## Simon Stevin

**-**

## Stevin, Simon

# STEVIN, SIMON

(*b*. Bruges, Netherlands [now Belgium], 1548; *d*. The Hague, Netherlands, *ca*. March 1620) *mathematics, engineering*.

Stevin was the illegitimate son of Antheunis Stevin and Cathelijne van de Poort, both wealthy citizens of Bruges. There is little reliable information about his early life, although it is known that he worked in the financial administration of Bruges and Antwerp and traveled in Poland, Prussia, and Norway for some time between 1571 and 1577. In 1581 he established himself at Leiden, where he matriculated at the university in 1583. His religious position is not known, nor is it known whether he left the southern Netherlands because of the persecutions fostered by the Spanish occupation. At any rate, in the new republic of the northern Netherlands Stevin found an economic and cultural renaissance in which he at once took an active part. He was first classified as an “engineer,” but after 1604 he was quartemaster-general of the army of the States of the Netherlands. At the same time he was mathematics and science tutor to Maurice of Nassau, prince of Orange, for whom he wrote a number of textbooks. He was often consulted on matters of defense and navigation, and he organized a school of engineers at Leiden and served as administrator of Maurice’s domains. In 1610 he married Catherine Cray; they had four children, of whom one, Hendrick, was himself a gifted scientist who, after Stevin’s death, published a number of his manuscripts.

Stevin’s work is part of the general scientific revival that resulted from the commercial and industrial prosperity of the cities of the Netherlands and northern Italy in the sixteenth century. This development was further spurred by the discovery of the principal works of antique science—especially those of Euclid, Apollonius, Diophantus, and Archimedes–which were brought to western Europe from Byzantium, then in a state of decline, or from the Arabic centers of learning in Spain. A man of his time, Stevin wrote on a variety of topics. A number of his works are almost wholly original, while even those that represent surveys of science as it existed around 1600 contain his own interpretations;
all are characterized by a remarkably lucid and methodical presentation. Stevin chose to write almost all of his books in the vernacular, in accordance with the spirit of self-confidence of the newly established republic. In the introduction to his *De Beghinselen der Weeghconst*of 1586, he stated his admiration for Dutch as a language of wonderful power in shaping new terms; and a number of the words coined by Stevin and his contemporaries survive in the rich Dutch scientific vocabulary.

Stevin’s published works include books on mathematics, mechanics, astronomy, navigation, military science, engineering, music theory, civics, dialectics, bookkeeping, geography, and house building. While many of these works were closely related to his mercantile and administrative interests, a number fall into the realm of pure science. His first book, the *Tafelen van Interest* (1582), derives entirely from his early career in commerce; in it Stevin set out the rules of single and compound interest and gave tables for the rapid computation of discounts and annuities. Such tables had previously been kept secret by big banking houses, since there were few skilled calculators, although after Stevin’s publication interest tables became common in the Netherlands.

In *De Thiende*, a twenty-nine-page booklet published in 1585, Stevin introduced decimal fractions for general purposes and showed that operations could be performed as easily with such fractions as with integers. He eliminated all difficulties in handling decimal fractions by interpreting 3.27, for example, as 327 items of the unit 0.01. Decimal fractions had previously found only occasional use in trigonometric tables; although Stevin’s notation was somewhat unwieldy, his argument was convincing, and decimal fractions were soon generally adopted. At the end of the tract, Stevin went on to suggest that a decimal system should also be used for weights and measures, coinage, and divisions of the degree of arc.

In *L’arithmétique*, also published in 1585, Stevin gave a general treatment of the arithmetic and algebra of his time, providing geometric counterparts. (An earlier work, the *Problemata geometrica* of 1583 had been entirely devoted to geometry; strongly marked by the influence of Euclid and Archimedes, it contained an especially interesting discussion of the semi-regular bodies that had also been studied by Dürer.) Stevin was of the opinion that all numbers–including squares, square roots, negative or irrational quantities–were of the same nature, an opinion not shared by contemporary mathematicians but one that was vindicated in the development of algebra. Stevin introduced a new notation for polynomials and gave simplified and unified solutions for equations of the second, third, and fourth degrees; in an appendix published at a later date he showed how to approximate a real root for an equation of any degree.

