Academics From The United Kingdom

"No monument should stand over [my] grave, only an apple-tree, in memory of the three apples; the two of Eve and Paris, which made hell out of earth, and that of Newton, which elevated the earth again into the circle of heavenly bodies."

"Now I a fourfold vision see, And a fourfold vision is given to me ; 'Tis fourfold in my supreme delight, And threefold in soft Beulah's night, And twofold Always. May God us keep From Single vision, & Newton's sleep !"

"Kepler succeeded in showing that the planets move along elliptic paths and that the sun lies at a focus of each of these s... Each planet moves so that a straight line drawn to connect it with the sun sweeps out equal areas in equal times. ...The discoveries ...enabled Newton to formulate the laws of mechanics in general and those of gravitation in particular. ...He was able to develop Kepler's laws into a comprehensive physical theory only because he managed first to create the necessary mathematical tools... differential and integral calculus, the basic mathematical techniques for dealing with variable quantities, such as the movement of bodies in the course of time. ...[H]e succeeded in drawing from Kepler's empirical laws the principles of motion that applied [to] every instant of time and thus shaped planetary motion into complete orbits."

"Newton's own motto, "hypotheses non fingo" was, in a sense, disregarded by Newton himself: he rejected hypotheses only where they violated his own "regula philosophandi", that is to say, his principle of their strict parsimony. In terms of present-day methodology, we reject hypotheses as scientifically meaningless if they are incapable even of indirect test; and we reject them as superfluous or as implausible if they are too complex and artificial to conform with well established canons of inductive probability. But freedom of scientific theorizing must be preserved wherever the conditions of meaningfulness and of economy appear to be satisfied."

"The greatest scientist who ever lived was Isaac Newton...[about Principia Mathematica] By all odds it's the greatest scientific book ever written or ever will be written, I think."

"According to Sir Isaac Newton's Calculations, the last Comet that made its Appearance in 1680, imbib'd so much Heat by its Approaches to the Sun, that it would have been two thousand times hotter than red hot Iron, had it been a Globe of that Metal; and that supposing it as big as the Earth, and at the same Distance from the Sun, it would be fifty thousand Years in cooling, before it recovered its natural Temper. In the like manner, if an Englishman considers the great Ferment into which our Political World is thrown at present, and how intensely it is heated in all its Parts, he cannot suppose that it will cool again in less than three hundred Years. In such a Tract of Time it is possible that the Heats of the present Age may be extinguished, and our several Classes of great Men represented under their proper Characters. Some eminent Historian may then probably arise that will not write recentibus odiis (as Tacitus expresses it) with the Passions and Prejudices of a contemporary Author, but make an impartial Distribution of Fame among the Great Men of the present Age."

"Newton and Locke are examples of the deep sagacity which may be acquired by long habits of thinking and study."

"Les hommes construisent trop de murs et pas assez de ponts."

"Tact is the knack of making a point without making an enemy."

"Atheism is so senseless. When I look at the solar system, I see the earth at the right distance from the sun to receive the proper amounts of heat and light. This did not happen by chance."

"If I had stayed for other people to make my tools and things for me, I had never made anything."

"I can calculate the motions of the heavenly bodies, but not the madness of the people."

"Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis."

"The Simplicity of Figures depend upon the Simplicity of their Genesis and Ideas, and an Æquation is nothing else than a Description (either Geometrical or Mechanical) by which a Figure is generated and rendered more easy to the Conception."

"The Ellipse is the most simple of the Conic Sections, most known, and nearest of Kin to a Circle, and easiest describ'd by the Hand in plano. Though many prefer the Parabola before it, for the Simplicity of the Æquation by which it is express'd. But by this Reason the Parabola ought to be preferr'd before the Circle it self, which it never is. Therefore the reasoning from the Simplicity of the Æquation will not hold. The modern Geometers are too fond of the Speculation of Æquations."

"In my Judgment no Lines ought to be admitted into plain Geometry besides the right Line and the Circle."

"Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry, as we learn from Pappus."

"Geometrical Speculations have just as much Elegancy as Simplicity, and deserve just so much praise as they can promise Use."

"Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Antients did so industriously distinguish them from one another, that they never introduc'd Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegancy of Geometry consists. Wherefore that is Arithmetically more simple which is determin'd by the more simple Æquations, but that is Geometrically more simple which is determin'd by the more simple drawing of Lines; and in Geometry, that ought to be reckon'd best which is Geometrically most simple. Wherefore, I ought not to be blamed, if with that Prince of Mathematicians, Archimedes and other Antients, I make use of the Conchoid for the Construction of solid Problems."

