Astronomers From England

"I do not mind at all that [Newton] is not a Cartesian provided he does not offer us suppositions like that of attraction."

"I esteem his [Newton's] understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction."

"Newton said that he made his discoveries by 'intending' his mind on the subject; no doubt truly. But to equal his success one must have the mind which he 'intended.' Forty lesser men might have intended their minds till they cracked, without any like result. It would be idle either to affirm or to deny that the last half-century has produced men of science of the calibre of Newton. It is sufficient that it can show a few capacities of the first rank, competent not only to deal profitably with the inheritance bequeathed by their scientific forefathers, but to pass on to their successors physical truths of a higher order than any yet reached by the human race. And if they have succeeded as Newton succeeded, it is because they have sought truth as he sought it, with no other object than the finding it."

"The prejudice for Sir Isaac has been so great, that it has destroyed the intent of his undertaking, and his books have been a means of hindering that knowledge they were intended to promote. It is a notion every child imbibes almost with his mother's milk, that Sir Isaac Newton has carried philosophy to the highest pitch it is capable of being carried, and established a system of physics upon the solid basis of mathematical demonstration."

"Newton's version of gravity violates common sense. How can one thing tug at another across vast spans of space? ...Newton's formalism nonetheless provided an astonishingly accurate means of calculating the orbits of planets; it was too effective to deny."

"It was God who breathed life into matter and inspired its many textures and processes. ...Rather than turn away from what he could not explain, he plunged in more deeply. ...There were forces in nature that he would not be able to understand mechanically, in terms of colliding billiard balls or swirling vortices. They were vital, vegetable, sexual forces—invisible forces of spirit and attraction. Later, it had been Newton, more than any other philosopher, who effectively purged science of the need to resort to such mystical qualities. For now, he needed them."

"The history of the apple is too absurd. Whether the apple fell or not, how can any one believe that such a discovery could in that way be accelerated or retarded? Undoubtedly, the occurrence was something of this sort. There comes to Newton a stupid, importunate man, who asks him how he hit upon his great discovery. When Newton had convinced himself what a noodle he had to do with, and wanted to get rid of the man, he told him that an apple fell on his nose; and this made the matter quite clear to the man, and he went away satisfied."

"Newton's proof of the law of refraction is based on an erroneous notion that light travels faster in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature."

"Newton had other postulates by which he could get the law of angular momentum, but Newtonian laws were wrong. There's no forces, it's all a lot of balony. The particles don't have orbits, and so on."

"Newton's age has long since passed through the sieve of oblivion, the doubtful striving and suffering of his generation has vanished from our ken; the works of some few great thinkers and artists have remained, to delight and ennoble those who come after us. Newton's discoveries have passed into the stock of accepted knowledge."

"In order to put his system into mathematical form at all, Newton had to devise the concept of differential quotients and propound the laws of motion in the form of total differential equations—perhaps the greatest advance in thought that a single individual was ever privileged to make."

"In accordance with Newton's system, physical reality is characterised by concepts of space, time, the material point and force (interaction between material points). Physical events are to be thought of as movements according to law of material points in space. The material point is the only representative of reality in so far as it is subject to change. The concept of the material point is obviously due to observable bodies; one conceived of the material point on the analogy of movable bodies by omitting characteristics of extension, form, spatial locality, and all their 'inner' qualities, retaining only inertia, translation, and the additional concept of force."

"Newton was at heart a Cartesian, using pure thought as Descartes intended, and using it to demolish the Cartesian dogma of vortices."

"Multiple-prism arrays were first introduced by Newton (1704) in his book Opticks. In that visionary volume Newton reported on arrays of nearly isosceles prisms in additive and compensating configurations to control the propagation path and the dispersion of light. Further, he also illustrated slight beam expansion in a single isosceles prism."

"But to return to the Newtonian Philosophy: Tho' its Truth is supported by Mathematicks, yet its Physical Discoveries may be communicated without. The great Mr. Locke was the first who became a Newtonian Philosopher without the help of Geometry; for having asked Mr. Huygens, whether all the mathematical Propositions in Sir Isaac's Principia were true, and being told he might depend upon their Certainty; he took them for granted, and carefully examined the Reasonings and Corollaries drawn from them, became Master of all the Physics, and was fully convinc'd of the great Discoveries contained in that Book."

"Galileo first studied the motion of terrestrial objects, pendulums, free-falling balls, and projectiles. He summarized what he observed in the mathematical language of proportions. And he extrapolated from his experimental data to a great idealization now called the “inertia principle,” which tells us, among other things, that an object projected along an infinite, frictionless plane will continue forever at a constant velocity. His observations were the beginnings of the science of motion we now call “mechanics.”... Newton also invented a mathematical language (the "Fluxions" method, closely related to our present-day ) to express his mechanics, but in an odd historical twist, rarely applied that language himself."

"[Newton] achieved the clearest appreciation of the relation between the empirical elements in a scientific system and the hypothetical elements derived from a philosophy of nature."

"The best and safest method of philosophizing seems to be, first to enquire diligently into the properties of things, and to establish these properties by experiment, and then to proceed more slowly to hypothesis for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them, unless so far as they may furnish experiments."

"If I have seen further it is by standing on ye sholders of Giants."

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy."

"Bullialdus wrote that all force respecting the Sun as its center & depending on matter must be reciprocally in a duplicate ratio of the distance from the center."

"1. Fidelity & Allegiance sworn to the King is only such a fidelity and obedience as is due to him by the law of the land; for were that faith and allegiance more than what the law requires, we would swear ourselves slaves, and the King absolute; whereas, by the law, we are free men, notwithstanding those Oaths. 2. When, therefore, the obligation by the law to fidelity and allegiance ceases, that by the Oath also ceases..."

"It seems to me, that if the matter of our sun and planets and all the matter of the universe, were evenly scattered throughout all the heavens, and every particle had an innate gravity towards all the rest, and the whole of space throughout which this matter was scattered was but finite, the matter on [toward] the outside of this space would, by its gravity, tend towards all the matter on the inside, and, by consequence, fall down into the middle of the whole space, and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space it could never convene into one mass; but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one another throughout all that infinite space."

"When I wrote my treatise about our System, I had an eye upon such principles as might work with considering men for the belief of a Deity and nothing can rejoice me more than to find it useful for that purpose. But if I have done the public any service this way, 'tis due to nothing but industry and a patient thought."

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers."

"I keep the subject constantly before me, and wait 'till the first dawnings open slowly, by little and little, into a full and clear light."

"In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposition in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method."

"I have studied these things — you have not."

"I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

"In default of any other proof, the thumb would convince me of the existence of a God."

"We account the Scriptures of God to be the most sublime philosophy. I find more sure remarks of authenticity in the Bible than in any profane history whatever."

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

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

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

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

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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..."

"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."

"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."

"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?"

"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."

"[Newton] bought a book of Iudicial Astrology out of a curiosity to see what there was in that science & read in it till he came to a figure of the heavens which he could not understand for want of being acquainted with Trigonometry, & to understand the ground of that bought an English Euclid with an Index of all the problems at the end of it & only turned to two or three which he thought necessary for his purpose & read nothing but the titles of them finding them so easy & self evident that he wondered any body would be at the pains of writing a demonstration of them & laid Euclid aside as a trifling book, & was soon convinced of the vanity & emptiness of the pretended science of Iudicial astrology."

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