Stevin Research Articles

Simon Stevin's equal division of the octave

Summary Many pioneers of the Scientific Revolution such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about musical theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in musical theory. One of the issues involved was technically known as ‘the division of the octave’, the problem, that is, of which notes to make music with. Simon Stevin's contribution to this issue, in his treatise Vande Spiegheling der Singconst (‘On the Theory of Music’), is usually conceived of as a remarkably early plea for equal temperament, which is the tuning system we nowadays all take for granted. In this paper I show that, even though it is true that Stevin calculated the figures for what is now known as equal temperament, in fact the subject of temperament has almost nothing to do with his accompanying considerations, and that, therefore, his calculation...

Simon Stevin and Pieter Saenredam: A Study of Mathematics and Vision in Dutch Science and Art

Geometrical perspective after ca. 1550 became increasingly abstracted from artists' concerns. The new style of projective geometry is represented in Holland by Simon Stevin, who shows a typically Dutch concern to bring mathematical principles into the practical realm. His writings were known to Pieter Saenredam, whose perspectival techniques show important affinities to the visual characteristics of Stevin's projective geometry, particularly with respect to the transformed shape of geometrical configurations on the flatness of the picture plane from specifically defined viewpoints. Saenredam's geometrical sensibilities interact in a complex way with the intuitive aspects of his art.

Simon Stevin and Pieter Saenredam: A Study of Mathematics and Vision in Dutch Science and Art

Simon Stevin and Pieter Saenredam: A Study of Mathematics and Vision in Dutch Science and Art

The free rectangular band of inverse semigroups on a set

This paper provides a model for the free rectangular band of inverse semigroups on a set and the free perfect rectangular band of inverse monoids on a set, thus solving a problem originally posed by Pastijn (“Rectangular bands of inverse semigroups”, Simon Stevin 56 (1982) 3–95). It is shown that the free rectangular band of inverse semigroups and the free perfect rectangular band of inverse monoids on X may be described as suitable expansions of the free completely simple semigroup on X. A Rees representation for the free perfect rectangular band of inverse monoids on X is also provided.

Tuning and temperament in organ flue pipes

The scaling of ranks of organ flue pipes to produce a coherent, characteristic, and tonally balanced ensemble is a problem which has confronted organ builders for many centuries, but the temperament used to tune these pipes has likewise been of concern. With an analysis of the Fantasia Chromatica by Jan Pieterszoon Sweelinck, and its contrapuntal fabric, the proposition by Simon Stevin of “finding 11 mean proportional parts between 2 and 1, learned through the 45th proposition of my French arithmetic” serves as a solution for a modification in temperament of the organ pipes at the Oude Kerk in Amsterdam where it was performed by Sweelinck.

A striving toward equal temperament: Prince Tsai‐yu in 1595 at Peking, and Simon Stevin shortly thereafter at Amsterdam

Did East meet West in 1595? Equal tempered approximations 1595, Peking and Amsterdam or the riddle of the abacus and logarithms. Both Tsai‐yu and Stevin set down the mathematical figures for equal temperament. Tsai‐yu calculated the 12th root of 2 by means of the abacus, carefully computing the appropriate root for each note separately—correct to nine decimals. Stevin's calculations on the other hand, finding 11 mean‐proportional parts between 2 and 1, were based upon the 45th proposition of his French arithmetic.

Experiments in Granular Flow

The earliest example of a granular flow is the sand in an hourglass. Investigations into the question of how it really works began with a paper by Hagen (1852), but since the hourglass has been replaced by other chronometers, only a few specialists know the present state of its theory. Another old example is the art of ploughing, which our ancestors knew much more about than we do. Still, their knowledge was practical rather than theoretical. Hence, when draught animals were replaced by tractors, engineers were surprised to find that the drag of a plough is almost independent of speed. Although rich soil is not exactly a granular material, in this respect it behaves like dry sand, which nobody cares to plough. Nowadays only a few experts are concerned with the flow of powders and bulk solids (cf Brown & Richards 1970), whereas confrontation with aeroand hydro­ dynamic problems is commonplace. Hence, the dynamics of granular material has failed to attract general interest to the same degree as fluid dynamics, although first papers were written by well-known hydrodynamicists such as Hagen (1852) and Reynolds (1885). The flow of a discontinuum is a challenge to theoreticians, although it gives opportunities to experimenters too. Because we know so little of the behavior of granular matter from daily experience, we are often surprised by test results. By contrast, the statics of granular material has been the topic of soil mechanics for a long time. For example, on the recommendation of Simon Stevin, the first chair for an engineering science was established in 1600 for a professor of fortification at Leiden University. A theory of earth pressure and resistance that is still the backbone of practical calculations was given by Coulomb in 1776, about 50 years before Cauchy rigorously defined stress and strain. The statics of an idealized soil that is neither moist nor cohesive is, of course, the natural starting point for a review on granular flow.

Simon Stevin: Science in the Netherlands around 1600. E. J. Dijksterhuis

Previous articleNext article No AccessBook ReviewsSimon Stevin: Science in the Netherlands around 1600. E. J. Dijksterhuis A. Van HeldenA. Van Helden Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Isis Volume 62, Number 4Winter, 1971 Publication of the History of Science Society Article DOIhttps://doi.org/10.1086/350818 Views: 3Total views on this site Copyright 1971 History of Science Society, Inc.PDF download Crossref reports no articles citing this article.

