovanni Antonio Delfino (1559) published small works in an endeavour to restore the system of homocentric spheres.
Although directed by tendencies diametrically opposed to the true scientific spirit, the efforts made by Averroists to restore the astronomy of homocentric spheres were perhaps a stimulus to the progress of science, inasmuch as they accustomed physicists to the thought that the Ptolemaic system was not the only astronomical doctrine possible, or even the best that could be desired. Thus, in their own way, the Averroists paved the way for the Copernican revolution. The movements forecasting this revolution were noticeable in the middle of the fourteenth century in the writings of Nicholas of Cusa, and in the beginning of the fifteenth century in the notes of Vinci, both of these eminent scientists being well versed in Parisian physics.
Celio Calcagnini proposed, in his turn, to explain the daily motion of the stars by attributing to the Earth a rotation from West to East, complete in one sidereal day. His dissertation, "Quod c lum stet, terra vero moveatur", although seeming to have been written about 1530, was not published until 1544, when it appeared in a posthumous edition of the author's works. Calcagnini declared that the Earth, originally in equilibrium in the centre of the universe, received a first impulse which imparted to it a rotary motion, and this motion, to which nothing was opposed, was indefinitely preserved by virtue of the principle set forth by Buridan and accepted by Albert of Saxony and Nicholas of Cusa. According to Calcagnini the daily rotation of the Earth was accompanied by an oscillation which explained the movement of the precession of the equinoxes. Another oscillation set the waters of the sea in motion and determined the ebb and flow of the tides. This last hypothesis was to be maintained by Andrea Cesalpino (1519-1603) in his "Quæstiones peripateticæ" (1569), and to inspire Galileo, who, unfortunately, was to seek in the phenomena of the tides his favourite proof of the Earth's rotation.
The "De revolutionibus orbium c lestium libri sex" were printed in 1543, a few months after the death of Copernicus (1473-1543), but the principles of the astronomic system proposed by this man of genius had been published as early as 1539 in the "Narratio prima" of his disciple, Joachim Rhæticus (1514-76). Copernicus adhered to the ancient astronomical hypotheses which claimed that the World was spherical and limited, and that all celestial motions were decomposable into circular and uniform motions; but he held that the firmament of fixed stars was immovable, as also the sun, which was placed in the centre of this firmament. To the Earth he attributed three motions: a circular motion by which the centre of the Earth described with uniform velocity a circle situated in the plane of the ecliptic and eccentric to the sun; a daily rotation on an axis inclined towards the ecliptic, and finally, a rotation of this axis around an axis normal to the ecliptic and passing through the centre of the Earth. The time occupied by this last rotation was a little longer than that required for the circular motion of the centre of the Earth which produced the phenomenon of the precession of the equinoxes. To the five planets Copernicus ascribed motions analogous to those with which the Earth was provided, and he maintained that the moon moved in a circle around the Earth.
Of the Copernican hypotheses, the newest was that according to which the Earth moved in a circle around the sun. From the days of Aristarchus of Samos and Seleucus no one had adopted this view. Medieval astronomers had all rejected it, because they supposed that the stars were much too close to the Earth and the sun, and that an annual circular motion of the Earth might give the stars a perceptible parallax. Still, on the other hand, we have seen that various authors had proposed to attribute to the Earth one or the other of the two motions which Copernicus added to the annual motion. To defend the hypothesis of the daily motion of the Earth against the objections formulated by Peripatetic physics, Copernicus invoked exactly the same reasons as Oresme, and in order to explain how each planet retains the various parts of its elements, he adopted the theory of gravity proposed by the eminent master. Copernicus showed himself the adherent of Parisian physics even in the following opinion, enunciated accidentally: the acceleration of the fall of heavy bodies is explained by the continual increase which impetus receives from gravity.
