All Quotes

"Now we can cross the Shifting Sands."

"Are you guys ready? Let's roll."

"Rain had always been a harbinger of tragedy for me."

"Bonaparte...l'île d'Elbe...le roi de Rome."

"Ich denke an frühere Zeiten."

"[To his murderers] If all the swords in England were pointed against my head, your threats would not move me."

"Christ, you know it ain't easy You know how hard it can be. The way things are going, they're going to crucify me."

"The newspapers said, "Say, what you're doing in bed?" I said "We're only trying to get us some peace.""

"Instant Karma's gonna get you Gonna knock you off your feet Better recognize your brothers Everyone you meetWhy in the world are we here? Surely not to live in pain and fear Why on Earth are you there When you're everywhere Go and get your share Well, we all shine on Like the moon and the stars and the sun Yeah, we all shine on C'mon and on and on, on, on"

"Mother, you had me, but I never had you."

"His decipherment of Nature might be crude, yet he had the courage to insist that the mechanical sense could be made of the workings of Nature, throughout the realms of physics, chemistry, and even physiology. By reasserting the unity and rationality of Nature, he did as much as any man to put seventeenth-century scientists back on the intellectual road first trodden by the Greeks."

"The mechanical philosophy is a case of being victimized by metaphor. I choose Descartes and Newton as excellent examples of metaphysicians of mechanism malgré eux, that is to say, as unconscious victims of the metaphor of the great machine. Together they have founded a church, more powerful than that founded by Peter and Paul, whose dogmas are now so entrenched that anyone who tries to reallocate the facts is guilty of more than heresy."

"Having laid down his rules of method, Descartes proceeded to deviate from them. We expect a demonstration of the truth after the principles have already been found, such as been prescribed by Plato. But we get a different way of accounting for the facts: "the way of hypothesis" proscribed by Plato. Unable to proceed further deductively, he resorted to the invention of and choice among different hypothesis, the choice being determined by crucial experiments. Thus he gave up the certainty of the a priori method in favor of the conjectural a posteriori. This meant that in his practice, the synthesis preceded analysis, for it preceded that form of it known as inductive testing."

"The truth is sum, ergo cogito — I am, therefore I think, although not everything that is thinks. Is not consciousness of thinking above all consciousness of being? Is pure thought possible, without consciousness of self, without personality? Can there exist pure knowledge without feeling, without that species of materiality which feelings lends to it? Do we not perhaps feel thought, and do we not feel ourselves in the act of knowing and willing? Could not the man in the stove [Descartes] have said: "I feel, therefore I am"? or "I will, therefore I am"? And to feel oneself, is it not perhaps to feel oneself imperishable?"

""Catatau" by Paulo Leminski captures that impulse as he imagines the French philosopher René Descartes driven mad by Brazil, a country where everything gets mixed and defies categorization."

"The first thing that we know about ourselves is our imperfection. This is what Descartes meant when he said: 'I know God before I know myself.' The only mark of God in us is that we feel that we are not God."

"After Bruno's death, during the first half of the seventeenth century, Descartes seemed about to take the leadership of human thought... in promoting an evolution doctrine as regards the mechanical formation of the solar system... but his constant dread of persecution, both from Catholics and Protestants, led him steadily to veil his thoughts and even to suppress them. The execution of Bruno had occurred in his childhood, and in the midst of his career he had watched the Galileo struggle in all its stages. He had seen his own works condemned by university after university under the direction of theologians and placed upon the Roman Index. ...Since Roger Bacon, perhaps, no great thinker had been so completely abased and thwarted by theological oppression."

"Man occupies a special place in the Cartesian scheme. He alone is endowed with mind. Descartes believed that animals did not possess one, that they were simply extremely complicated automatons. Other thinkers have rejected this point of view and proposed to endow all matter in the universe—living or inanimate—with consciousness. This "panpsychism" has been promoted by, among others, Teilhard de Chardin and, more recently by the British-American physicist Freeman Dyson, who holds that mind is present in every particle of matter."

