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PREFACE TO THE PHILOSOPHIAE NATURALIS PRINCIPIA MATHEMATICA
BY SIR ISAAC NEWTON. (1686)
YINCE the ancients (as we are told by Pappus) made
great account of the science of mechanics in the in
vestigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavored to subject the phenomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy. The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he
Sir Isaac Newton, the great English mathematician and physicist, was born at Woolsthorpe in 1642, and died at Kensington in 1727. He held a professorship at Cambridge, represented the University in Parliament, as master of the mint reformed the English coinage, and for twenty-five years was president of the Royal Society. His theory of the law of universal gravitation, the most important of his many discoveries, is expounded in his “ Philosophiae Naturalis Principia Mathematica," usually known merely as the “ Principia," from which this Preface is translated.
circles. Geometr be drawne'scribe these acician and parties held
enters upon geometry; then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, fetched from without, it is able to produce so many things. Therefore geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts are chiefly conversant in the moving of bodies, it comes to pass that geometry is commonly referred to their magnitudes, and mechanics to their motion. In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. This part of mechanics was cultivated by the ancients in the five powers which relate to manual arts, who considered gravity (it not being a manual power) no otherwise than as it moved weights by those powers. Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the system of the World; for by the propositions mathematically demonstrated in the first book, we there derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.
In the publication of this work, the most acute and universally learned Mr. Edmund Halley not only assisted me with his pains in correcting the press and taking care of the schemes, but it was to his solicitations that its becoming public is owing; for when he had obtained of me my demonstrations of the figure of the celestial orbits, he continually pressed me to communciate the same to the Royal Society, who afterwards, by their kind encouragement and entreaties, engaged me to think of publishing them. But after I had begun to consider the inequalities of the lunar motions, and had entered upon some other things relating to the laws and measures of gravity, and other forces; and the figures that would be described by bodies attracted according to given laws; and the motion of several bodies moving among themselves; the motion of bodies in resisting mediums; the forces, densities, and motions of mediums; the orbits of the comets, and such like; I put off that publication till I had made a search into those matters, and could put out the whole together. What relates to the lunar motions (being imperfect) I have put all together in the corollaries of proposition 66, to avoid being obliged to propose and distinctly demonstrate the several things there contained in a method more prolix than the subject deserved, and interrupt the series of the several propositions. Some things, found out after the rest, I chose to insert in places less suitable, rather than change the number of the propositions and the citations. I heartily beg that what I have here done may be read with candor; and that the defects I have been guilty of upon this difficult subject may be not so much reprehended as kindly supplied, and investigated by new endeavors of my readers. Cambridge, Trinity College,
ISAAC NEWTON. May 8, 1686.
PREFACE TO FABLES,
BY JOHN DRYDEN. (1700)
VIS with a poet, as with a man who designs to build,
and is very exact, as he supposes, in casting up the
- cost beforehand; but, generally speaking, he is mistaken in his account, and reckons short of the expense he first intended. He alters his mind as the work proceeds, and will have this or that convenience more, of which he had not thought when he began. So has it happen'd to me; I have built a house, where I intended but a lodge; yet with better success than a certain nobleman,' who, beginning with a dog kennel, never liv'd to finish the palace he had contriv'd.
From translating the first of Homer's Iliads (which I intended as an essay to the whole work) I proceeded to the translation of the twelfth book of Ovid's Metamorphoses, because it contains, among other things, the causes, the beginning, and ending, of the Trojan war. Here I ought in reason to have stopp'd; but the speeches of Ajax and Ulysses lying next in my way, I could not balk 'em. When I had compass'd them, I was so taken with the former part of the fifteenth book, (which is the masterpiece of the whole Metamorphoses,) that I enjoin'd myself the pleasing task of rend'ring it into English. And now I found, by the number of my verses, that they began to swell into a little volume; which gave me an occasion of looking backward on some beauties of my author, in his former books. There
John Dryden (1631-1700), the great dramatic and satirical poet of the later seventeenth century, whose translation of Virgil's “. Æneid". appears as a prose writer than as a poet. The present essay, prefixed to a volume of narrative poems, is largely concerned with Chaucer;, and in its genial and penetrating criticism, expressed with characteristic clearness and vigor, can be seen the ground for naming Dryden the first of English literary critics, and the founder of modern prose style.
Scott suggests that the allusion is to the Duke of Buckingham, who was often satirized for the slow progress of his great mansion at Cliefden.
in another volume of the Harvard Classics, deserves hardly less distinction
occurr'd to me the Hunting of the Boar, Cinyras and Myrrha, the good-natur'd story of Baucis and Philemon, with the rest, which I hope I have translated closely enough, and given them the same turn of verse which they had in the original; and this, I may say without vanity, is not the talent of every poet. He who has arriv'd the nearest to it, is the ingenious and learned Sandys, the best versifier of the former age; if I may properly call it by that name, which was the former part of this concluding century. For Spenser and Fairfax both flourish'd in the reign of Queen Elizabeth ; great masters in our language, and who saw much farther into the beauties of our numbers than those who immediately follow'd them. Milton was the poetical son of Spenser, and Mr. Waller of Fairfax, for we have our lineal descents and clans as well as other families. Spenser more than once insinuates that the soul of Chaucer was transfus'd into his body, and that he was begotten by him two hundred years after his decease. Milton has acknowledg'd to me that Spenser was his original, and many besides myself have heard our famous Waller own that he deriv'd the harmony of his numbers from the Godfrey of Bulloign, which was turn'd into English by Mr. Fairfax. But to return. Having done with Ovid for this time, it came into my mind that our old English poet, Chaucer, in many things resembled him, and that with no disadvantage on the side of the modern author, as I shall endeavor to prove when I compare them; and as I am, and always have been, studious to promote the honor of my native country, so I soon resolv'd to put their merits to the trial, by turning some of the Canterbury Tales into our language, as it is now refin'd; for by this means, both the poets being set in the same light, and dress'd in the same English habit, story to be compar'd with story, a certain judgment may be made betwixt them by the reader, without obtruding my opinion on him. Or, if I seem partial to my countryman and predecessor in the laurel, the friends of antiquity are not few; and besides many of the learn'd, Ovid has almost all the beaux, and the whole fair sex, his declar'd patrons. Perhaps I have assum'd somewhat more to myself than they allow me, because I have adventur'd to sum up the evidence; but the readers