*De Deursichtighe* is a mathematical treatment of perspective, a subject much studied by artists and architects, as well as mathematicians, in the fifteenth and sixteenth centuries. Stevin’s book gives an important discussion of the case in which the plane of the drawing is not perpendicular to the plane of the ground and, for special cases, solves the inverse problem of perspective, that is, of finding the position of the eye of the observer, given the object and the perspective drawing of it. A number of other works are also concerned with the application of mathematics to practical problems, and in these the instances in which Stevin had to perform what amounts to an integration are particularly interesting. While mathematicians up to his time had followed the Greek example and given each proof by *reductio ad absurdum*, Stevin introduced methods that, although still cumbersome, paved the way toward the simpler methods of the calculus.

*De Beghinselen der Weeghconst* is Stevin’s chief work in mechanics. Published in 1586, some fifty years before Galileo’s discoveries, it is devoted chiefly to statics. From the evidence that it provides, Stevin would seem to be the first Renaissance author to develop and continue the work of Archimedes. The book contains discussions of the theory of the lever, the theorems of the inclined plane, and the determination of the center of gravity; but most particularly it includes what is perhaps the most famous of Stevin’s discoveries, the law of the inclined plane, which he demonstrated with the *clootcrans*, or wreath of spheres.

The *clootcrans*, as conceived by Stevin, consists of two inclined planes (*AB* and *BC*), of which one is twice the length of the other. A wreath of spheres placed on a string is hung around the triangle *ABC*, all friction being disregarded. The wreath will not begin to rotate by itself, and the lower section *GH* . . . *MNO*, being symmetrical, may be disregarded. It is thus apparent that the pull toward the left exerted by the four spheres that lie along *AB* must be equal to the pull to the right exerted by the two spheres that lie along *BC*–or, in other words, that the effective component of gravity is inversely proportional to the length of the inclined plane. If one of the inclined planes is then placed vertically, the ratio between the component along the inclined plane and the total force of gravity becomes obvious. This is, in principle, the theory of the parallelogram of forces.

Beneath his diagram of the *clootcrans* Stevin inscribed a cherished maxim, “Wonder en is gheen wonder” – “What appears a wonder is not a wonder” (that is, it is actually understandable), a rallying cry for the new science. He was so delighted with his discovery that he used the diagram of his proof as a seal on his letters, a mark on his instruments, and as a vignette on the title pages of his books; the device also appears as the colophon of this *Dictionary*.

Stevin’s next work on mechanics. *De Beghinselen des Waterwichts*, is the first systematic treatise on hydrostatics since Archimedes. In it, Stevin gave a simple and immediately comprehensible explanation for the Archimedean principle of displacement; before a body *C* is immersed, consider a volume of water equal to that of *C*. Since the latter body was at rest, it must have experienced, on displacement, an upward force equal to its weight,while *C* itself will, upon being placed in the water, experience the same degree of buoyancy. Stevin similarly chose to explain the hydrostatic paradox by imagining parts of the water to be solidified, so that neither equilibrium nor pressure was disturbed. He also wrote a number of shorter works in which he applied the principles of mechanics to practical problems of simple machines, balances, the windlass, the hauling of ships, wheels powered by men, the block-and-tackle, and the effect of a bridle upon a horse.

Stevin’s chief book on astronomy, *De Hemelloop*, was published in 1608; it is one of the first presentations of the Copernican system, which Steven unconditionally supported, several years before Galileo and at a time when few other scientists could bring themselves to do likewise. Calling the Copernican hypothesis “the true theory,’ Stevin demonstrated that the motions of the planets can be inductively derived from observations; since there were no complete direct observations, he used the ephemerides of Johann Stadius in their stead. He first explained the Ptolemaic model (in which the earth is at the center and the sun and planets move in epicycles) by this means, then offered a similar explanation of the Copernican system, in which he improved on the original theory in several minor points.

In a seafaring nation like the Dutch republic matters of navigation were, of course, of great importance. In addition to his astronomical works, Stevin gave a theory of the tides that was–as it must have been, fifty years before Newton–purely empirical. He also, in a short treatise entitled *De Havenvinding*, approached the subject of determining the longitude of a ship, a problem that was not fully solved until the nineteenth century. Several previous authors had suggested that longitude might be determined by measuring the deviation of the magnetic needle from the astronomical meridian, a suggestion based on the assumption that the earthwide distribution of terrestrial magnetism was known. Since the determination of latitude was well known, such a measurement would allow the sailor to chart longitudinal position against the latitudinal circle.