"In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction; the bare Descriptions of the Lines only are here to be consider'd and these alone were consider'd by those Geometricians who joyn'd a Circle with a right Line. And as these are easy or hard, the Construction becomes easy or hard: And therefore it is foreign to the Nature of the Thing, from any Thing else to establish Laws about Constructions. Either therefore let us, with the Antients, exclude all Lines besides the Circle, and perhaps the Conick Sections, out of Geometry, or admit all, according to the Simplicity of the Description. If the Trochoid were admitted into Geometry, we might, by its Means, divide an Angle in any given Ratio. Would you therefore blame those who should make Use of this Line... and contend that this Line was not defin'd by an Æquition, but that you must make use of such Lines as are defin'd by Æquations?"

"The Circle is a Geometrical Line, not because it may be express'd by an Æquation, but because its Description is a Postulate. It is not the Simplicity of the Æquation, but the Easiness of the Description, which is to determine the Choice of our Lines for the Construction of Problems. For the Æquation that expresses a Parabola, is more simple than That that expresses a Circle, and yet the Circle, by reason of its more simple Construction, is admitted before it. The Circle and the Conick Sections, if you regard the Dimension of the Æquations, are of the fame Order, and yet the Circle is not number'd with them in the Construction of Problems, but by reason of its simple Description, is depressed to a lower Order, viz. that of a right Line; so that it is not improper to express that by a Circle that may be expressed by a right Line. But it is a Fault to construct that by the Conick Sections which may be constructed by a Circle. Either therefore you must take your Law and Rule from the Dimensions of Æquations as observ'd in a Circle, and so take away the Distinction between Plane and Solid Problems; or else you must grant, that that Law is not so strictly to be observ'd in Lines of superior Kinds, but that some, by reason of their more simple Description, may be preferr'd to others of the same Order, and may be number'd with Lines of inferior Orders in the Construction of Problems."

"The Antients, as we learn from Pappus, in vain endeavour'd at the Trisection of an Angle, and the finding out of two mean Proportionals by a right line and a Circle. Afterwards they began to consider the Properties of several other Lines. as the Conchoid, the Cissoid, and the Conick Sections, and by some of these to solve these Problems. At length, having more throughly examin'd the Matter, and the Conick Sections being receiv'd into Geometry, they distinguish'd Problems into three Kinds: viz. (1.) Into Plane ones, which deriving their Original from Lines on a Plane, may be solv'd by a right Line and a Circle; (2.) Into Solid ones, which were solved by Lines deriving their Original from the Consideration of a Solid, that is, of a Cone; (3.) And Linear ones, to the Solution of which were requir'd Lines more compounded. And according to this Distinction, we are not to solve solid Problems by other Lines than the Conick Sections; especially if no other Lines but right ones, a Circle, and the Conick Sections, must be receiv'd into Geometry. But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, that you are not to construct a Problem by a Line of a superior Kind, that may be constructed by one of an inferior one. In the Contemplation of Lines, and finding out their Properties, I like their Distinction of them into Kinds, according to the Dimensions thy Æquations by which they are defin'd. But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one."

"After the same Manner in Geometry, if a Line drawn any certain Way be reckon'd for Affirmative, then a Line drawn the contrary Way may be taken for Negative: As if AB be drawn to the right, and BC to the left; and AB be reckon'd Affirmative, then BC will be Negative; because in the drawing it diminishes AB..."

"Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought. And after this Way the most difficult problems are resolv'd, the Resolutions whereof would be sought in vain from only common Arithmetick. Yet Arithmetick in all its Operations is so subservient to Algebra, as that they seem both but to make one perfect Science of Computing; and therefore I will explain them both together."

"A good watch may serve to keep a recconing at Sea for some days and to know the time of a Celestial Observ[at]ion: and for this end a good Jewel watch may suffice till a better sort of Watch can be found out. But when the Longitude at sea is once lost, it cannot be found again by any watch."

"One [method] is by a Watch to keep time exactly. But, by reason of the motion of the Ship, the Variation of Heat and Cold, Wet and Dry, and the Difference of Gravity in different Latitudes, such a watch hath not yet been made."

"And now to explain colours. I suppose that as bodies excite sounds of various tones and consequently vibrations, in the air of various bignesses, so when rays of light by impinging on the stiff refracting superficies excite vibrations in the ether, these rays excite vibrations of various bignesses... therefore, the ends of the capillamenta of the optic nerve which front or face the retina being such refracting superficies, when the rays impinge on them they must there excite these vibrations, which vibrations (like those of sound in a trumpet) will run along the pores or crystalline pith of the capillamenta through the optic nerves into the sensorium (which light itself cannot do), and there, I suppose, affect the sense with various colours, according to their bigness and mixture—the biggest with the strongest colours, reds and yellows; the least with the weakest, blues and violets; middle with green; and a confusion of all with white, much after the manner, that in the sense of hearing, nature makes use of aereal vibrations of several bignesses to generate sounds of divers tones; for the analogy of nature is to be observed."

