Engineers

"The first conception of a changing conception of number are found in Regiomontanus. He was a man who still stood with one foot in the world of the Ancients, and hence considered numbers as arithmoi, or sets of units. However... the other foot... stood firmly in the modern world, as all magnitudes are quantities 'that are measured in relation to a certain unit'. According to Regiomontanus... 'it is better to approximate the truth, than to ignore it.' With Stevin, this reluctance disappears altogether. His definition of number builds on Regiomontanus, but it was also revolutionary, for he dropped the classical definition altogether and accepted the modern notion: "Nombre est cela par lequel s'explique la quantité de chascune chose," [Number is that by which the quantity of each thing is revealed,] "nombre n'est poinct quantité discontinue" [number is not at all disontinuous quantity] and "que l'unité est nombre" [the unit is a number]. Stevin did not consider numbers as a discontinuous spectrum, but as a continuum"

"The Dutch engineer Simon Stevin learned about the pressure exerted by water on the walls of canals, and made precise observations of the nature of stable and unstable equilibrium of bodies. He also studied the motion of bodies on slopes."

"For Stevin, the "signs" that in earlier times a "golden age" (aurea aetas) of science actually existed are these: 1. The traces of a perfected astronomical knowledge found in Hipparchus and Ptolemy, whose writings he understands as mere "vestiges" of primeval knowledge... 2. Algebra, as we have become acquainted with it through Arabic books and which represents one of the strangest "vestiges" of the "wise age." No trace of it is found in the Chaldeans, the Hebrews, the Romans, and even the Greeks... 3. Evidence of the foreign origin Greek geometry. ... 4. Information concerning the height of the clouds, which appears in an Arabic work and which Stevin does not hesitate to trace back to the science of the "wise age." "Alchemy," which was unknown to the Greeks and whose most expert representative Stevin saw as Hermes Trismegistos."

"Long before Mouton's proposals of 1670... Simon Stevin... published, first in Flemish and in the same year, 1585, in French, a treatise in which the first explanation of decimal fractions is given. In the same treatise Stevin proposes that not only weights and moneys but also linear, square, and cubic measure and even degrees and minutes should be reduced to a decimal system. This proposal, together with the explanation of the decimal fractions, establishes for Simon Stevin a proud place in the history of the development of scientific systems of measurement."

"The first systematic discussion of decimal fractions with full appreciation of their significance was given by Simon Stevin... His work in Flemish, entitled La Thiende... was republished again in 1585 in French with the title La Disme; in 1608 an English translation by Robert Norton, The Art of Tenths or Decimall Arithmetike, appeared in London. This work is addressed to astronomers, surveyors, masters of money (of the mint), and to all merchants. ...All Stevin says applies today, hardly with a change of letter. ...The immediate application of decimal fractions was made particularly to the trigonometric functions and to logarithms"