Stevin, in his booklet, gave a clear explanation of this method; he differed from Petrus Plancius and Mercator in that he did not rely upon a priori conceptions of the way in which geomagnetic deviation depends upon geographical position. Although he was willing to offer a conjecture about this dependence, Stevin insisted on the necessity of collecting actual measurements from all possible sources and urged the establishment of an empirical, worldwide survey. His method was sound, although as data began to accumulate it became clear that the magnetic elements were subject to secular variation. The problem of determining longitude was at last solved more simply by the invention of the ship’s chronometer.

In *Van de Zeijlstreken*, Stevin set out a method, based on one proposed by Nuñez in 1534, of steering a ship along a loxodrome, always keeping the same course, to describe on the globe a line cutting the meridians at a constant angle. Although the feat was beyond the grasp of the seaman of Stevin’s time, his exposition nonetheless contributed to a clear formulation of the principles upon which it was based and helped make the method itself better known both in the Netherlands and abroad.

A considerable body of Stevin’s other work developed from his military duties and interests. The Dutch army had been completely reorganized through the efforts of Maurice and counts William Louis and John of Nassau; their innovations, which were widely adopted by other countries, included the establishment of regular drills and maneuvers, the development of fortifications (combined with new methods of attacking a besieged city), and army camps planned after those of the Romans. As quartermaster general. Stevin observed these reforms, as well as actual battles, and wrote in detail, in his usual lucid and systematic style, of sieges, camps, and military equipment.

Stevin’s *De Sterctenbouwing* is a treatise on the art of fortification, Although cost prohibited the implementation of the ideas Stevin set out in it, these notions were put to practical effect a century later by Vauban and Coehoorn. *De Legermeting* is a less theoretical work, a description of field encampment during Maurice;s campaigns, with the encampment before the Battle of Juliers (in 1610) as a particular example. Stevin gave an account of the layout of the camp, inspired by the writings of polybius (since later Roman authors were not then known). together with the modifications made by Maurice. He listed all the equipment required in the campaign, and gave detailed instructions concerning the building of huts and the housing of dependents and suppliers. In the last section of the work he made a comparative study of the different methods of deploying soldiers in files and companies, and again recommended distribution by a decimal system. All told, his book gives a vivid impression of the army life of his period.

Of his works on engineering, two books are devoted to the new types of sluices and locks that Stevin himself had helped to devise. He cites their particular usefulness in scouring canals and ditches through the use of tidal action, and cites their application for the waterways of Danzig and other German coastal cities. In these short works he also discusses the formation of sandbanks, peat and quicksand, and the modifications of the course of a river; his explanation of the changes of the surface of the earth, which he attributes to natural forces only, is quite modern.

In *Van de Molens*, Stevin discusses wind-driven drainage mills, crucially important to the flat regions of the Netherlands. Stevin proposed the construction of a new type of mill with more slowly revolving scoop wheels and a smaller number of wider floats, and he further modified the means of transmission of power by making use of conical toothed wheels. A number of mills were built or rebuilt according to his specifications; that they were not completely successful may lie in imperfections in the execution of his design. Stevin also applied the principles of mechanics to windmills, in a series of computations that allowed him to determine, given the size and the number of the cogs, both the minimum wind pressure required on each square foot of the sails to lift the water is raised by each revolution of the sails. He gave results of his measurement of fifteen mills.

In another book, *Van de Spiegeling der Singconst*, Stevin turned to the theory of musical tuning, a subject that had enthralled mathematicians from antiquity on. Musicians had also long been concerned with devising a scale in which the intervals of the pure octave (2:1), the pure fifth (3:2) and the pure third (5:4) could be rigorously combined. The chief problem lay in the resolution of the progression by four fifths (96:144:216:324:486) and the interval with the double octave (96 × 2 × 2 =384): this ratio, which should be the third, 480:384, is rather the imperfect ratio 486:384. While a number of other mathematicians and musicians had attempted to reach a resolution by minor modifications in the scale, Stevin boldly rejected their methods and declared that all semitones should be equal and that the steps of the scale should each correspond to the successive values of 2^{n/12}; he dismissed the difference between the third and the fifth as unimportant. Stevin’s scale is thus the “equal temperament” now in general use; at the time he proposed it he had been anticipated only by Vincenzio Galilei (1581) and the Chinese prince Chi Tsai-Y¨ (1584). It is unlikely that Stevin knew the latter’s work.

