Simon Stevin added to category
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[[File:SimonStevinQuetelet.jpg|thumb|<center>Lauters Lacoste frontispiece in<br />[[Adolphe Quetelet]], [https://books.google.com/books?id=GbQ_AAAAcAAJ ''Simon Stevin'']<br />(1850)</center>]]
'''{{w|Simon Stevin}}''' (1548–1620), sometimes called '''Stevinus''', was a Flemish mathematician, physicist and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical.
== Quotes ==
* We call the wise age that in which men had a wonderful knowledge of science which we recognize without fail by certain signs, although without knowing who they were, or in what place, or when. ...It has become a matter of common usage to call the barbarous age that time which extends from about 900 or a thousand years up to about 150 years past, since men were for 700 or 800 years in the condition of imbeciles without the practice of letters or sciences—which condition had its origin in the burning of books through troubles, wars, and destructions; afterwards affairs could, with a great deal of labor, be restored, or almost restored, to their former state; but although the afore-mentioned ''preceding'' times could call themselves a wise age in respect to the barbarous age just mentioned, nevertheless we have not consented to this definition of such a wise age, ''since both taken together are nothing but a true barbarous age'' in comparison to that unknown time at which we state that it [i.e., the wise age] was, without any doubt, in existence.
** ''Géographie'', in Les Oeuvres Mathématiques de Simon Stevin de Bruges (1634) ed. [[w:Albert Girard|Girard]], p. 106-108, as quoted by [[w:Jacob Klein (philosopher)|Jacob Klein]], ''Greek Mathematical Thought and the Origin of Algebra'' (1968)
* [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.
** ''Géographie'', in Les Oeuvres Mathématiques de Simon Stevin de Bruges (1634) ed. Girard, p. 109, as quoted by Jacob Klein]], ''Greek Mathematical Thought and the Origin of Algebra'' (1968)
* [[Diophantus]] is modern.
** ''Géographie'', in Les Oeuvres Mathématiques de Simon Stevin de Bruges (1634) ed. [[w:Albert Girard|Girard]], p. 106-108, as quoted by [[w:Burt C. Hopkins|Burt C. Hopkins]], ''The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein'' (2011) p. 295
=== ''Disme: the Art of Tenths, Or, Decimall Arithmetike'' (1608) ===
<small>Tr. Robert Norton, [https://books.google.com/books?id=aVdIAQAAMAAJ source]</small>
* The second Definition. Number is that which expresseth the quantitie of each thing.
* The sixt Definition. A Whole number is either a unitie, or a compounded multitude of unities.
* The seventh Definition. The Golden Rule, or Rule of three, is that by which to three tearmes given, the fourth proportionall tearme is found.
[[File:StevinDismeMultPythagoreanTable.jpg|thumb|Pythagorean Table for Multiplication of whole Numbers, Stevin's ''Disme: the Art of Tenths, Or, Decimall Arithmetik'' (1608) Tr. Robert Norton]]
* 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 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: <math>\frac{x}{4} = \frac{3}{2}</math>]. ...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.
* ...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 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.
* 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 [[Ptolemy|Ptolome]] & [[w:Regiomontanus|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.
* 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.
== Quotes about Stevin ==
[[File:60 Simon Stevin.jpg|thumb]]
* We find also the Famous ''{{w|Simon Stevin}}'', 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,<br />''The Part is of the same Nature with the whole,<br />The Unit is a Part of a Multitude of Units,<br />Therefore the Unit is of the same Nature with a MuItitude of Units, and consequently of Number.''<br />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.<br />The Second Argument which ''Stevin'' produces is of no more force.<br />''If then the Unit were not a Number, Subtracting one out of three, the Number given would remain, which is absurd.''<br />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. ...<br />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.<br />Thus doth ''Stevin'' frequently wrangle about the Definition of words, as when he perplexes himself to prove that Number is not a quantity [[w:Discrete mathematics|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.
** [[w:Antoine Arnauld|Antoine Arnauld]], [[Pierre Nicole]], ''La logique ou l'art de penser contenant outre les règles communes, plusieurs observations nouvelles, propres à former le jugement'' (1683) ''[https://books.google.com/books?id=UcJaAAAAYAAJ The Port Royal Art of Thinking: In Four Parts]'' (1818) Translation, pp. 239-240.
* 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.
** Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient, ''The Historical Roots of Elementary Mathematics'' (1976) pp. 229-230.
* 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 <math>x^3 + x^2</math> and <math>x^2 + 7x + 6</math> 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.
** [[Florian Cajori]], ''A History of Mathematics'' (1893) pp. 147-148.
* 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.
** [[Florian Cajori]], ''A History of Mathematics'' (1893) p. 171.
* One of the greatest curiosities of the history of science that [[John Napier|Napier]] constructed logarithms before exponents were used. To be sure, [[w:Michael Stifel|Stifel]] and Stevin made some attempts to denote powers by indices, but this notation was not generally known,—not even to [[w:Thomas Harriot|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 [[François Viète|F. Vieta]] represented <math>A^3</math> by "A cubus" and Stevin <math>x^3</math> by a figure 3 within a small circle [around it], [[René Descartes|Descartes]] wrote <math>a^3</math>.