"Sailing carriages are said to have been used in very remote times in China, and as far back as 1617, in the collection of travels by ... But before that date sailing chariots had actually been constructed in Holland by the celebrated mathematician Simon Stevin (born at Bruges, 1548, died 1620), a much-esteemed friend of the Stadtholder, Prince Maurice of Nassau. These vehicles attracted consider able attention from the men of science of the seventeenth century. Our own Bishop Wilkins is loud in their praise, and Grotius wrote several poems on the carriages and on their constructor. Fortunately, too, there is an engraving, now extremely rare, by Swanenburch, after a design by Jacques de Gheyn, which brings out the arrangement very clearly. It is dated 1612... Another issue of the plates, supposed to be the third, is dated 1652, and a reduced and reversed reproduction is stated by Müller, De Nederlandsche Geschiedenis in Platen, to be found in Bleau's Tooneel der Steden, 1649. A reduced copy of the central plate, showing the carriage only, is given in Le Magazin Pittoresque for 1844, and it is from that copy that the accompanying illustration (Fig. 1) has been produced. ... In a pamphlet, possibly issued with the engraving, bearing the title Windt-Wagens: Les Artificiels Chariots à Voiles du Compte Maurice... is given an account of a journey made apparently in the year 1600 along the beach from the now fashionable Dutch watering-place Scheveningen to Petten, a distance of forty-two miles to the north, which was covered in two hours, a speed which seems almost incredible. The passengers included Prince Maurice himself, who steered; Grotius, then a lad of fifteen; the Spanish Admiral, Francis Mendoza, at that time a prisoner in the hands of Prince Maurice after the battle of Nieuport; and others to the number of twenty-eight. The trial appears to have been a great success, but in spite of this, unless, indeed, the trip performed by De Peiresc in 1606 was made in it, there appears to be absolutely no record of its having been afterwards used, and, stranger still, it is quite unknown what became of the carriage in the end. It is referred to in Howell's Letters as being one of two wonderful things to be seen near the Hague: "A waggon, or ship, or a monster mixed of both, like the Hippocentaur, who was half man and half horse; this engine that hath wheels and sails, will hold above twenty people, and goes with the wind, being drawn or mov'd by nothing else, and will run, the wind being good, and the sails hois'd up, above fifteen miles an hour upon the even hard sands: they say this invention was found out to entertain Spinola when he came hither to treat of the last truce." The anonymous author of The Present State of Holland, 1765, says of Scheveningen: " This village is famous also for a sailing chariot belonging to Prince Maurice, and kept here." He adds: "The last time it made its appearance on the strand was about 17 years ago, when through the unskilfulness of the steersman it had like to have run into the sea, and put the passengers into no small fright." This in all probability refers to the smaller carriage mentioned above as represented in the drawing of Jacques de Gheyn, which was to be seen at Scheveningen as late as 1802; its fate since that date is unknown. There is an account of another, but partially successful trial, with this carriage in 1790 upon the occasion of a royal marriage, and it is known that it was sold by auction in 1795. Stevin's contrivances appear to have set the anonymous author referred to above at work upon his own account, on what must be regarded as the forerunner of the motor perambulators, with which we shall no doubt become familiar ere long."

"Stevin, Stevinus, (Simon) a Flemish mathematician of Bruges, who died in 1633. He was master of mathematics to prince Maurice of Nassau, and inspector of the dykes in Holland. It is said he was the inventor of the sailing chariots, sometimes made use of in Holland. He was a good practical mathematician and mechanist, and was author of several useful works: as treatises on Arithmetic, Algebra, Geometry, Statics, Optics, Trigonometry, Geography, Astronomy, Fortification, and many others, in the Dutch language which were translated into Latin, by Snellius and printed in 2 volumes folio. There are also two editions in the French language, in folio, both printed at Leyden, the one in 1608, and the other in 1634, with curious notes and additions by ."

"The works on which the fame of Diophantus rests are: 1. the Arithmetica (originally in thirteen Books) 2. a tract On Polygonal Numbers. Six Books only of the former and a fragment of the latter survive. ...In 1585 Simon Stevin published a French version of the first four Books, based on Xylander."

"The idea of extending the decimal place-value system to include fractions was discovered by several mathematicians. The most influential... was Simon Stevin... who popularized the system in a booklet called De Thiende (“The tenth”), first published in 1585. By extending place value to tenths, hundredths, and so on, Stevin created the system... More importantly, he explained how it simplified calculations... Stevin was aware that his system provided a way to attach a "number" (...decimal expansion) to every... length. ...In his Arithmetic he declared that... roots were just numbers. ...that "there are no absurd, irrational, irregular, inexplicable, or surd numbers" ...all terms for irrational numbers ...Stevin was proposing ...to flatten the incredible diversity of "quantities" or "magnitudes" into one expansive notion of number, defined by decimal expansions. ...this amounted to a fairly clear notion of... the positive real numbers. Stevin's proposal was made immensely more influential by the invention of logarithms. Like the sine and the cosine, these were practical computational tools. ...they needed to be tabulated, and the tables were given in decimal form. Very soon, everyone was using decimal representation. ...The positive real numbers are... an immensely larger number system, whose internal complexity we still do not fully understand."