Another of Stevin’s many publications was a book on civic life *Het Burgherlick Leven*. The work is a handbook designed to guide the citizen through periods of civil disorder, a matter of some concern in a nation that had only recently won its freedom through rebellion, and in which religious freedom was still a matter for discussion. Stevin only rarely refers to these circumstances in his book, however; he rather presents his precepts as being completely objective and derived from common sense. The first of his tenets is that the citizen should obey anyone in a position of *de facto* authority, no matter how this authority has been obtained. Since histor consists of a succession of princes. Stevin questions how historical rights can be established, then goes on state that the citizen’s duty is to obey the laws, no matter if they
appear wrong or unjust. He cites the necessity of religion as a means of instilling virtue in children, but adds that if a man’s religion is different from that of his countrymen, the dissenter should either conform or leave. All told, his views are typical of those current in a post-revolutionary period in which consolidation was more important than individual freedoms.

In the last years of his life, Stevin returned to the study of mathematics. He reedited his mathematical works and collected them into the two folio volumes of his *Wisconstighe Ghedachtenissen* (published in 1605–1608). These mathematical memoirs were also published, at almost the same time, in Latin and French translations.

Stevin’s writings in general are characterized by his versatility, his ability to combine theory and practice, and the clarity of his argument. They demonstrate a mind confident of the prevalence of reason and common sense and convinced of the comprehensibility of nature. His style, especially the personal way in which he addresses the reader, is particularly charming.

## BIBLIOGRAPHY

I. Original Works. A committee of Dutch scientists has edited *The Principal Works of Simon Stevin*, 5 vols. (Amsterdam, 1955–1968), which contains a bibliography and extensive introductions to each of the works.

Stevin’s major works include *Tafelen van Interest* (Antwerp, 1582; Amsterdam, 1590), a French trans. of which appears in *De Thiende* (Leiden, 1585); *Problematum geometricorum-Libri V* (Antwerp, 1583); and *De Thiende* (Leiden, 1585; Gouda, 1626, 1630; Antwerp– The Hague, 1924). Translations of *De Thiende* are H. Gericke and K. Vogel, *De Thiende von Simon Stevin* (Frankfurt am Main, 1965); Robert Norton, *Disme, the Art of Tenths* (London, 1608); J. Tuning, “La disme,” in *Mémoires mathématiques* (Leiden, 1608), also reprinted in **1** *sis*, **23** (1925); Henry Lyte, *The Art of Tenths* (London, 1619), and “The Disme of Simon Stevin,” in *Mathematics Teacher*, **14** (1921), 321, also in D. E. Smith, *Source Book of Mathematics* (New York-London, 1929).

Subsequent writings include *L’arithmétique* (Leiden, 1585, 1625), which contains French translations of *Tafelen van Interest* and *De Thiende; Vita Politica, Het Burgherlick Leven* (Leiden, 1590; Amsterdam, 1939); *De Stercktenbouwing* (Leiden; 1594; Amsterdam, 1624), also trans. by F. A. von Dantzig (Frankfurt, 1608, 1623), and by Albert Girard, *Les oeuvres Mathématiques de Simon Stevin* (Leiden, 1634); *Castrametatio, Dat is legermeting. Nieuwe Maniere van Sterctebou door Spilseuysen* (Rotterdam, 1617), trans. in French (Leiden–Rotterdam, 1618) and in Albert Girard, trans., *Les oeuvres mathématiques de Simon Stevin* (Leiden, 1634), and in German (Frankfurt, 1631); *Van de Spiegeling der Singconst. Van de Molens* (Amsterdam, 1884).

II. Secondary Literature. A bibliography of Stevin’s works is in *Bibliotheca Belgica. Bibliographie générale des Pays-Bas*, ser. 1, XXIII (Ghent–The Hague, 1880–1890). On Stevin and his work, see R. Depau, *Simon Stevin* (Brussels, 1942), which is in French and contains a bibliography of the articles on Stevin; E. J. Dijksterhuis, *Simon Stevin* (The Hague, 1943), in Dutch, with bibliography of Stevin’s works, and which is in an abbreviated English version: R. Hooykaas and M. G. J. Minnaert, eds., *Simon Stevin: Science in the Netherlands Around 1600* (The Hague, 1970); and A. J. J. van de Velde, “Simon Stevin 1548–1948,” in *Mededelingen Kongelige Vlaamse Academie*, **10** (1948), 10.