Copernicus and his disciple Rhæticus very probably regarded the motions which their theory ascribed to the Earth and the planets, the sun's rest and that of the firmament of fixed stars, as the real motions or real rest of these bodies. The "De revolutionibus orbium cælestium libri sex" appeared with an anonymous preface which inspired an entirely different idea. This preface was the work of the Lutheran theologian Osiander (1498-1552), who therein expressed the opinion that the hypotheses proposed by philosophers in general, and by Copernicus in particular, were in no wise calculated to acquaint us with the reality of things: "Neque enim necesse est eas hypotheses esse veras, imo, ne verisimiles quidem, sed sufficit hoc unum si calculum observationibus congruentem exhibeant". Osiander's view of astronomical hypotheses was not new. Even in the days of Grecian antiquity a number of thinkers had maintained that the sole object of these hypotheses was to "save appearances", sozein ta phainomena; and in the Middle Ages, as well as in antiquity, this method continued to be that of philosophers who wished to make use of Ptolemaic astronomy whilst at the same time upholding the Peripatetic physics absolutely incompatible with this astronomy. Osiander's doctrine was therefore readily received, first of all by astronomers who, without believing the Earth's motion to be a reality, accepted and admired the kinetic combinations conceived by Copernicus, as these combinations provided them with better means than could be offered by the Ptolemaic system for figuring out the motion of the moon and the phenomena of the precession of the equinoxes.
One of the astronomers who most distinctly assumed this attitude in regard to Ptolemy's system was Erasmus Reinhold (1511-53), who, although not admitting the Earth's motion, professed a great admiration for the system of Copernicus and used it in computing new astronomical tables, the "Prutenicæ tabulæ" (1551), which were largely instrumental in introducing to astronomers the kinetic combinations originated by Copernicus. The "Prutenicæ tabulæ" were especially employed by the commission which in 1582 effected the Gregorian reform of the calendar. Whilst not believing in the Earth's motion, the members of this commission did not hesitate to use tables founded on a theory of the precession of the equinoxes and attributing a certain motion to the earth.
However, the freedom permitting astronomers to use all hypotheses qualified to account for phenomena was soon restricted by the exigencies of Peripatetic philosophers and Protestant theologians. Osiander had written his celebrated preface to Copernicus's book with a view to warding off the attacks of theologians, but in this he did not succeed. Martin Luther, in his "Tischrede", was the first to express indignation at the impiety of those who admitted the hypothesis of solar rest. Melanchthon, although acknowledging the purely astronomical advantages of the Copernican system, strongly combatted the hypothesis of the Earth's motion (1549), not only with the aid of arguments furnished by Peripatetic physics but likewise, and chiefly, with the assistance of numerous texts taken from Holy Writ. Kaspar Peucer (1525-1602), Melanchthon's son-in-law, whilst endeavouring to have his theory of the planets harmonize with the progress which the Copernican system had made in this regard, nevertheless rejected the Copernican hypotheses as absurd (1571).
It then came to be exacted of astronomical hypotheses that not only, as Osiander had desired, the result of their calculations be conformable to facts, but also that they be not refuted "either in the name of the principles of physics or in the name of the authority of the Sacred Scriptures". This criterion was explicitly formulated in 1578 by a Lutheran, the Danish astronomer Tycho Brahe (1546-1601), and it was precisely by virtue of these two requirements that the doctrines of Galileo were to be condemned by the Inquisition in 1616 and 1633. Eager not to admit any hypothesis that would conflict with Aristotelean physics or be contrary to the letter of the Sacred Scriptures, and yet most desirous to retain all the astronomical advantages of the Copernican system, Tycho Brahe proposed a new system which virtually consisted in leaving the Earth motionless and in moving the other heavenly bodies in such a way that their displacement with regard to the Earth might remain the same as in the system of Copernicus. Moreover, although posing as the defender of Aristotelean physics, Tycho Brahe dealt it a disastrous blow. In 1572 a star, until then unknown, appeared in the constellation of Cassiopeia, and in showing accurate observations that the new astral body was really a fixed star, Tycho Brahe proved conclusively that the celestial world was not, as Aristotle would have had us believe, formed of a substance exempt from generation and destruction.
