Works About The History Of Science

"Aristotle... in the Metaphysics, Book XII, Chapter 8... built... the most sublime part of his philosophy... concerning the gods... who... sends his students to the astronomers and who defers to the astronomers in respect to their authority and... testitimony...[H]e would never have scorned or... myself, if... necessity... had made us contemporaries. For he orders his students "to read through both,"...[i.e.,] Eudoxus and , for the one had corrected the errors of the other; and today that would be to read both Ptolemy and Tycho: "but to follow" not, he says, the more ancient, but "the more accurate." And so... if the astronomer, using the arguments which modern times have put forward concerning the heavens, has indicated that creatures arose in the heavens and will disappear once more—in opposition to the opinion of him who alleges experience, but experience not sufficiently long."

"Accordingly, if certain subtleties which are difficult to grasp should not be laid before beginners, or if they should not be preferred to the accepted and necessary teachings, it does not follow that... those things should neither be written nor read privately."

"[T]he truth concerning the mutable nature of the heavens can be taught conveniently... [I]t is not without its use in explaining even those parts of the philosophy of Aristotle which are clearly false, as Book VIII of the Physics concerning celestial movement and Book II of On the Heavens concerning the eternity of the heavens—so... a comparison could be made between the philosophy of the gentiles and the truth of Christian dogma."

"Why do you call them the proper movements of the planets? 1. Because the apparent daily movement—with which the doctrine on the sphere is concerned—and which is common to both the planets and the fixed stars, and so to the whole world, is seen to travel from the east to the west; but the far slower single movements of the single planets travel in the opposite direction from west to east; and therefore it is certain that these movements cannot depend upon that common movement of the world—which we have discussed so far—but should be assigned to the planets themselves, and thus they are generically proper to the planets."

"[T]his work of mine, the Harmonies, is nothing except... a certain picture of the edifice of astronomy; and though it may be erased at the pleasure of him who spits upon it, nevertheless the house called astronomy stands by itself: and I know that astronomy is not condemned by His Most Serene Highness but is held of great value on account of its certitude in predicting movements: perhaps, therefore, he will judge its architect—who is almost the only renovator after the Master Tycho and who thought it worth while to devote his life to this work—to be not unworthy of his favour."

"But this kind of argument against Aristotle will perhaps seem too contentious. Therefore let us use his own testimony... for he is not everywhere consistent: in the Metaphysics he attributes movement to the celestial bodies for its own sake and teaches "that they are moved in order that they may be moved"; but in On the Heavens, being admonished by the things themselves, he attributes something... like the terrestrial... multiplex and turbulent to the stars or... their movers, who by... these mechanisms and movements seek another end... in this way... he adduces the fewness of movements in the moon as... the inferior... closer kinship to the Earth."

"State the opinion of the ancient astronomers as to how the planets move. The ancients, Eudoxus and , and their follower Ptolemy did not advance beyond circles... for in Book XIII of the ', Chapter 2, Ptolemy writes as follows:"But let no one judge that these interweavings of circles which we postulate are difficult, on the ground that... manual imitation of these interweavings is... intricate. For it is not right for our human things to be compared on a basis of equality with the immortal gods, and for us to seek the evidence for very lofty things from examples of very unlike things. ...Indeed we must try hard to fit the most simple hypotheses to the celestial movements... but if that is not successful, whatever sort of hypotheses can be used. ...[W]e should not judge what is simple in celestial bodies by the examples of things which seem to us to be simple ...For ...he who wishes to judge celestial things in this way will not recognize as simple any of those movements which take place in the heavens, not even the invariable constancy of the first movement: because it is ...impossible to find among men this thing (namely, something which stays in the same state perpetually). Therefore we must not form our judgement upon terrestrial things, but upon the natures of the things which are in the heavens and upon the unchanging steadfastness of their movements. So... in this way all the movements are seen to be simple, and much more simple than those movements which seem to us to be simple. For we are unable to suspect them of any labor or any difficulty in their revolutions." So [says] Ptolemy."