"[He] came back to Paris towards the middle of October [1644]. At his Arrival, An Edition of his Principles of philosophy... and the Latine Translation of his Essays [he found] finished, and the Copies came out of Holland. The Treatise of Principles did not come out, neither did that Piece he called his World, nor his Course of Philosophy, both of which were suppress'd. He had a mind to divide them into other Parts: The First of which contains the Principles of Humane Knowledge, which one may call the first Philosophy or Metaphysicks: wherein it hath very much relation and connexion with his Meditations. The Second contains what is most general in Philosophy, and the Explanation of the first Laws of Nature, and of the principles of natural things, the Proprieties of Bodies, Space, and Motion, &c.The Third contains a particular Explanation, of the System of the World, and more especially of what we mean by the Heavens and Celestial Bodies.The Fourth contains whatsoever belongs to the Earth. That which is most remarkable in this Work, is, That the Author after having first of all established the distinction and difference he puts between the Soul and the Body, when he hath laid down, for the Principles of corporeal things, bigness, figure and local motion; all which are things in themselves so clear and intelligible, that they are granted and received by every one whatsoever; he hath found out a way to explain all Nature in a manner, and to give a reason of the most wonderful Effects, without altering the Principles; yea, and without being inconsistent with himself in any thing whatsoever. Yet... he [had] not the presumption for all that to believe he had hit upon the explication of all natural things, especially such that do not fall under our senses, in the same manner as they really and truly are in themselves. He should do something indeed, if he could but come the nearest that it was possible to likelihood or verisimilitude, to which others before him could never reach; and if he could bring the matter about, that, whatsoever he had written should exactly agree with all the Phenomena's of Nature, this he judged sufficient for the use of Life, the profit and benefit of which seems to be the main and only end one ought to propose to himself in Mechanicks, Physick, or Medicine; and in all Arts that may be brought to perfection by the help of Physick or natural Philosophy. But of all things he hath explained, there is not one of them that doth not seem at least morally certain in respect of the profit of life, notwithstanding they may be uncertain in respect of the absolute Power of God. Nay, there are several of them that are absolutely, or more than morally certain; such as are Mathematical Demonstrations, and those evident ratiocinations he hath framed concerning the existence of material things. Nevertheless, he was indued with that Modesty, as no where to assume the authority of positively deciding, or ever to assert any thing for undeniable. Altho' what he intended to offer, under the Name of Principles of Philosophy, was brought to that Conclusion, that one could not lawfully nor reasonably require more for the perfecting his design; yet did it give some cause to his Friends, to hope to see the Explication of all other things, which made people say, That his Physick was not compleat. He promised himself likewise to explain after the same manner, the nature of other more particular Bodies, that belong to the Terrestrial Globe; as, Minerals, Plants, Animals, and Man in particular; After which, he proposed to himself (according as God should please to lengthen out his days) to treat with the same exactness of all Physick or Medicine, of Mechanicks, and of the whole Doctrine of Morality or Ethicks; whereby to present the World with an entire Body of Philosophy."

"If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity."

"Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes."

"The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides."

"The centre of gravity of a parallelogram is the point of intersection of its diagonals."

"In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side."

"It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively."

"He dedicated his Book of Principles to his most Illustrious Disciple, Elizabeth, Princess Palatine of the Rhine... The Princess had been Educated in the Knowledge of abundance of Languages, and in whatsoever Learning is comprised under the name of Litterae humaniores, or Politiores; but the elevation of, and profoundness of her genius and natural parts, would not suffer her to dwell long upon these Arts, by which the greatest Wits of her Sex, who are satisfied with desiring to seem somebody, are commonly limited. She desir'd to proceed to those parts of Learning, that the strongest Application of Men had advanced, and accomplish'd her self with, and became a great proficient in Philosophy and Mathematicks; till such time as seeing the Essays of Monsieur Des Cartes his Philosophy, she conceived such high esteem and affection for his Doctrine, that she look'd upon all she had learn'd till that time as good as nothing; and so put her self under his Tuition for to raise a new Structure upon his Principles. Thereupon she sends to him, to come and see her, that she might drink in the true Phi∣osophy at the Fountain Head; and the great desire to do her Service nearer, was one of the reasons that drew him to Leiden & to Eindegeest. Never did Master more happily improve the docibility, aptness, penetration, and withal the solidity of a Scholar's Mind. Having accustomed her insensibly to the profound Meditation of the grand Mysteries of Nature, and sufficiently exercising of her in the most abstracted Questions of Geometry, and the most sublime ones of Metaphysicks. There was no longer any thing abstruse or mysterious to her; and he ingeniously confesseth and owneth, that he had not yet met with any besides her (he excepted Regius in another place) that ever arrived at a perfect understanding of the Works he had published till that time. By this Testimony that he bore to the extraordinary Capacity of the Princess, he intended to distinguish her from those who were not able to apprehend his Metaphysicks, altho' they might have some insight into Geometry; and from those that were not able to understand his Geometry, altho' they might be pretty well vers'd in Metaphysical Truths. She continued to Philosophise with him Viva voce, till a certain Accident obliged her to absent herself from the Presence of the Queen of Bohemia her Mother, and to quit her abode in Holland for Germany; then she changed her Acquaintance into an Intelligence by Letter, which she kept afoot with him, by the Ministery of the Princesses her Sisters."