"Simon Stevin... wrote in Latin a book on mathematics, which was published in Leijden in 1608, in which he includes several chapters on bookkeeping. These were a reproduction of a book published in the Dutch language on "bookkeeping for merchants and for princely governments," which appeared in Amsterdam in 1604, and was rewritten in The Hague in 1607, in the form of a letter addressed to Maximiliaen de Bethune, Duke of Seulley. This Duke was superintendent of finance of France and had numerous other imposing titles. He had been very successful in rehabilitating the finances of France and Stevin, knowing him through Prince Maurits of Orange, was very anxious to acquaint him with the system which he had installed and which had proven so successful. ...Stevin's book becomes very important to Americans, because he materially influenced the views of his friend Richard Dafforne, who through his book "The Merchants' Mirrour," published in 1636, became practically the English guide and pioneer writer of texts on bookkeeping."

"I shall lead the industrious learner a few steps farther in order to his understanding the resolution of all manner of compound equations in numbers, and... shall explain Simon Stevin's General Rule, which, with the help of the rules in the following eleventh Chapter, will discover all the roots of any possible equation in numbers, either exactly, if they be rational, or very nearly true, if irrational."

"The chapter of this valuable book... (...which I had reprinted... as an Appendix to Mr. Frend's Principles of Algebra,) relates to the method invented by Simon Stevinus... for finding... the first near value of x, or the root of any proposed Algebräick equation, by repeated conjectures and trials with easy numbers of one or two decimal figures: after having found which we may proceed to determine the value of the said root to a greater degree of exactness by one or more applications of Mr. Raphson's method of approximation. The title of this 10th Chapter of Mr. Kersey's Algebra is as follows: An Explanation of Simon Stevin's General Rule to extract one Root out of any possible Equation of Numbers, either exactly or very nearly true."

"In the... fifteenth century, the sexagesimal division of the radius, in terms of which cords and goniametrical line-segments were expressed, was generally superseded, though not immediately replaced, by a decimal system of positional notation. Instead, mathematicians sought to avoid fractions by taking the Radius equal to a number of units of length of the form 10^n...The first to apply this method was the German astronomer Regiomontanus... the second half of the sixteenth and the first decades of the seventeenth century... observed of a gradual development of this method of Regiomontanus into a complete system of decimal positional fractions. Yet none of the steps taken by... writers is comparable in importance and scope with the progress achieved by Stevin in his De Thiende."

"Positional numeration had been in full use for many centuries before it was realized that among the advantages of the method was its great facility in handling fractions. Even then the realization was far from complete, as may be gleaned from the cumbersome superscripts and subscripts used by Stevin and Napier. ...all that was necessary to bring the scheme to full effectiveness was a mark such as our modern decimal point... Yet... the innovators... with the exception of Kepler and Briggs, either did not recognize this fact, or else had no faith that they could induce the public to accept it. Indeed, a century after Stevin's discovery, a historian... remarked Quod homines tot sententiae (As many opinions as there are people), and it took another century before decimal notation was finally stabilized and the superfluous symbols dropped. [Included table indicates Simon Stevin's notation for 24.375 was: 24 3^{(1)} 7^{(2)} 5^{(3)}.]"

"One of the greatest curiosities of the history of science that Napier constructed logarithms before exponents were used. To be sure, Stifel and Stevin made some attempts to denote powers by indices, but this notation was not generally known,—not even to T. Harriot, whose algebra appeared long after Napier's death. That logarithms flow naturally from the exponential symbol was not observed until much later. ...While F. Vieta represented A^3 by "A cubus" and Stevin x^3 by a figure 3 within a small circle [around it], Descartes wrote a^3."

"Among the ancients, Archimedes was the only one who attained clear and correct notions on theoretical statics. He had acquired firm possession of the idea of pressure, which lies at the root of mechanical science. But his ideas slept nearly twenty centuries until the time of S. Stevin and Galileo Galilei. Stevin determined accurately the force necessary to sustain a body on a plane inclined at any angle to the horizon. He was in possession of a complete doctrine of equilibrium. While Stevin investigated statics, Galileo pursued principally dynamics."