M. G. J. Minnaert

## Simon Stevin

# Simon Stevin

Simon Stevin (1548-1620) was an influential mathematician and engineer with a broad range of interests. He offered new insights and discoveries in the development of decimal numbers and the laws of inclines, gravity, hydrostatics, and fortification. Although Stevin never earned the same lasting reputation as Galileo or Isaac Newton, his contributions to the advancement of mathematical theory are noteworthy.

Very little regarding Stevin's early life is known with certainty. He noted in many of his books that he was a native of Bruges, a city in Flanders, which later became Belgium. According to the inscription on a later portrait, he was born in 1548. Records of his deeds name him as the son of wealthy parents, Antheunis Stevin and Cathelyne van der Poort. Conceived out of wedlock, he was most likely raised by his mother, but no information concerning his childhood is available.

In 1577, Stevin occupied an administrative position in the financial department of the government of Flanders. Prior to that, he was employed as a bookkeeper and cashier for the city of Antwerp. Reportedly he had traveled extensively through Poland, Prussia, and Norway from 1571 to 1577. By 1581 he had settled in the Dutch city of Leiden. Already in his 30s, Stevin finally began his formal education by enrolling in a Latin school and later entering the University of Leiden. He graduated on February 16, 1583, under the Latinized version of his name, Simon Stevinus.

After graduation, Stevin undertook numerous projects of mathematical writing and practical inventions. In 1584 he negotiated with the city of Delft to use an innovative system of drainage he developed. He also applied for patents for numerous inventions concerning drainage and dredging, along with an improved windmill and a mechanical roasting spit, which Stevin considered a toy.

From the beginning of his writings and engineering innovations, Stevin displayed a dual interest in pure thought and practical application. Although he asserted that knowledge with no use in practical living was not worth pursuing, he followed many of his practical projects to theoretical ends. He often went beyond the scope of his original plans, and in so doing enhanced the growth of mathematical understanding. His work was crucial to the development of mathematical theory in the late 16th century.

## Published Important Mathematical Works

Stevin began publishing his writings on mathematics while still a student. In 1582 he employed a printing shop in Antwerp to produce *Tables of Interest,* which outlined the rules for computing interest and provided tables for understanding discounts and annuities. Until that time, the calculation of interest was a mathematical process known only to the banking industry, which guarded the formula closely to protect its financial interests. After the release of *Tables of Interest,* for the first time common people could calculate the interest costs and benefits of their investments.

In 1583, Stevin published *Geometrical Problems.* From the start, Stevin proved himself an innovator by publishing his books in Flemish. Writing in one's own language was highly unusual in a time when works of a scholarly nature were published in Latin. Over the next three years Stevin produced several of his most important mathematical works, including *Dialectics* (also known as *Art of Demonstration* ), *The Dime, The Decimal,* and *L'Arithmetique.*

## Developed a System of Decimals

*The Dime* and *The Decimal,* both published in 1585, proved important in the advancement of the accepted use of a decimal system. The decimal system had been known for centuries, but Stevin's explanation provided an understandable and usable, albeit cumbersome, system of decimals. The common accepted practice among mathematicians at the time was to use fraction form with written notations. Although he fell short of devising a complete decimal system with a positional decimal point, Stevin provided the foundation on which other mathematicians would soon follow with these elaborations.

According to E. J. Duksterhuis in *Simon Stevin: Science in the Netherlands Around 1600,* other mathematicians were also gradually moving toward a decimal system. However, none of the advancements made were "comparable in importance and scope with the progress achieved by Stevin in *The Dime.* " Duksterhuis lists three points of special importance. First, Stevin invented a method of indicating the value of each digit without using fraction notation. Second, characteristic of Stevin's interest in the practical use of mathematics, he demonstrated useful applications for his system. Finally, Stevin presented his invention clearly and systematically so that it could be easily understood and followed by others.

Stevin's system of decimals was based on integers, which he called the units of commencement. Following from those were new units that Stevin named Prime, Second, Three, and so on. These were written by placing signs after the numbers. The sign consisted of a circled number, which designated the unit value. The system proved cumbersome in complex computations. Stevin recognized this and offered a shorter method of notation in which only one distinguishing sign was needed.

According to Stevin, the notation represented full integers, not fractions or parts of integers. In this sense, he did not set out to create decimal numbers. He believed that claiming integer status for all digits in the number was advantageous to its practical application. Mathematicians following Stevin, namely John Napier, soon adopted the use of a positional decimal point, thus eliminating the need for positional signs. In *A History of Mathematics,* Carl B. Boyer suggests that although highly trained mathematicians were familiar with a crude decimal system, "among the common people, however, and even among mathematical practitioners, decimal fractions became widely known only when Stevin undertook to explain the system in full and elementary detail. He wished to teach everyone."