"[T]he philosophers speak of the visible heavens; and Christ of the invisible heavens, or, as the schools say, of the , or, as the simple Christians take it, of the blessed seats, which no corruption will ever touch: since not Tycho, not I, but Christ Himself pronounces concerning this visible world: "Heaven and Earth shall pass away," and the Psalmist, "they shall grow old like a garment"; and Peter, "They shall be destroyed root and all, and be consumed by burning in the fire.""

"[F]or me there is so much importance in the true doctrine of others or even in correcting the doctrines which are not... well established, that my mind is never at leisure for the game of inventing new doctrines that are contrary to the true."

"What is the subject of the doctrine of the schemata? The proper movements of the planets; we call them the secondary movements; and the planets, the secondary movables."

"The Epitome Astronomiae Copernicanae, contains much of the material from Kepler's earlier works... It was written for a more general audience, and... gained a relatively wide readership. ...[Here] Kepler's mature physics, metaphysics, and astronomy were presented together for the first time. ...[I]t is an invaluable resource for exploring the evolution of Kepler's thought, fleshing out his conception of the relationship between physics, metaphysics, and astronomy, and—since... intended as a textbook—uncovering what Kepler believed he needed to do to promote his new astronomy."

"Why do you say that a celestial body, which is unchanging with respect to its matter, cannot be moved by assent alone? For if the celestial bodies are neither heavy nor light, but most suited for circular movement, then do they resist the motor mind? Even if a celestial globe is not heavy in the way in which a stone on the earth is... and is not light in the way in which among us fire is... nevertheless by reason of its matter it has a natural... powerlessness of crossing from place to place, and it has a natural inertia or rest whereby it rests... where it is placed alone. ...[I]n order that it may be moved out of its... rest, it has need of some power... stronger than its matter and its naked body, and which should overcome its natural inertia. For such a faculty is above the capacity of nature and is a sprout of form, or a sign of life."

"[B]ecause certain people cannot grasp the subtleties of things, they lay the charge of novelty-hunting upon me."

"[I]t would be first in my program... to warn... of the distinction between the love—or thirst, to use the Aristotelian word—for the knowledge of natural things and the lust for contradicting and holding the opposite opinion. All philosophers... and all the poets... recognize a divine ravishment in investigating the works of God: and not merely in investigating them privately but even in teaching them publicly: and... the false charge of esoteric novelty-hunting cannot cling to this ravishment.There is God in us, and our warmth comes from His movements: This Spirit has descended from the heavenly seats."

"And that will occur in order that the alterations in the heavens should not destroy their eternity, if there should be such an eternity, just as the terrestrial alterations, which are perrennial and return in a circle, destroy the Earth’s eternity which was equally believed by Aristotle."

"Aristotle is the man... who in On the Heavens... Chapter 9... asks: "Do the stars give forth sounds which are modulated harmonically? and answers no: ...I grant that no sounds are given forth but I affirm and demonstrate that the movements are modulated according to harmonic proportions."

"As regards the academies, they are... concerned not to have the program of teaching change very often... the things which have to be chosen are not those which are most true but those which are most easy."

"You can count few academies in which it is a part of the program to explain the Metaphysics of Aristotle: yet Aristotle wrote the Metaphysics too, a very useful work..."

"[T]he boundary posts of investigation should not be set up in the narrow minds of a few... "The world is a petty thing, unless everyone finds the whole world in that which he is seeking," as Seneca says. ...[T]he boundary posts of true speculation are the same as those of the fabric of the world; but the Christian religion has put up some fences around false speculation... in order that error may not rush headlong but may become... harmless..."

"I build my whole astronomy upon Copernicus' hypotheses concerning the world, upon the observations of , and lastly upon the Englishman, William Gilbert's philosophy of magnetism."

"[T]he following thesis is upheld by incontrovertible demonstrations: that in the farthest movements of any two planets, the universe was stamped with the adornment of harmonic proportions; and, accordingly, in order that this adornment might be brought into concord with the movements, the eccentricities which fell to the lot of each planet had to be brought into concord. ...[H]ow great an addition this makes in illustrating the glory of the fabric of the world, and of God the Architect."

"These extracts from the letter, most of which have to do with the investigation of very hidden causes which is to be viewed in this little book, should be spoken and understood. And now it is time for the reader to pass on to the little book."