"To Simon Stevin of Bruges in Belgium, a man who did a great deal of work in most diverse fields of science, we owe the first systematic treatment of decimal fractions. In his La Disme (1585) he describes in very express terms the advantages, not only of decimal fractions, but also of the decimal division in systems of weights and measures. Stevin applied the new fractions "to all the operations of ordinary arithmetic." What he lacked was a suitable notation. ...Stevin found the greatest common divisor of x^3 + x^2 and x^2 + 7x + 6 by the process of continual division, thereby applying to polynomials Euclid's mode of finding the greatest common divisor of numbers, as explained in Book VII of his Elements. Stevin was enthusiastic not only over decimal fractions, but also over the decimal division of weights and measures. He considered it the duty of governments to establish the latter. He advocated the decimal subdivision of the degree. No improvement was made in the notation of decimals till the beginning of the seventeenth century."

"It was not until about 1600 that the idea of writing fractions in the form of decimals was promoted in Western Europe. The Dutch mathematician Simon Stevin was the first to throw clear light upon the advantages of the decimal notation. In a pamphlet, De Thiende (The Dime), he advocated the use of decimal fractions. He urged that governments adopt the decimal system and also decimal coins, weights, and measures. This did not happen on a large scale, however, until the French Revolution."

"We find also the Famous ', Mathematician to the Prince of Orange, having defined Number to be, That by which is explained the quantity of every Thing, he becomes so highly inflamed against those that will not have the Unit to be a Number, as to exclaim against Rhetoric, as if he were upon some solid Argument. True it is that he intermixes in his Discourses a question of some Importance, that is, whether a Unit be to Number, as a Point is to a Line. But here he should have made a distinction, to avoid the confusing together of two different things. To which end these two questions were to have been treated apart; whether a Unit be Number, and whether a Unit be to Number, as a Point is to a Line; and then to the first he should have said, that it was only a Dispute about a Word, and that an Unit was, or was not a Number, according to the Definition, which a Man would give to Number. That according to Euclid's Definition of Number; Number is a Multitude of Units assembled together: it was visible, that a Unit was no Number. But in regard this Definition of Euclid was arbitrary, and that it was lawful to give another Definition of Number, Number might be defined as Stevin defines it, according to which Definition a Unit is a Number; so that by what has been said, the first question is resolved, and there is nothing farther to be alleged against those that denied the Unit to be a Number, without a manifest begging of the question, as we may see by examining the pretended Demonstrations of Stevin. The first is, The Part is of the same Nature with the whole, The Unit is a Part of a Multitude of Units, Therefore the Unit is of the same Nature with a MuItitude of Units, and consequently of Number. This Argument is of no validity. For though the part were always of the same nature with the whole, it does not follow that it ought to have always the same name with the whole; nay it often... has not the same Name. A Soldier is part of an Army, and yet is no Army... a Half-Circle is no Circle... if we would we could not... give to Unit more than its name of Unit or part of Number. The Second Argument which Stevin produces is of no more force. If then the Unit were not a Number, Subtracting one out of three, the Number given would remain, which is absurd. But... to make it another Number than what was given, there needs no more than to subtract a Number from it, or a part of a Number, which is the Unit. Besides, if this Argument were good, we might prove in the same manner, that by taking a half Circle from a Circle given, the Circle given would remain, because no Circle is taken away. ... But the second Question, Whether an Unit be to Number, as a Point is to a Line, is a dispute concerning the thing? For it is absolutely false, that an Unit is to number as a point is to a Line. Since an Unit added to number makes it bigger, but a Line is not made bigger by the addition of a point. The Unit is a part of Number, but a Point is no part of a Line. An Unit being subtracted from a Number, the Number given does not remain; but a point being taken from a Line, the Line given remains. Thus doth Stevin frequently wrangle about the Definition of words, as when he perplexes himself to prove that Number is not a quantity discreet, that Proportion of Number is always Arithmetical, and not Geometrical, that the Root of what Number soever, is a Number, which shews us that he did not properly understand the definition of words, and that he mistook the definition of words, which were disputable, for the definition of things that were beyond all Controversy."