"And so, supposing that light impinging on a refracting or reflecting ethereal superficies puts it into a vibrating motion, that physical superficies being by the perpetual applause of rays always kept in a vibrating motion, and the ether therein continually expanded and compressed by turns, if a ray of light impinge on it when it is much compressed, I suppose it is then too dense and stiff to let the ray through, and so reflects it; but the rays that impinge on it at other times, when it is either expanded by the interval between two vibrations or not too much compressed and condensed, go through and are refracted."

"Were I to assume an hypothesis, it should be this, if propounded more generally, so as not to assume what light is further than that it is something or other capable of exciting vibrations of the ether. First, it is to be assumed that there is an ethereal medium, much of the same constitution as air, but far rarer, subtiller, and more strongly elastic. ...In the second place, it is to be supposed that the ether is a vibrating medium, like air, only the vibrations much more swift and minute; those of air made by a man's ordinary voice succeeding at more than half a foot or a foot distance, but those of ether at a less distance than the hundredth-thousandth part of an inch. And as in air the vibrations are some larger than others, but yet all equally swift... so I suppose the ethereal vibrations differ in bigness but not in swiftness. ...In the fourth place, therefore, I suppose that light is neither ether nor its vibrating motion, but something of a different kind propagated from lucid bodies. They that will may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes springing from shining bodies at great distances one after the other, but yet without any sensible interval of time. ...To avoid dispute and make this hypothesis general, let every man here take his fancy; only whatever light be, I would suppose it consists of successive rays differing from one another in contingent circumstances, as bigness, force, or vigour, like as the sands on the shore... and, further, I would suppose it diverse from the vibrations of the ether. ...Fifthly, it is to be supposed that light and ether mutually act upon one another. ...æthereal vibrations are therefore the best means by which such a subtile agent as light can shake the gross particles of solid bodies to heat them."

"I have that honour for him as to believe that he wrote good sense; and therefore take that sense to be his which is the best."

"Who is a liar, saith John, but he that denyeth that Jesus is the Christ? He is Antichrist that denyeth the Father & the Son. And we are authorized also to call him God: for the name of God is in him. Exod. 23.21. And we must believe also that by his incarnation of the Virgin he came in the flesh not in appearance only but really & truly , being in all things made like unto his brethren (Heb. 2 17) for which reason he is called also the son of man."

"Whence are you certain that ye Ancient of Days is Christ? Does Christ anywhere sit upon ye Throne?"

"God created everything by number, weight and measure."

"Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things."

"Oh, Diamond! Diamond! thou little knowest what mischief thou hast done!"

"Strange secrets are let out by Death Who blabs so oft the follies of this world."

"If Browning were less difficult to read, he would surely be the dominant poet in this century. I feel the ecstasy with which he exclaims, “Oh, good gigantic smile o’ the brown old earth this autumn morning!" And how he sets my brain going when he says, because there is imperfection, there must be perfection; completeness must come of incompleteness; failure is an evidence of triumph for the fulness of the days. Yes, discord is, that harmony may be; pain destroys, that health may renew; perhaps I am deaf and blind that others likewise afflicted may see and hear with a more perfect sense! From Browning I learn that there is no lost good, and that makes it easier for me to go at life, right or wrong, do the best I know, and fear not. My heart responds proudly to his exhortation to pay gladly life's debt of pain, darkness and cold. Lift up your burden, it is God's gift, bear it nobly."

"He is called an optimist; but the word suggests a calculated contentment which was not in the least one of his vices. What he really was was a romantic. He offered the cosmos as an adventure rather than a scheme. He did not explain evil, far less explain it away: he enjoyed defying it. He was a troubadour even in theology and metaphysics: like the Jongleurs de Dieu of St. Francis. He may be said to have serenaded heaven with a guitar, and even, so to speak, tried to climb there with a rope ladder."

"He concentrated on the special souls of men; seeking God in a series of personal interviews."

"Perhaps one has to be very old before one learns to be amused rather than shocked."

"Like dogs in a wheel, birds in a cage, or squirrels in a chain, ambitious men still climb and climb, with great labor, and incessant anxiety, but never reach the top."

"Love is energy of life."

"There is no truer truth obtainable By Man than comes of music."

"But little do or can the best of us: That little is achieved through Liberty."

"Wanting is—what? Summer redundant, Blueness abundant, Where is the blot?"

"Sky—what a scowl of cloud Till, near and far, Ray on ray split the shroud: Splendid, a star!"

"Can we love but on condition that the thing we love must die?"

"Good, to forgive; Best, to forget! Living, we fret; Dying, we live."

"God's justice, tardy though it prove perchance, Rests never on the track until it reach"

""With this same key Shakespeare unlocked his heart" once more! Did Shakespeare? If so, the less Shakespeare he!"