The Church had not remained indifferent to the hypothesis of the Earth's motion until the time of Tycho Brahe, as it was amongst her members that this hypothesis had found its first defenders, counting adherents even in the extremely orthodox University of Paris. At the time of defending this hypothesis, Oresme was Canon of Rouen, and immediately after he was promoted to the Bishopric of Lisieux; Nicholas of Cusa was Bishop of Brixen and cardinal, and was entrusted with important negotiations by Eugenius IV, Nicholas V, and Pius II; Calcagnini was prothonotary Apostolic; Copernicus was Canon of Thorn, and it was Cardinal Schomberg who urged him to publish his work, the dedication of which was accepted by Paul III. Besides, Oresme had made clear how to interpret the Scriptural passages claimed to be opposed to the Copernican system, and in 1584 Didacus a Stunica of Salamanca found in Holy Writ texts which could be invoked with just as much certainty in favour of the Earth's motion. However, in 1595 the Protestant senate of the University of Tübingen compelled Kepler to retract the chapter in his "Mysterium cosmographicum", in which he had endeavoured to make the Copernican system agree with Scripture.
Christopher Clavius (1537-1612), a Jesuit, and one of the influential members of the commission that reformed the Gregorian Calendar, seemed to be the first Catholic astronomer to adopt the double test imposed upon astronomical hypotheses by Tycho Brahe, and to decide (1581) that the suppositions of Copernicus were to be rejected, as opposed both to Peripatetic physics and to Scripture; on the other hand, at the end of his life and under the influence of Galileo's discoveries, Clavius appeared to have assumed a far more favourable attitude towards Copernican doctrines. The enemies of Aristotelean philosophy gladly adopted the system of Copernicus, considering its hypotheses as so many propositions physically true, this being the case with Pierre de La Ramée, called Petrus Ramus (1502-72), and especially with Giordano Bruno (about 1550-1600). The physics developed by Bruno, in which he incorporated the Copernican hypothesis, proceeded from Nicole Oresme, and Nicholas of Cusa; but chiefly from the physics taught in the University of Paris in the fourteenth century. The infinite extent of the universe and the plurality of worlds were admitted as possible by many theologians at the end of the thirteenth century, and the theory of the slow motion which gradually causes the central portions of the Earth to work to the surface had been taught by Albert of Saxony before it attracted the attention of Vinci. The solution of Peripatetic arguments against the Earth's motion and the theory of gravity called forth by the comparison of the planets with the Earth would appear to have been borrowed by Bruno from Oresme. The apostasy and heresies for which Bruno was condemned in 1600 had nothing to do with the physical doctrines he had espoused, which included in particular Copernican astronomy. In fact it does not seem that, in the sixteenth century, the Church manifested the slightest anxiety concerning the system of Copernicus.
It is undoubtedly to the great voyages that shed additional lustre on the close of the fifteenth century that we must attribute the importance assumed in the sixteenth century by the problem of the tides, and the great progress made at that time towards the solution of this problem. The correlation existing between the phenomenon of high and low tide and the course of the moon was known even in ancient times. Posidonius accurately described it; the Arabian astronomers were also familiar with it, and the explanation given of it in the ninth century by Albumazar in his "Introductorium magnum ad Astronomiam" remained a classic throughout the Middle Ages. The observation of tidal phenomena very naturally led to the supposition that the moon attracted the waters of the ocean and, in the thirteenth century, William of Auvergne compared this attraction to that of the magnet for iron. However, the mere attraction of the moon did not suffice to account for the alternation of spring and neap tides, which phenomenon clearly indicated a certain intervention of the sun. In his "Questions sur les livres des Météores", which appeared during the latter half of the fourteenth century, Themon, "Son of the Jew", introduced in a vague sort of way the idea of superposing two tides, the one due to the sun and the other to the moon.