"If all this be not put in practize... it wil be beneficiall to our successors, if future men shal hereafter be of such nature as our predecessors, who were never negligent of so great advantage. ...they may all deliver them selves when they will, from so much and so great labour."

"Our intention in this Disme is to worke all by whole numbers: for seing that in any affayres, men reckon not of the thousandth part of a mite, grayne, &c. as the like is also used of the principall Geometricians, and Astronomers, in computacions of great consequence, as Ptolome & Johannes Monta-regio have not described their Tables of Arches, Chords, or Sines, in extreme perfection (as possibly they might have done by Multinomiall numbers,) because that imperfection (considering the scope and end of those Tables) is more convenient then such perfection."

"The first Part. Of the Definitions of the Dismes. The first Definition. Disme is a kind of Arithmeticke, invented by the tenth progression, consisting in Characters of Cyphers; whereby a certaine number is described, and by which also all accounts which happen in humane affayres, are dispatched by whole numbers, without fractions or broken numbers."

"...the use of the Disme ...to teach such as doe not already know the use and practize of Numeration, and the foure principles of common Arithmetick, in whole numbers, namely, Addition, Substraction, Multiplication, & Division, together with the Golden Rule, sufficient to instruct the most ignorant in the usuall practize of this Art of Disme or Decimall Arithmeticke"

"The Rule of Three, or Golden Rule of Arithmeticall whole Numbers. Be the three termes given 2 3 4. ...To finde their fourth proporcionall Terme: that is to say, in such Reason to the third terme 4, as the second terme 3, is to the first terme 2 [Modern notation: \frac{x}{4} = \frac{3}{2}]. ...Multiply the second terme 3, by the third terme 4, & giveth the product 12: which dividing by the first terme 2, giveth the Quotient 6: I say that 6 is the fourth proportional terme required."

"Multiplication of whole Numbers ...Note, that for the more easie solution of this proposition, it were necessary to have in memory the multiplication of the 9 simple Characters among themselves, learning them by rote out of the Table here placed..."

"The seventh Definition. The Golden Rule, or Rule of three, is that by which to three tearmes given, the fourth proportionall tearme is found."

"The sixt Definition. A Whole number is either a unitie, or a compounded multitude of unities."

"The second Definition. Number is that which expresseth the quantitie of each thing."

"Diophantus is modern."

"[The books of Euclid pass on to us] something admirable and very necessary to see and to read, namely the order in the method of writing on mathematics in that aforementioned time of the wise age."

"I only just hint this to show what use this engine may be put to in working of mills, especially where coals are cheap. I have only this to urge, that water in its fall from any determinate height, has simply a force answerable and equal to the force that raises it."

"In June, 1699, Captain Savery exhibited a model of his engine before the Royal Society, and the experiments he made with it succeeded to their satisfaction. It consisted of a furnace and boiler B: from the latter, two pipes, provided with cocks C, proceeded to two steam vessels S, which had branch pipes from a descending main D, and also to a rising main pipe A: each pair of branch pipes had check] valves a, b to prevent the descent of the water raised by the condensation or by the force of steam. Only one vessel, S, is shown, the other being immediately behind it. One of the steam vessels being filled with steam, condensation was produced by projecting cold water, from a small cistern E, against the vessel; and into the partial vacuum made by that means, the water, by the pressure of the atmosphere, was forced up the descending main D, from a depth of about twenty feet; and on the steam being let into the vessels again, the valve b closed, and prevented the descent of the water, while the steam having acquired force in the boiler, its pressure caused the water to raise the valve a, and ascend to a height proportional to the excess of the elastic force of the steam above the pressure of the air."

"I soon relinquished the idea of constructing an engine upon its principle, from being sensible it would be liable to some of the objections against Savery's engine, viz., the danger of bursting the boiler, and the difficulty of making the joints tight, and also that a great part of the power of the steam would be lost, because no vacuum was formed to assist the descent of the piston. I, however, described this engine in the fourth article of the specification of my patent of 1769; and again in the specification of another patent in the year 1784, together with a mode of applying it to the moving of wheel-carriages."