** [[Florian Cajori]], ''A History of Mathematics'' (1893) p.149 & 178.
* 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 [[John Napier|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 [[Johannes Kepler|Kepler]] and [[w:Henry Briggs (mathematician)|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: <math>24</math> <math>3^{(1)} 7^{(2)} 5^{(3)}</math>.]
** Tobias Dantzig, ''Number: The Language of Science'' (1930)
* 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 <math>10^n</math>...The first to apply this method was the German astronomer [[w:Regiomontanus|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''.
** E.J. Dijksterhuis, ''Simon Stevin: Science in the Netherlands around 1600'' (2012) pp. 17-18.
* 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. [[w:Joseph Raphson|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.
** William Frend, John Kersey, ''[https://books.google.com/books?id=GZpYAAAAMAAJ Tracts on the Resolution of Affected Algebräick Equations by Dr. Halley's, Mr. Raphson's, and Sir Isaac Newton's, Methods of Approximation]'' (1800) Preface, pp. lviii-lix.
* 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.
** William Frend, "An Explication of Simon Stevin's General Rule, ..." ''[https://books.google.com/books?id=6VsUAAAAQAAJ The Principles of Algebra]'' (1796) p. 503.
* 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.
** John Bart Geijsbeek, ''[https://books.google.com/books?id=uQ9AAAAAYAAJ Ancient Double-entry Bookkeeping: Lucas Pacioli's Treatise...]'' (1914) p. 11.
[[File:Simon-stevin.jpeg|thumb]]
* The works on which the fame of [[Diophantus]] rests are:<br />1. the ''Arithmetica'' (originally in thirteen Books) 2. a tract ''On Polygonal Numbers''.<br />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 [[w:Wilhelm Xylander|Xylander]].
** Sir [[Thomas Little Heath]], ''A History of Greek Mathematics'' (1921) [https://books.google.com/books?id=LUUzAQAAMAAJ Vol. 2], pp. 448-455.
* For Stevin, the "signs" that in earlier times a "golden age" (aurea aetas) of science actually existed are these:<br />1. The traces of a perfected astronomical knowledge found in Hipparchus and Ptolemy, whose writings he understands as mere "vestiges" of primeval knowledge...<br />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...<br />3. Evidence of the foreign origin Greek geometry. ...<br />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."<br />"Alchemy," which was unknown to the Greeks and whose most expert representative Stevin saw as [[w:Hermes Trismegistus|Hermes Trismegistos]].
** [[w:Jacob Klein (philosopher)|Jacob Klein]], ''Greek Mathematical Thought and the Origin of Algebra'' (1968)
* 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.
** [[w:Morris Kline|Morris Kline]], ''Mathematics for the Nonmathematician'' (1967)
* The first conception of a changing conception of number are found in [[w:Regiomontanus|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.'<br />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
** Ad Meskens, ''Travelling Mathematics - The Fate of Diophantos' Arithmetic'' (2010) pp. 126-127.
* Trigonometrical solutions may... be extended to quadrilateral and other multilateral figures, plane as well as spherical, as may be seen in Simon Stevin.
** Vasiliĭ Nikitich Nikitin, Prokhov Ignatévich Suvorov, ''Elements of Plane and Spherical Trigonometry'' (1786)
* Some will have it that the ''Balance'', and ''Steel-yard'' derive their Origin and fundamental Principles, from these two general ''Axioms'' in ''Mechanicks'' (viz.) that ''Equal Weights weigh equally at equal Distances, but unequally, it unequal Distances'': and this other, ''that unequal Weights weigh unequally at equal Distances, but that they weigh equally at unequal Distances, provided that their Distances are in a reciprocal Proportion to their Weights''. Those who would be satisfied as to these Demonstrations, may find them In [[w:Guidobaldo del Monte|Guido Ubaldus]], [[Galileo Galilei|Galileus]], Simon Stevin, John Buteo, in Guevara, and several other Mechanical Writers, who have enlarged very much upon this Subject.
** Kazimierz Siemienowicz, ''[https://books.google.com/books?id=W0oCAAAAQAAJ The Great Art of Artillery]'' (1729) Tr. G. Shelvocke, p. 45.
* Stevin (1585): 3<sup>②</sup> + 4 egales à 2<sup>①</sup> + 4. Modern form: <math>3 x^2 + 4 = 2x + 4</math>.</sup>
** [[w:David Eugene Smith|David Eugene Smith]], ''History of Mathematics'' (1925) Vol. 2
== External links ==
{{wikipedia}}
* ''Disme: the Art of Tenths, Or, Decimall Arithmetike'' by Simon Stevin (1608) Tr. Robert Norton
* [http://adcs.home.xs4all.nl/stevin/index-en.html Wonder, not miracle motto of Simon Stevin] by Ad Davidse Cathie Schrier, with some of his work.
* [[Category:Engineers]]
* [[Category:Mathematicians]]
* [[Category:Scientists]]