E. W. Beth. On machines which prove theorems. Simon Stevin, vol. 32 (1958), pp. 49–60.

E. W. Beth. On machines which prove theorems. Simon Stevin, vol. 32 (1958), pp. 49–60.

Anniversaries in 1970 of Interest to Physicists

During the year 1970 there are major anniversaries of the birth or death of seven men whose accomplishments and influence have been of importance to the development of physics. They are: Alexandre Edmond Becquerel, Henry Andrews Bumstead, Heinrich Gustav Magnus, Jean Baptiste Perrin, William John Macquorn Rankine, Simon Stevin, and John Tyndall. Brief accounts of their careers are given here.

The Principal Works of Simon Stevin. Vol. V: Engineering

The Principal Works of Simon Stevin. Vol. V: Engineering

Stevin, a new pseudoguaianolide isolated from stevia rhombifolia H.B.K.

Stevin a constituent of Stevia rhombifolia H.B.K. has been shown to be a new pseudoguaianolide with structure Ia.

The Principal Works of Simon Stevin. Volume IV, The Art of War

The Principal Works of Simon Stevin. Volume IV, The Art of War

The Principal Works of Simon Stevin. Volume IV, The Art of War. Edited by <italic>W. H. Schukking</italic>. (Amsterdam: C. V. Swets & Zeitlinger. 1964. Pp. v, 525.)

Journal Article The Principal Works of Simon Stevin. Volume IV, The Art of War. Edited by W. H. Schukking. (Amsterdam: C. V. Swets & Zeitlinger. 1964. Pp. v, 525.) Get access The Principal Works of Simon Stevin. Volume IV, The Art of War. Edited by Schukking W. H.. (Amsterdam: C. V. Swets & Zeitlinger. 1964. Pp. v, 525.) Charles H. Carter Charles H. Carter Tulane University Search for other works by this author on: Oxford Academic Google Scholar The American Historical Review, Volume 71, Issue 3, April 1966, Pages 983–984, https://doi.org/10.1086/ahr/71.3.983 Published: 01 April 1966

The Art of War. (Vol. IV of "The Principal Works of Simon Stevin")

The Art of War. (Vol. IV of "The Principal Works of Simon Stevin")

Stevin's Mathematical Works

The Principal Works of Simon Stevin Edited by Prof. D. J. Struik. Vol. 2A: Mathematics. Pp. v + 1–456. Vol. 2B: Mathematics. Pp. iii + 457–976. (Amsterdam: Swets and Zeitlinger, 1958.) n.p.

Historically Speaking,— Simon Stevin and the decimal fractions

Simon Stevin, the Flemish-Dutch engineer and mathematician, is best known in the history of mathematics as the inventor of the decimal fractions. This is substantially true, even if we acknowledge the fact that decimal fractions were used before Stevin.

Simon Stevin–A Founder of Mechanics

The Principal Works of Simon Stevin Edited by Ernst Crone, E. J. Dijksterhuis, R. J. Forbes, M. G. J. Minnaert and A. Pannekoek. Vol. 1: General Introduction; Mechanics. Pp. v + 617. (Amsterdam: C. V. Swets and Zeitlinger, 1955.) 52 guilders.

W. Peremans. Some theorems on free algebras and on direct products of algebras. Simon Stevin, vol. 29 (1952), pp. 51–59.

W. Peremans. Some theorems on free algebras and on direct products of algebras. Simon Stevin, vol. 29 (1952), pp. 51–59.

The Artificial Arithmetick in Decimals of Robert Jager (London, 1651)

The history of the decimal idea has been treated at length by G. SARTON (i). The first explanation of decimal fractions and measures is found in SIMON STEVIN's De Thiende (I585); and a French translation entitled La Disme was prepared and published by the author in the same year. In i6o8 ROBERT NORTON translated De Thiende into English under the title Disme: The art of tenths, or decimall arithmetike. This seems to have the honor of being the first book on the subject in English. Various books were published in England during the seventeenth century explaining the use of decimals. D. E. SMITH, in his Invention of the Decimal Fraction (2), mentions The art of tens, or decimall arithmeticke, by HENRY LYTE, London, I6I9; and SARTON also refers to it in his paper. SARTON also mentions WILLIAM BARTON's Arithmeticke abreviated. Teaching the art of tennes or decimals to worke all questions in fractions as whole numbers without reduction, London, I634. CAJORI (3) discusses the decimal notation as it was used in the seventeenth century, and refers to other English authors and their books. Several years ago the Hamilton College Library acquired a copy of a little book entitled: Artificial Arithmetick in Decimals, by ROBERT JAGER, Gent., London, i651. It is about io x 14.5 cms. in size and contains XIV + 256 pages; in several instances the pagination is incorrect. In searching for information concerning this book we have found that it is mentioned by CAJORI, 1. C., P. 325; that it is listed in WATT'S Bibliotheca Britannica; that there is a copy in the British Museum; and that the author is listed in ALLIBONE's Dictionary of Authors, with the single fact