"What I say here is not to give room for believing, that Mr. Savery, who has since published this invention at London, is not actually the inventor. I do not doubt that the same thought may have occurred to him, as well as to others, without having learnt it elsewhere."

"Amongst the several Engines which have been contriv'd for the raising of Water for the Supply of Houses and Gardens, none has been more justly surprising, than that for the raising of Water by Fire; the particular Contrivance and sole Invention of a Gentleman, with whom I had the Honour long since to be well acquainted; I mean, the ingenious Captain Savery, sometime since deceased, but then a most noted engineer, and one of the Commissioners of the Sick and Wounded. ...It was a considerable Time before this curious Person, who has been so great an Honour to his Country, could, (as he himself tells us) bring this his Design to Perfection, on account of the Aukwardness of the Workmen, who were necessarily to be imploy'd in the Affair; but at last he conquer'd all Difficulties, and procur'd a Recommendation of it from the Royal Society, in Transac. No. 252. and soon after, a Patent from the Crown, for the sole making this Engine; And I have heard him say my self, that the very first Time he play'd it, it was in a Potter's House at Lambeth, where, tho' it was a small Engine, yet it forc'd its Way thro' the Roof, and struck up the Tiles in a Manner that Surpris'd all the Spectators."

"Should the engine, to the apprehension of some, seem intricate and difficult to be worked, after all the description I have given of it in this book, yet I can, and do assure them, that the attending and working the engine is so far from being so, that it is familiar and easy to be learned by those of the meanest capacity, in a very little time; insomuch that I have boys of thirteen or fourteen years of age, who now attend and work it to perfection, and were taught to do it in a few days; and I have known some learn to work the engine in half an hour. We have a proverb, that interest never lies; and I am assured that you gentlemen of the mines and collieries, when you have once made this engine familiar in your works, and to yourselves and servants; not only the profit, but abundance of other advantages and conveniences which you will find to attend your works in the use thereof, will create in you a favourable opinion of the labours of Your real Friend and humble Servant, THOMAS SAVERY"

"A reference framework is required in order to locate events in time and space. With some contractions and omissions, Figure 1.1 shows the conventional divisions for the classical and medieval periods. Even before the birth of the idea of nationality, it is quite acceptable to refer to specific countries, such as Greece and Italy, whose boundaries are well defined. It is also usual to refer to areas in which there is felt to have been some degree of cultural unity —— for example, the Roman Empire and Islam. Sometimes space and time are embraced by one image: the Roman Empire can mean either the first four centuries of our era or the area under Roman dominion. Used with care, these concepts have value for some historical purposes, but they can be very misleading. In the first place, we have to bear in mind the shifting of frontiers; in AD 750, for example, the Iberian peninsula was predominantly Muslim while Asia Minor was Christian — by 1450 the reverse was the case. Also, and this can be more serious, the conventional divisions are associated most closely with political and military realities, and often have little bearing on intellectual or social activities."

"We see for the first time in al-Jazari's work several concepts important for both design and construction: the lamination of timber to minimize warping, the static balancing of wheels, the use of wooden templates (a kind of pattern), the use of paper models to establish designs, the calibration of orifices, the grinding of the seats and plugs of valves together with emery powder to obtain a watertight fit, and the casting of metals in closed mold boxes with sand."

"As result a new kind of theory to be applied on a class of motions ... these geometric motions are that which acquire different parts of a system of bodies, without neither perturb themselves nor the other and consequently these motions do not depend of the action or reaction among the bodies, but only upon the conditions of their connections, and thus being determined only by geometry and not dependent of the rules of dynamics."

"The rational mechanics of Galileo, Descartes and Newton was not, then, directly applied to machines and is not surprising that parallelly it was maintained a "corpus" of experimental knowledge, more or less formalized, addressed to practical constractors... It will be necessary to wait until the end of the eighteenth century to that Lazare Carnot's sciences of machines could be formally integrated to rational mechanics."

"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."