In 1528 this idea was very clearly endorsed by Federico Grisogone of Zara, a Dalmatian who taught medicine at Padua. Grisogone declared that, under the action of the moon exclusively, the sea would assume an ovoid shape, its major axis being directed towards the centre of the moon; that the action of the sun would also give it an ovoid shape, less elongated than the first, its major axis being directed towards the centre of the sun; and that the variation of sea level, at all times and in all places, was obtained by adding the elevation or depression produced by the solar tide to the elevation or depression produced by the lunar tide. In 1557 Girolamo Cardano accepted and briefly explained Grisogone's theory. In 1559 a posthumous work by Delfino gave a description of the phenomena of the tides, identical with that deduced from the mechanism conceived by Grisogone. The doctrine of the Dalmatian physician was reproduced by Paolo Gallucci in 1588, and by Annibale Raimondo in 1589; and in 1600 Claude Duret, who had plagiarized Delfino's treatise, published in France the description of the tides given in that work.
When writing on statics Cardano drew upon two sources, the writings of Archimedes and the treatises of the School of Jordanus; besides, he probably plagiarized the notes left by Vinci, and it was perhaps from this source that he took the theorem: a system endowed with weight is in equilibrium when the centre of gravity of this system is the lowest possible.
Nicolo Tartaglia (about 1500-57), Cardano's antagonist, shamelessly purloined a supposedly forgotten treatise by one of Jordanus's commentators. Ferrari, Cardano's faithful disciple, harshly rebuked Tartaglia for the theft, which nevertheless had the merit of re-establishing the vogue of certain discoveries of the thirteenth century, especially the law of the equilibrium of a body supported by an inclined plane. By another and no less barefaced plagiarism, Tartaglia published under his own name a translation of Archimedes's "Treatise on floating bodies" made by William of Moerbeke at the end of the thirteenth century. This publication, dishonest though it was, helped to give prominence to the study of Archimedes's mechanical labours, which study exerted the greatest influence over the progress of science at the end of the sixteenth century, the blending of Archimedean mathematics with Parisian physics, generating the movement that terminated in Galileo's work. The translation and explanation of the works of Archimedes enlisted the attention of geometricians such as Francesco Maurolycus of Messina (1494-1575) and Federico Commandino of Urbino (1509-75), and these two authors, continuing the work of the great Syracusan, determined the position of the centre of gravity of various solids; in addition Coinmandin translated and explained Pappus's mathematical "Collection", and the fragment of "Mechanics" by Heron of Alexandria appended thereto. Admiration for these monuments of ancient science inspired a number of Italians with a profound contempt for medieval statics. The fecundity of the principle of virtual displacements, so happily employed by the School of Jordanus, was ignored; and, deprived of the laws discovered by this school and of the additions made to them by Vinci, the treatises on statics written by over-enthusiastic admirers of the Archimedean method were notably deficient. Among the authors of these treatises Guidobaldo dal Monte (1545-1607) and Giovanni Battista Benedetti (1530-90) deserve special mention.
Of the mathematicians who, in statics, claimed to follow exclusively the rigorous methods of Archimedes and the Greek geometricians, the most illustrious was Simon Stevinus of Bruges (1548-1620). Through him the statics of solid bodies recovered all that had been gained by the School of Jordanus and Vinci, and lost by the contempt of such men as Guidobaldo del Monte and Benedetti. The law of the equilibrium of the lever, one of the fundamental propositions of which Stevinus made use, was established by him with the aid of an ingenious demonstration which Galileo was also to employ, and which is found in a small anonymous work of the thirteenth century. In order to confirm another essential principle of his theory, the law of the equilibrium of a body on an inclined plane, Stevinus resorted to the impossibility of perpetual motion, which had been affirmed with great precision by Vinci and Cardano. Stevinus's chief glory lay in his discoveries in hydrostatics; and the de