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.

# Simon Stevin

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).

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