## Other Studies

In 1586 Stevin published several of his most famous writings: *The Elements of the Art of Weighing, The Practice of Weighing,* and *The Elements of Hydrostatics.* In *The Elements of the Art of Weighing,* Stevin again foreshadowed future mathematical discoveries while continuing the work of Greek scientist Archimedes in his discovery of the law of inclined planes. In describing his discovery, he drew a circle of connected, equal weights, called *clootcrans,* or a wreath of spheres. He was so elated with his discovery that he exclaimed, "What appears a wonder is not a wonder!" Like many in his day, Stevin believed the universe to be a vast array of mysteries that could be explained and understood through diligent study. Most of his subsequent publications included the circle of spheres and his newly adopted motto. Like his advancements in decimals, his discoveries of incline interaction grew out of his uncanny ability to circumvent detailed theory in favor of an understanding of the essence of the mathematical equation. During the 17th century, Sir Isaac Newton would fully develop the theoretical implications of Stevin's discovery.

Along with his contributions to the study of decimals and inclines, Stevin also made a significant advancement in hydrostatics, the study of the pressure that fluids extend or receive. Stevin discovered that the shape of the container does not affect the amount of pressure exerted by the compression of a fluid. Instead, it depends on the height of the liquid and the area of the surface. Always looking for applications for his discoveries, Stevin used his new understanding of hydrostatics to build advanced water mills in several locations and provided improvements to existing water mills.

There is also evidence that suggests that Stevin was the first to discover the law of gravity popularly attributed to Galileo. According to a report published in Flemish by Stevin in 1586, he and a friend dropped two balls of lead, one ten times the weight of the other, from a height of 30 feet. When the objects were dropped at the same time, Stevin discovered that the sounds of impact were simultaneous. This suggested that some force exerted the same pull on objects of different weights.

## Civic Affairs and Defense

In 1588 Stevin turned his attention to civic matters, publishing the treatise *Civic Life.* In 1595 he returned to mathematics with the publication of the pamphlet *Appendice Algebraique.* In the same year, Stevin developed a name for himself in yet another field, publishing the highly regarded work *The Art of Fortification.*

By the end of the 16th century, Stevin came to work for Prince Maurice of Nassau as a private tutor. This job led to a new involvement in civic affairs. Stevin was appointed to an engineering position, and in 1603 named quartermaster of the States Army. At the beginning of the 16th century, the Low Countries (now the Netherlands and Belgium) were in turmoil. A revolutionary movement had begun in the 1580s in an attempt to achieve freedom from Spain. Prince Maurice became an influential leader of the resistance movement. He depended on his master tutor for direction and advice. Although Stevin's exact role in the rebellion is unknown, it is apparent that he deeply impacted the prince. In turn, his presence on numerous committees dealing with military matters influenced the activities of the forces. He was also employed to organize a school for engineers that ultimately was incorporated into the University of Leiden.

During his tenure with Maurice, Stevin compiled and wrote numerous textbooks for the prince's studies. Between 1605 and 1608, the works were published in an extensive volume entitled *Mathematical Memoirs.* He published only two more works in his lifetime. Released in a single volume in 1617, *Marking Out of Army Camps* and *New Manner of Fortification* dealt with practical issues Stevin encountered in his work as a civic servant. *New Manner of Fortification* offered an ingenious defense strategy of flooding the country in the case of an attack, a tactic suited for the water-logged states of the Low Countries. Although Stevin advocated for the creation of an office of Superintendent of Fortification and recommended himself to run it, his request was rejected.

During the final decades of his life, Stevin married a young woman named Catherine Cray, with whom he had four children before his death sometime during the first few months of 1620. His son Hendrick, who became a scientist, gathered his father's work and did much to preserve it for later generations.

## Books

*A Biographical Encyclopedia of Scientists,* edited by John Daintith, Sarah Mitchell, and Elizabeth Tootill, Facts on File, 1981.

Boyer, Carl B., *A History of Mathematics,* John Wiley and Sons, 1968.

*The Cambridge Dictionary of Scientists.* edited by David Millar, John Millar, and Margaret Millar, Cambridge University Press, 1996.

Duksterhuis, E. J., *Simon Stevin: Science in the Netherlands Around 1600,* Martinus Nijhoff, 1970.