"By what reasons are you led to make the sun the moving cause or the source of movement for the planets? 1. Because it is apparent that in so far as any planet is more distant from the sun... it moves the more slowly—so that the ratio of the periodic times is the ratio of the 34th powers of the distances from the sun. Therefore we reason from this that the sun is the source of movement. 2. Below we shall hear the same... use in the case of the single planets—so that the closer any one planet approaches the sun during any time, it is borne with an increase of velocity in exactly the ratio of the square.3. Nor is the dignity or the fitness of the solar body opposed to this, because it is... beautiful... of a perfect roundness... very great and is the source of light and heat, whence all life flows out into the vegetables: to such an extent that heat and light can be judged to be... instruments fitted to the sun for causing movement in the planets. 4. But in especial... the sun’s rotation in its own space around its immobile axis, in the same direction in which all the planets proceed: and in a shorter period than Mercury, the nearest to the sun and fastest of all the planets."

"The most interesting person in this group of Pythagoreans was... Kepler... a technical astronomer well versed in the mathematical arcana of the subject, who knew how to construct an... argument on the basis of observations. ...[A] ...style of argument ...reveals an underlying view of the world similar to... Fludd and Kircher. Kepler recognized harmonies... as correspondences among the different parts of the universe. ...[I]n arguing for Copernican cosmology—the central sun, the outer sphere of the fixed stars, and the intermediate region of the planets—with the Trinity. Kepler... compare[d] the sun with the common sense of animals... in the head, the globes that surround the sun with... sense organs, and the fixed stars with sensible objects. He... compared the sun with the central fireplace... the heart of the world, the seat of reason and life... reminiscent of... Paracelsus and the chymical philosophers..."

"For... it is disclosed by the telescope... and can be seen... that the solar body is covered with spots, which cross the disk of the sun or its lower hemisphere within 12 or 13 or 14 days, slowly at the beginning and at the end, but rapidly in the middle, which argues that they are stuck to the surface of the sun and turn with it..."

"Then what is it which makes the planets move around the sun, each planet within the boundaries of its own region, if there are not any solid spheres, and if the globes themselves cannot be fastened to anything else and made to stick there, and if without solid spheres they cannot be moved from place to place by any soul? Even if things are very far removed from us and... are difficult to explain and give rise to... uncertain judgements... if we follow probability and... not to postulate anything... contrary to us, it will... be clear that no mind is to be introduced which should turn the planets by the dictation of reason and... that no soul is to be put in charge of this revolution, in order that it should impress something into the globes by the balanced contest of the forces, as takes place in the revolution around the axis; but that there is one only solar body, which is situated at the centre of the whole universe, and to which this movement of the primary planets around the body of the sun can be ascribed."

"[I]f... even this inquiry is accused of being esoteric... the head of astronomy is struck off. And since astronomy is studied either for its own sake as a philosophy or for the sake of making astronomical predictions... the taking away from me of the primary end slays this whole subtle astronomy and plainly makes it useless."

"I now descend to the work... the Harmonies... [H]e who condemns the itch to devise new things and the presumption to profess new and grandiose things will find in the epilogue to the Fifth Book that which he will mark critically. For here the sun-spots and little flames are brought forward as evidence of there being exhalations from the sun which are analogous to exhalations from the Earth: here things corresponding to the generation of animals... in the planets—here the confines of the mysteries of Christian religion are touched: we knock at the doors of the science of the , of , of the idolatry of the Persians, and of those who worship the sun as god—as the interjection of frequent warnings does not dissimulate. ...[R]eason ...leads "from the Muses to Apollo": nevertheless, since the other parts of the work are established by means of their proper demonstrations, the chapter, or epilogue, can be considered as cut off from the rest."

"I even in private free myself from the blame of seeking after novelty by suitable proofs: let my doctrines say whether there is love of truth in me or love of glory: for most of the ones I hold have been taken from other writers..."

"Antiquity teaches us... how vainly man sets up boundary posts where God has not set them... how severely all the astronomers were blamed by the first Christians. ...Yet today we set up academies everywhere: we order that philosophy be taught, that astronomy be taught, that the antipodes be taught."

