Simon Stevin

Flemish mathematician, scientist, and engineer

• Born: 1548
• Birthplace: Brugge, Flanders (now in Belgium)
• Died: February 1, 1620
• Place of death: The Hague, Holland (now in the Netherlands)

Stevin is best known for his advocacy of the decimal system, his discoveries in hydrostatics, his work on the inclined plane, and his musical theory of consonance. His many and varied contributions have merited him a place in histories of mathematics, accounting, science, engineering, and music.

Early Life

Simon Stevin (steh-VIHN) lived through an age of turbulent change that would eventually divide his homeland. He was born in Brugge, a former port in the southern Netherlands that, because of silting, had lost its access to the sea. Although Antheunis Stevin and Cathelijne van de Poort, Simon’s parents, were wealthy, Simon was born out of wedlock (his mother had earlier borne two illegitimate daughters with Brugge’s burgomaster).

Because of his later expertise in languages, including Latin and Greek, and his knowledge of ancient mathematics and science, Stevin must have received an excellent education, but not much is known about the details. Some scholars think that he learned bookkeeping at a private school, whereas others believe that he may have attended the Catholic university at Louvain.

His first position was in bookkeeping and tax collecting for Brugge’s city administration. He later moved to the commercial city of Antwerp, where he worked as an accountant for a rich merchant. During this time, revolution erupted in the Netherlands, destroying the union of the Catholic south and Protestant north. Stevin left the Netherlands and traveled to Prussia, Poland, and Norway. When he returned to his divided country in 1581, he settled in Leiden. He attended the University of Leiden, which was recently founded to train jurists, physicians, and Protestant theologians for the new Dutch Republic. Unlike Louvain, which emphasized traditional Humanistic studies, Leiden became a center for the study of new scientific ideas. Stevin made excellent use of both his classical and modern education in his career.

Life’s Work

Stevin published his first book in 1582. Its subject was simple and compound interest, and he computed tables for the rapid calculation of annuities. This and his later work were based on the writings of Luca Pacioli, the Italian “father of accounting,” who took a pragmatic approach to bookkeeping. Stevin understood the long history of accounting, but he built on this understanding to help create several modern accounting practices. For example, accounting historians consider him to be the inventor of the income statement, a summary of revenues and expenses for a given period.

After his work in business mathematics, Stevin turned to geometry, decimal fractions, and algebra. In 1583, he published a book on geometrical problems, which grew out of his fascination with the works of the ancient mathematician Archimedes. Although he was not the first to use decimal fractions, his book on this subject was the stimulus for their widespread use by bookkeepers. He also encouraged the use of decimals in coinage and in weights and measures. In algebra, he invented a powerful and widely used exponential notation that conveniently designated ordinary, fractional, and negative powers.

While working on these books, and as a citizen of the Low Countries, he became interested in the control of water. In 1588, the States-General granted him a patent for a high-capacity drainage mill that was able to lift four times as much water as old mills, and several of these wind-driven mills were built. He also invented a system of sluices, the floodgates of which could be opened to inundate lands before an enemy could occupy them.

The year 1586 is considered Stevin’s annus mirabilis, or wonderful year, because of the amount of significant work he produced. One of Stevin’s most important books was on hydrostatics, the science that deals with liquids at rest and under pressure, and was published that year. For some, this work warranted him the title of “founder of modern hydrostatics.” In it, he clearly stated the hydrostatic law that a liquid’s pressure depends only on its vertical height, not on the shape of its container.

Also published in 1586 was an influential book on the art of weighing. As in his work on mathematics and hydrostatics, this Flemish book built on the earlier studies of Archimedes, in particular on the problem of the equilibrium of a stationary object under the influence of a vertical force such as gravity. In fact, he is most famous for the clootcrans theorem, his clever derivation of the law of the inclined plane through a device called the wreath of spheres. Using a triangle with unequal sides and a string of evenly weighted beads, he proved the law that “two bodies on two different, inclined planes are in balance if their weights are proportional to the lengths of the two planes.”

A further discovery in 1586 was Stevin’s experimental demonstration that the velocity of two freely falling lead spheres, one ten times heavier than the other, was independent of this weight difference. Galileo is often given credit for refuting Aristotle’s claim that heavy objects fall faster than light ones, but he most likely never did the actual experiment, and even if he did, it would have taken place after Stevin’s well-evidenced demonstration.