"Among the earliest thinkers of the seventeenth and eighteenth centuries, who employed their mental powers toward the destruction of old ideas and the up-building of new ones, ranks Rene Descartes. Though he professed orthodoxy in faith all his life, yet in science he was a profound sceptic. He found that the world's brightest thinkers had been long exercised in metaphysics, yet they had discovered nothing certain; nay, they had even flatly contradicted each other. ...The certainty of the conclusions in geometry and arithmetic brought out in his mind the contrast between the true and false ways of seeking the truth. He thereupon attempted to apply mathematical reasoning to all sciences."

"His philosophy has long since been superseded by other systems, but the analytical geometry of Descartes will remain a valuable possession forever."

"His Geometry is not easy reading. An edition appeared subsequently with notes by his friend De Beaune, which were intended to remove the difficulties."

"Descartes' geometry was called "analytical geometry," partly because unlike the synthetic geometry of the ancients it is actually analytical in the sense that the word is used in logic; and partly because the practice had then already arisen, of designating by the term analysis the calculus [i.e., symbolic calculation or computation] with general quantities."

"The first important example solved by Descartes in his geometry is the "problem of Pappus"... Of this celebrated problem the Greeks solved only the special case... By Descartes it was solved completely, and it afforded an excellent example of the use which can be made of his analytical method in the study of loci. Another solution was given later by Newton in the Principia."

"In mechanics Descartes can hardly be said to have advanced beyond Galileo. ...His statement of the first and second laws of motion was an improvement in form, but his third law is false in substance. The motions of bodies in their direct impact was imperfectly understood by Galileo, erroneously given by Descartes, and first correctly stated by Wren, Wallis, and Huygens."

"It is frequently stated that Descartes was the first to apply algebra to geometry. This statement is inaccurate, for Vieta and others had done this before him. Even the Arabs some times used algebra in connection with geometry. The new step that Descartes did take was the introduction into geometry of an analytical method based on the notion of variables and constants, which enabled him to represent curves by algebraic equations. In the Greek geometry, the idea of motion was wanting, but with Descartes it became a very fruitful conception. By him a point on a plane was determined in position by its distances from two fixed right lines or axes. These distances varied with every change of position in the point. This geometric idea of co-ordinate representation, together with the algebraic idea of two variables in one equation having an indefinite number of simultaneous values, furnished a method for the study of loci, which is admirable for the generality of its solutions. Thus the entire conic sections of Apollonius is wrapped up and contained in a single equation of the second degree."

"In the Greek geometry the idea of motion was wanting but with Descartes it became a very fruitful conception. ...This geometric idea of co-ordinate representation, together with the algebraic idea of two variables in one equation having an indefinite number of simultaneous values, furnished a method for the study of loci, which is admirable for the generality of its solutions. Thus the entire conic sections of Apollonius is wrapped up and contained in a single equation of the second degree."

"It is frequently stated that Descartes was the first to apply algebra to geometry. This statement is inaccurate, for Vieta and others had done this before him. Even the Arabs sometimes used algebra in connection with geometry."

"Methods of drawing tangents were invented by Roberval and Fermat... Descartes gave a third method. Of all the problems which he solved by his geometry, none gave him as great pleasure as his mode of constructing tangents. It is profound but operose, and, on that account, inferior to Fermat's. His solution rests on the method of Indeterminate Coefficients, of which he bears the honour of invention. Indeterminate coefficients were employed by him also in solving bi-quadratic equations."