"It is to Sir Isaac Newton's Application of Geometry to Philosophy, that we owe the routing of this Army of Goths and Vandals in the philosophical World; which he has enriched with more and greater Discoveries, than all the Philosophers that went before him: And has laid such Foundations for future Acquisitions, that even after his Death, his Works still promote natural Knowledge. Before Sir Isaac, we had but wild Guesses at the Cause of the Motion of the Comets and Planets round the Sun', but now he has clearly deduced them from the universal Laws of Attraction (the Existence of which he has proved beyond Contradiction) and has shewn, that the seeming Irregularities of the Moon, which Astronomers were unable to express in Numbers, are but the just Consequences of the Actions of the Sun and Earth upon it, according to their different Positions. His Principles clear up all Difficulties of the various Phænomena of the Tides; and the true Figure of the Earth is now plainly shewn to be a flatted Spheroid higher at the Equator than the Poles, notwithstanding many Assertions and Conjectures to the contrary."

"When mons. Descartes's philosophical Romance, by the Elegance of its Style and the plausible Accounts of natural Phænomena, had overthrown the Aristotelian Physics, the World received but little Advantage by the Change: For instead of a few Pedants, who, most of them, being conscious of their Ignorance, concealed it with hard Words and pompous Terms; a new Set of Philosophers started up, whose lazy Disposition easily fell in with a Philosophy, that required no Mathematicks to understand it, and who taking a few Principles for granted, without examining their Reality or Consistence with each other, fancied they could solve all Appearances mechanically by Matter and Motion; and, in their smattering Way, pretended to demonstrate such things, as perhaps Cartesius himself never believed ; his Philosophy (if he bad been in earnest) being unable to stand the test of the Geometry which he was Master of."

"All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon. But then we must call in Geometry and Arithmetics, to our Assistance, unless we are willing to content ourselves with natural History and conjectural Philosophy. For, as many causes concur in the production of compound effects, we are liable to mistake the predominant cause, unless we can measure the quantity and the effect produced, compare them with, and distinguish them from, each other, to find out the adequate cause of each single effect, and what must be the result of their joint action."

"To few Freemasons of the present day, except to those who have made Freemasonry a subject of especial study, is the name of Desaguliers very familiar. But it is well that they should know that to him, perhaps, more than to any other man, are we indebted for the present existence of Freemasonry as a living Institution, for it was his learning and social position that gave a standing to the Institution, which brought to its support noblemen and men of influence so that the insignificant assemblage of four London Lodges at the Apple-Tree Tavern has expanded into an association which now shelters the entire civilized world. And the moving spirit of all this was John Theophilus Desaguliers."

"Such is the disposition of men, that we value what is speculative and precarious, more than what is safe and beneficial."

"The nature of this trade, certainly not the most honourable in the world, affords room for much investigation and remark in a moral or humane point of view: in a political or commercial light it is perhaps less conspicuously an object of attention. It consists chiefly of commodities that are considered as holding a first rate place in the animal and the mineral world, for which in return the Africans receive the most rascally articles that the ingenuity of Europeans has found means to produce. In return to our fellow creatures, for gold, and for ivory, we exchange the basest of those articles that are suited to the taste or the fancy of a despicable set of barbarians. Whether the spirituous liquirs or the fire-arms that are sent there are most calculated for the destruction of the purchasers, might become a question not very easy to determine. The noxious quality of the one is at least equalled by the danger of attending the use of the other. There does not seem to be that regard to honour in this trade, which ought to make part of the nice character of the English merchant, unimpeachable, unimpeached, upon the 'Change of London or of Amsterdam. It seems as if we kept our honour for ourselves, and that with those barbarians (who are more our inferiors in address and cunning, than perhaps in any thing else) no honour, humanity, or equity, were at all necessary."

"All those things that make a nation richer, stronger, or more happy; or that tend to exalt national character, but that will not pay individuals, deserve public encouragement."

"Men in general are very slow to enter into what is reckoned a new thing; and there seems to be a very universal as well as great reluctance to undergo the drudgery of acquiring information that seems not to be absolutely necessary."

"The Egyptian people and army are supporting the Syrian uprising."