During the late sixteenth and early seventeenth centuries, the religious and political turmoil in the Netherlands intensified, and the Dutch prince Maurice of Nassau played an important role in helping to establish the Dutch Republic. Prince Maurice had met Stevin when they were both students at Leiden, and in 1604, Stevin became quartermaster in the Dutch army under the prince. Stevin’s knowledge of practical mechanics made him extremely useful. For example, he wrote a treatise on the art of fortification that Prince Maurice used during his military campaigns. Stevin also studied how to best train, equip, and make use of troops in war, and how to effectively finance these tasks. He was one of the first to write a book on governmental accounting, and “Bookkeeping for War and Other Extraordinary Finances” was an important part of this treatise. For the Dutch navy, he figured how to use magnetic declinations and a Mercator map to accurately guide ships.

In addition to his official work for the Dutch military, Stevin also tutored Prince Maurice in science and mathematics. He often wrote out the prince’s lessons in great detail, and the prince, deeply impressed, had them published between 1605 and 1608. This massive work of fifteen hundred pages contained a comprehensive account of Stevin’s accomplishments in mathematics, accounting, mechanics, and astronomy. His chief book on astronomy was also published during this time (1608), and it contained his analysis of the Copernican heliocentric system, which he strongly supported.

While he was engaged in his military work, Stevin amazingly found time for the scientific study of music. In particular, he devised an influential theory of consonance to explain which combinations of musical sounds are pleasant. He was unique in rejecting the ancient Pythagorean idea that pleasing sounds coincided with simple integral ratios. He argued that geometric, not arithmetic, division of the octave yielded genuine consonantal ratios. Though some have criticized Stevin’s theory for its insensitivity to the practices of actual musicians, others have seen his work as anticipating the later development of a scale of equal temperament.

Despite marrying late in life (he was sixty-two), he and his wife, Catherine Gray, had two boys and two girls. During his final years, he was deeply admired for his many contributions to the Dutch Republic. He lectured in Dutch at the University of Leiden and helped organize its engineering school. His belief that the Dutch language was particularly suitable for mathematical and scientific works probably contributed to their lack of influence in foreign countries, where Latin was still the language preferred by most scholars.

Significance

Stevin was very much a Renaissance man, accomplished in such Humanistic fields and political and musical theory, such technical fields as military science and engineering, and such scientific fields as mechanics and astronomy. Because of his deep understanding of both ancient and modern science, he helped bridge the gap between the two approaches. Because he was both a theoretical scientist and a practical engineer, he was able to use his theories in mechanics to develop improved windmills, lifting devices, and military fortifications.

His many published books exhibit his versatility and curiosity, his ability to combine theory and practice, and his skill in crafting clear and creative arguments to support his many original ideas. A major figure in the scientific revolution, he exhibited the movement’s confidence in reason to solve the many puzzles of a natural world, a world he believed was governed by beautiful mathematical laws.

Bibliography

Boyer, Carl B. A History of Mathematics. Revised by Uta C. Merzbach. 2d ed. New York: John Wiley & Sons, 1991. This classic textbook, expanded and updated by Merzbach, contains an analysis of Stevin’s contributions to mathematics. Includes bibliographies with each chapter, a general bibliography, and an index.

Chatfield, Michael, and Richard Vangermeersch, eds. The History of Accounting: An International Encyclopedia. New York: Garland, 1996. This pioneering book contains a biographical article on Stevin that analyzes his contributions to such topics as balance sheets and compounds entries. Bibliographies at the ends of articles. Comprehensive index.

Dijksterhuis, E. J. Simon Stevin: Science in the Netherlands Around 1600. The Hague, the Netherlands: Martinus Nijhoff, 1970. This English translation of a work originally published in Dutch in 1943 has been abridged and edited by R. Hooykaas and M. G. J. Minnaert. It remains the best English account of Stevin’s life and work.

Grout, Donald J., Claude V. Palisca, and Peter J. Burkholder. A History of Western Music. 7th ed. New York: W. W. Norton, 2004. This textbook contains an analysis of Stevin’s contributions to music theory. Bibliographies at the ends of each chapter. Comprehensive index.