"An optimist may see a light where there is none, but why must the pessimist always run to blow it out?"

"I've always considered my work one piece and I consider that my work won't be finished until I am dead and buried and I hope that's a long, long time."

"I really thought that love would save us all."

"First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right angled cone (i.e., a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]..."

"The centre of gravity of any cylinder is the point of bisection of the axis."

"The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple [of the portion adjacent to the base]."

"Any segment of a right-angled conoid (i.e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment"

"The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3."

"Shall we not make an end to this fighting against this geometrical Briareus who uses our ships like cups to ladle water from the sea, drives off our sambuca ignominiously with cudgel-blows, and by the multitude of missiles that he hurls at us all at once outdoes the hundred-handed giants of mythology?"

"When... the Romans assaulted the walls in two places at once, fear and consternation stupefied the Syracusans.... But when Archimedes began to ply his engines, he at once shot against the land forces all sorts of missile weapons... that came down with incredible noise and violence... they knocked down those upon whom they fell in heaps, breaking all their ranks and files. ...huge poles thrust out from the walls, over the ships, sunk some by the great weights... from on high... others they lifted up into the air by an iron hand or beak like a crane's... and... plunged them to the bottom of the sea; or else the ships, drawn by engines within, and whirled about, were dashed against steep rocks... under the walls, with great destruction of the soldiers... aboard them. A ship was frequently lifted up to a great height in the air... and was rolled to and fro... until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall. At the engine [called Sambuca] that Marcellus brought upon the bridge of ships... while it was as yet approaching the wall, there was discharged a... rock of ten talents [600-700 lb. total] weight, then a second and a third, which, striking upon it with immense force and a noise like thunder, broke all its foundation to pieces... and completely dislodged it from the bridge. So Marcellus... drew off his ships to a safer distance, and sounded a retreat... They then took a resolution of coming up under the walls... in the night; thinking that as Archimedes used ropes stretched at length in playing his engines, the soldiers would now be under the shot, and the darts would... fly over their heads... But he... had... framed... engines accommodated to any distance, and shorter weapons; and... with engines of a shorter range, unexpected blows were inflicted on the assailants. Thus... instantly a shower of darts and other missile weapons was again cast upon them. And when stones came tumbling down... upon their heads, and... the whole wall shot out arrows at them, they retired. ...as they were going off, arrows and darts of a longer range inflicted a great slaughter among them, and their ships were driven one against another; while they themselves were not able to retaliate... For Archimedes had provided and fixed most of his engines immediately under the wall; whence the Romans, seeing that indefinite mischief overwhelmed them from no visible means, began to think they were fighting with the gods."

"When Jove looked down and saw the heavens figured in a sphere of glass he laughed and said to the other gods: "Has the power of mortal effort gone so far? Is my handiwork now mimicked in a fragile globe? An old man of Syracuse has imitated on earth the laws of the heavens, the order of nature, and the ordinances of the gods. Some hidden influence within the sphere directs the various courses of the stars and actuates the lifelike mass with definite motions. A false zodiac runs through a year of its own, and a toy moon waxes and wanes month by month. Now bold invention rejoices to make its own heaven revolve and sets the stars in motion by human wit. Why should I take umbrage at harmless and his mock thunder? Here the feeble hand of man has proved Nature's rival.""

"Archimedes said, “Give to me a fulcrum on which to plant my lever, and I will move the world.” And I say, give to woman the ballot, the political fulcrum, on which to plant her moral lever, and she will lift the world into a nobler purer atmosphere."

"Abstract enquiries into the most puzzling problems did not arise in the brain of Archimedes as a spontaneous and hitherto untouched subject, but rather as a reflection of prior enquiries in the same direction and by men separated from his days by as long a period — and far longer — than the one which separates you from the great Syracusian."

"Archimedes originally solved the problem of finding the solid content of a sphere before that of finding its surface, and he inferred the result of the latter problem from that of the former. ...another illustration of the fact that the order of propositions in the treatises of the Greek geometers as finally elaborated does not necessarily follow the order of discovery."