## Online

"Simon Stevin," *Math and Mathematicians: The History of Math Discoveries Around the World,*http://www.galenet.com (January 18, 2001).

"Simon Stevin," *Notable Mathematicians,*http://www.galenet.com (January 18, 2001).

"Simon Stevin," *World of Scientific Discovery,*http://www.galenet.com (January 18, 2001).

"Simon Stevin," *World of Invention,*http://www.galenet.com(January 18, 2001).

"Stevin, Simon," *Merriam-Webster's Biographical Dictionary,*http://www.galenet.com (January 18, 2001). □

## Stevin, Simon (1548-1620)

# Stevin, Simon (1548-1620)

*Belgian-born Dutch mathematician and engineer*

Simon Stevin (Latinized to Stevinus, as was the custom of the times) took as his motto, "Wonderful, yet not unfathomable," or, alternatively, "Nothing is the miracle it appears to be". In his pursuit to fulfill this motto, Stevinus made significant contributions to mathematics, engineering, and the earth sciences. As a mathematician, he was the first to advocate the use of tenths towards the establishment of decimals in mathematical calculations. As an engineer, he developed a method of releasing **floods** via Holland's vast canal system in the event of an invasion. The first achievement mentioned above has great bearing on mathematical calculations in the earth sciences and the second relates to a combination of engineering and the study of the behavior of running **water** . However, it was his contributions to hydrostatics, **astronomy, gravity** , and magnetic declination that established his importance to the development of the earth sciences.

Stevinus is often credited as the father of hydrostatics, the science that studies fluids at rest. Prior to his research, many scientists believed that the shape of a container of a liquid influenced the amount of pressure exerted by the liquid on its sides. By this reasoning, a circular lake might experience about the same water pressure all the way around the lake, but the pressure on the walls of a lake with an irregular shape would vary from one **area** to another. Stevinus mathematically demonstrated that only the area of the liquid's surface and its depth influenced the pressure against the sides. This information is often used by scientists in studying the engineering of wells and the **permeability** of rocks in the construction of dams as well as the strength of the dam itself.

One of his contributions to astronomy was his early defense of the Copernican model (a **Sun** centered **solar system** ). Stevinus wrote in support of the heliocentric theory before Italian astronomer **Galileo Galilei** (1564–1642) came to the same conclusion. However, Stevinus had neither the telescopic evidence of Galileo nor the astronomical data of German astronomer **Johannes Kepler** (1571–1630) to add significantly to the argument.

Of greater significance to the science of astronomy was a discovery that produced new evidence regarding the relationship between gravity and falling bodies. This evidence would eventually become critical to the understanding of how the Sun holds the planets in their orbits and theories about the entire universe. The discovery was made by dropping two bodies of different weights from a high tower. Stevinus recorded that both objects struck the ground at the same time, despite their weight differences. This information disproved the assumption of Greek philosopher Aristotle (384–322 b.c.) that heavier objects fall faster than lighter objects under all circumstances, an assumption that had stood unchallenged for almost 2,000 years. Most historians argue that Stevinus performed this experiment, or at least played a part in arranging the experiment. Although he preceded Galileo by about three years in recording this discovery, his achievement was later attributed to Galileo. Today, many historians hold that Galileo was not only the first to record the experiment, but that he dropped the weights off the Leaning Tower of Pisa (there is no clear evidence that Galileo carried out such an experiment from the Leaning Tower). Regardless of who recorded the experiment first, it was a giant step away from Aristotelean thinking and eventually led to the Universal Law of Gravitation as outlined by English physicist Isaac Newton (1642–1727).

Stevinus' final contribution involved magnetic declination. Since the time of the Spanish-Italian navigator Christopher Columbus (1451–1506), it was a widely known fact that compasses did not point true north and south. Instead, they pointed toward what is known as the magnetic north and south poles. Because of this anomaly, the reliability of the compass depended on location. The difference between the magnetic poles and true north and south poles is known as the magnetic declination. By calculating and mapping magnetic declination, the navigator's job becomes much easier and more accurate. Realizing this, Stevinus was the first to undertake this task. At the time of his death he had calculated magnetic declination for 43 points on Earth's surface.

Stevinus' dedication to his motto and his work may have kept him from marrying until very late in life, or at least it would seem so. In his sixty-fourth year he finally married and eventually fathered four children before his death in 1620.