"Astronomers should not be granted excessive license to conceive anything they please without reason: on the contrary, it is also necessary for you to establish the probable causes of your Hypotheses which you recommend as the true causes of the Appearances. Hence you must first establish the principles of your Astronomy in a higher science, namely Physics and Metaphysics."

"I... led on by... thirst for philosophy, first wiped away from the eyes of astronomy those mists of the multiplicity of movements in the single planets: then I gave a demonstration... that the movement of the planet is not uniform throughout its whole circuit—as Aristotle argued in Chapters 6 and 7; but that... the movement is increased and decreased at places in its period which are fixed and are opposite to one another; and I explained the efficient or instrumental causes... between the planet and the sun... as from what source..."

"It has been ten years since I published my Commentaries on the Movements of the Planet Mars. As only a few copies of the book were printed, and as it had so to speak hidden the teaching about celestial causes in thickets of calculations and the rest of the astronomical apparatus, and since the more delicate readers were frightened away by the price... too; it seemed... that I should be doing right and fulfilling my responsibilities, if I should write an epitome, wherein a summary of both the physical and astronomical teaching concerning the heavens would be set forth in plain and simple speech and with the boredom of the demonstrations alleviated."

"[A] comparison was undertaken between this book—or the related work On the Harmonies...—and Aristotle's books ' and Metaphysics... I have nothing to worry about in the case of Aristotle... His Most Serene Highness cannot dislike whatever is the more convincing, whether it be that the world was first made at a fixed beginning in time as was my work On the Harmonies, or will be destroyed at some time, or is merely liable to destruction, like the alterations of the ether and the celestial atmosphere; nor will he ever prefer the Master Aristotle to the truth of which Aristotle was ignorant."

"Then, as in each and every planet there is a very fast movement and a very slow movement and in a fixed proportion... and... Saturn and Jupiter have middling eccentricities, Mars a great eccentricity, the Sun and Venus slight eccentricities, and Mercury a very great eccentricity... I also brought forward a solution... and I took my solution from the Archetype of the harmonic cosmos: whence it is established that this cosmos cannot be better... and that it is impossible that the world should not have been created at a fixed beginning in time. This attempt of mine... should have been brought forth into the light with strength of mind... the highest confidence in the visible works of God... or at the exhortation of Aristotle himself, who judged that in these questions you should not suppress or be silent about probabilities any more than... certainties."

"Like the crests on the heads of peacocks, like the gems on the hoods of the cobras, mathematics is at the top of the Vedanga s."

"Samasya dwikaraṇi pramāṇam tṛtīyena vardhayettacca caturthenātmacatustriṃśonena saviśeṣaḥ."

"[I]t is one of the mistakes of scholars to believe that they are the sole transmitters of knowledge. ...[T]he characters, the methods of calculating, the improvements that took place from time to time, the zero when it appeared, and the customs as to solving business problems, would all have been made known from generation to generation along... trade routes from the Orient to the Occident. [I]t was to the tradesman and the wandering scholar that the spread of such learning was due, rather than to the school man."

"The numerals had existed, without the zero, for several centuries; they had been well known in India; there had been a continued interchange of thought between the East and West; and warriors, ambassadors, scholars, and the restless trader, all had gone back and forth, by land or more frequently by sea, between the Mediterranean lands and the centers of Indian commerce and culture. Boethius could very well have learned one or more forms of Hindu numerals from some traveler or merchant."

"Avicenna (980-1037 a.d.)... relates that when his people were living at Bokhara his father sent him to the house of a grocer to learn the Hindu art of reckoning, in which this grocer (oil dealer, possibly) was expert. Leonardo of Pisa, too, had a similar training."

"The Indian use of subscript dots to indicate the tens, hundreds, thousands, etc., is established by a passage in the Kitāb al-Fihrist (987 A.D.)... The numeral forms given are those which have usually been called Indian, in opposition to ģobār. In this document the dots are placed below the characters, instead of being superposed... The significance was the same."

"When we consider... that the dot is found for zero in the Bakhsālī manuscript, and that it was used in subscript form in the Kitāb al-Fihrist in the tenth century... we are forced to believe that this form may also have been of Hindu origin."