** See also ** Gravitational constant; Hydrostatic pressure; Polar axis and tilt; Solar system

## Simon Stevin

# Simon Stevin

**1548-1620**

**Flemish Mathematician and Engineer**

Simon Stevin was the first to systematically develop the ideas of Archimedes on the equilibrium of solid bodies and liquids. He established the law of equilibrium for bodies on an inclined plane, explained Archimedes' law for submerged bodies, and propounded the hydrostatic paradox. He also greatly influenced the use of decimal fractions.

Stevin, known also as Stevinus, was born in 1548 at Bruges in present-day Belgium. He earned his living as a bookkeeper before leaving the southern Netherlands in 1581 for Holland. Settling in Leiden, he established himself as an engineer. As an advisor for the construction of mills, locks, and harbors he received several patents and attracted the attention of Maurice of Nassau, stadholder of Holland and commanderin-chief of the States Army. Maurice held him in high regard and regularly sought out his advice in matters of defense and navigation. Stevin was entrusted with the organization of a school for military engineers at Leiden (1600) and appointed quartermaster in the army (1604). A bachelor most of his life, he married Cartherina Cray in 1616; they had four children. He died in 1620, most likely at his home in The Hague.

Stevin wrote on a variety of subjects ranging from commerce and navigation to hydrostatics and music theory. His first book, *Tafelen van Interest* (1582), presents rules for calculating single and compound interest as well as tables for computing discounts and annuities. Such information was well known in the banking establishment but considered a trade secret. Stevin's tables quickly gained wide usage in the Netherlands. He also published a slim pamphlet persuasively arguing for the systematic use of the decimal fraction. Though the notation of *De Thiende* (1585) was awkward, Steven found a sympathetic audience. His ideas gained wider currency when John Napier (1550-1617), inventor of logarithms, championed and then greatly facilitated their use with the introduction of the decimal point.

In *De Beghinselen der Weeghconst* (1586) Stevin introduced what is perhaps his most famous discovery, the law of the inclined plane. He showed geometrically that a linked chain of spheres must remain motionless when hung over two inclined planes joined to form a triangle, in effect demonstrating that the gravitational force is inversely proportional to the length of the inclined plane. His geometric proof is the basis for the parallelogram method for analyzing forces. In *De Beghinselen des Waterwichts* (1586) he provided the first systematic development of Archimedes' hydrostatics. He explained Archimedes' displacement principle for submerged bodies and showed that the pressure exerted by a liquid on a surface depends on the height of the liquid above that surface and is independent of the shape of the vessel containing it. Also in 1586, he experimentally refuted Aristotle's (384-322 b.c.) claim that heavier bodies fall faster than lighter ones.

In 1608 he revealed himself as one of the earliest converts to Copernicanism with the publication of *De Hemelloop*. Additionally, he developed a theory of the tides and tried his hand at solving the problem of determining longitude at sea, proposing a method based on deviations of compass needles from the astronomical meridian. Stevin's corpus also includes works on military fortification, music theory, civic life, and various treatises on engineering, including two books devoted to sluices and locks that he had helped design.

Stevin lived during a period of general scientific resurgence attendant upon the commercial and industrial prosperity of the Netherlands and northern Italy during the sixteenth century. Reflecting the new spirit of confidence of the time, Stevin chose to write in the vernacular. This required his introducing new scientific terms, many of which remain part of the Dutch scientific vocabulary.

**STEPHEN D. NORTON**

## Simon Stevin

# Simon Stevin

**1549-1620**

Dutch mathematician and military engineer who founded the science of hydrostatics by showing that the pressure exerted by a liquid upon a given surface depends on the height of the liquid and the area of the surface. While a quartermaster in the Dutch army, Stevin invented a way of flooding the polders in the path of an invading army by opening selected gates in the dike. He advised the Prince Maurice of Nassau on building fortifications for the war against Spain. Stevin in 1590 showed that Aristotelian physics was mistaken by showing that two lead balls of unequal weight hit the ground simultaneously when dropped from the tower of Delft. For a long time credit for this demonstration was given to Galileo.

## Stevin, Simon

Simon Stevin (sē´môn stəvīn´), 1548–1620, Dutch engineer and mathematician. His experiments in hydrostatics showed that the pressure exerted by a liquid is dependent only on its vertical height and not on the shape of the liquid's container, and demonstrated the principle of the hydraulic press. He probably anticipated Galileo's experiments with falling bodies. Stevin is also credited with the introduction of decimals into common usage.