"Anicius Manlius Severinus Boethius was born at Rome c. 475. Not many generations after his death, the period being one in which historical criticism was at its lowest ebb, the church found it profitable to look upon his execution as a martyrdom. He was accordingly looked upon as a saint, his bones were enshrined, and as a natural consequence his books were among the classics in the church schools for a thousand years. It is pathetic, however, to think of the medieval student trying to extract mental nourishment from a work so abstract, so meaningless, so unnecessarily complicated, as the arithmetic of Boethius."

"It could not have been at all unusual for the ancient Greeks to go to India, for Strabo lays down the route, saying that all who make the journey start from and traverse and before taking the direct road. The products of the East were always finding their way to the West, the Greeks getting their ginger from Malabar, as the Phoenicians had long before brought gold from Malacca."

"Woepcke points out that the Arabs on entering Spain (711 A.D.) would naturally have followed their custom of adopting for the computation of taxes the numerical systems of the countries they conquered... The theory is that the Hindu system, without the zero, early reached Alexandria (say 450 a.d.), and that the Neo-Pythagorean love for the mysterious and... the Oriental led to its use... that it was then passed along the Mediterranean, reaching Boethius in Athens or in Rome, and to the schools of Spain, being discovered in Africa and Spain by the Arabs even before they themselves knew the improved system with the place value."

"[W]e are uncertain as to the time and place of [the] introduction [of these numeral forms] into Europe. There are two general theories... The first is that they were carried by the Moors to Spain in the eighth or ninth century, and thence were transmitted to Christian Europe... The second, advanced by Woepcke, is that they... were already in Spain when the Arabs arrived there, having reached the West through the Neo-Pythagoreans. There are two facts to support this second theory: (1) the forms of these numerals are characteristic, differing materially from those which were brought by Leonardo of Pisa from Northern Africa early in the thirteenth century (before 1202 a.d.); (2) they are essentially those which tradition has so persistently assigned to Boethius (c. 500 A.D.), and which he would naturally have received, if at all, from these same Neo-Pythagoreans or from the sources from which they derived them."

"Bubnov holds that the forms first found in Europe are derived from ancient symbols used on the abacus, but that the zero is of Hindu origin. This theory does not seem tenable..."

"Sir Edwin Arnold, in The Light of Asia... speaks of Buddha’s training at the hands of the learned : "And Viswamitra said, 'It is enough, Let us to numbers. After me repeat Your numeration till we reach the lakh, One, two, three, four, to ten, and then by tens To hundreds, thousands.’ After him the child Named digits, decads, centuries, nor paused, The round lakh reached, but softly murmured on, Then comes the koti, nahut, ninnahut, Khamba, viskhamba, abab, attata, To kumuds, gundhikas, and utpalas, By pundarikas into padumas, Which last is how you count the utmost grains Of Hastagiri ground to finest dust; But beyond that a numeration is, The Kātha, used to count the stars of night, The Kōti-Kātha, for the ocean drops; Ingga, the calculus of circulars; Sarvanikchepa, by the which you deal With all the sands of Gunga, till we come To Antah-Kalpas, where the unit is The sands of the ten crore Gungas. If one seeks More comprehensive scale, th’ arithmic mounts By the Asankya, which is the tale Of all the drops that in ten thousand years Would fall on all the worlds by daily rain; Thence unto Maha Kalpas, by thé which the gods compute their future and their past.'""

"Thereupon Ācārya expresses his approval... and asks to hear the "measure of the line" as far as yōjana, the longest measure bearing name. This given, Buddha adds: ..." 'And master! If it please, I shall recite how many sun-motes lie From end to end within a yōjana.’ Thereat, with instant skill, the little prince Pronounced the total of the atoms true. But Viswamitra heard it on his face Prostrate before the boy; 'For thou,' he cried, 'Art Teacher of thy teachers—thou, not I, Art Guru.' ""

"[I]n the history of ancient India... primary schools... existed in earliest times, and of the seventy-two recognized sciences writing and arithmetic were the most prized. In the Vedic period [~]2000 to 1400 B.C., there was the same attention to astronomy that was found in the earlier civilizations of Babylon, China, and Egypt... Such advance... presupposes a fair knowledge of calculation, but of the manner of calculating we are quite ignorant..."