Simon Stevin

Chapter 1 · The Bookkeeper Who Went to University at Thirty-Five

Bruges, Antwerp, and the new Republic

1548 – 1583 · Bruges · Antwerp · Leiden

Simon Stevin was born at Bruges in 1548, illegitimate, in the Spanish Netherlands. He did not begin as a scholar. He worked as a bookkeeper and cashier in Antwerp and then as a clerk in the tax administration at Bruges.

This is the key to him. He learned mathematics as a working instrument — for accounts, interest, weights, measures and trade — before he ever met it as a subject. That is why his instincts are so consistently practical, and why he cared about whether an ordinary clerk could actually carry out a calculation.

He moved north to the newly independent Dutch Republic, and in 1583, at thirty-five, enrolled at the University of Leiden, which had been founded only eight years earlier. He was older than the professors' usual students by a decade and a half.

At Leiden he met Maurice of Nassau, son of William the Silent and later the Republic's military commander. The relationship shaped both their careers: Stevin became Maurice's tutor in mathematics, then his engineer, and eventually quartermaster-general of the Dutch army.

He wrote in Dutch, deliberately and against the convention of the age, arguing that Latin was a fence around knowledge. He coined a great deal of Dutch scientific vocabulary in the process — the modern Dutch words for mathematics and several of its branches are his.

Why this matters

Stevin came to mathematics through commercial bookkeeping, which is why his work is consistently judged by whether an ordinary person could actually use it.

You have the clerk who became quartermaster-general. What would you ask him?

Ask Stevin

• “What did bookkeeping teach you that university would not have?”
• “Why write in Dutch when every scholar in Europe read Latin?”
• “What was it like starting university at thirty-five?”
• “How did you come to teach a prince mathematics?”
• “Which Dutch words did you have to invent?”

Chapter 2 · The Wreath of Balls

A proof that runs on the impossibility of perpetual motion

1586 · Leiden

This is the argument Stevin wanted on his tombstone, and it is one of the most admired in physics.

Take a triangular prism standing on a level base, with two sloping faces of different steepness — one long and gentle, one short and steep. Over it drape a closed loop of string carrying fourteen identical balls at equal intervals, so the loop hangs over both slopes and dangles beneath the prism.

Now ask whether the loop will start to move by itself.

Suppose it does. Because the balls are evenly spaced all the way round the closed loop, after it has slipped along by one ball-space the arrangement looks *exactly* as it did before. So it would have the same reason to move again, and again, for ever. It would be a perpetual motion — which Stevin took as absurd.

So the loop hangs at rest. And now the conclusion follows. The balls hanging *below* the prism are symmetrical and balance each other, so they can be removed from the argument. What remains is the balls on the two slopes, and they must balance too — four on the gentle face against two on the steep, in the same ratio as the lengths of the faces.

From this Stevin derived how forces acting in different directions combine, by completing the figure: what is now called the parallelogram of forces, and the basis of every free-body diagram since.

“Wonder is no wonder.”

— Simon Stevin's motto, printed on the title page of De Beghinselen der Weeghconst (1586)

Why this matters

The clootcrans proof derives a quantitative law of forces from a single impossibility — that nothing moves for ever of its own accord — and needs no measurement at all.

You have the loop that cannot start moving. What is your question?

Ask Stevin

• “Why can the loop of balls not start moving on its own?”
• “Why are you allowed to remove the balls hanging underneath?”
• “How do you get from the loop to how forces combine?”
• “Why did you want this proof on your tombstone?”
• “What does your motto 'wonder is no wonder' mean?”

Chapter 3 · Two Lead Weights From a Tower in Delft

An experiment reported in a paragraph

c. 1586 · Delft

In *De Beghinselen der Weeghconst* Stevin reports, briefly, an experiment. He and Jan Cornets de Groot, burgomaster of Delft and father of the jurist Hugo Grotius, dropped two lead spheres from a height of about thirty feet onto a board below. One weighed ten times the other. The sound of their landing was a single sound; they struck together.

This is roughly three years before Galileo's earliest work on falling bodies, and the famous Leaning Tower demonstration attributed to Galileo is almost certainly a later story told by his biographer Viviani. Stevin's account is contemporaneous and printed.

But it is important not to overclaim it. Stevin reports one observation in a short paragraph. He does not repeat it systematically, does not vary the materials, does not measure times, and does not derive a law of falling bodies from it. He was refuting a specific Aristotelian claim — that speed of fall is proportional to weight — and having refuted it, he moved on.

Galileo did something different: he made falling bodies a research programme, slowed the motion down with inclined planes so that time could be measured, and extracted a quantitative law.

The honest summary is that Stevin got there first and did less with it. That distinction — between an observation and a programme — is worth more than the priority dispute.

Why this matters

Stevin's tower experiment predates Galileo's work and refutes Aristotle, but stops at one observation — a clear illustration of the difference between a result and a research programme.

You have the two weights and the single sound. What would you ask?

Ask Stevin

• “What exactly did you and de Groot do from that tower?”
• “Why did you not pursue it further?”
• “What Aristotelian claim were you actually refuting?”
• “Does it matter to you that Galileo gets the credit?”
• “How would you design the experiment with better instruments?”

Chapter 4 · Twenty-Nine Pages That Changed European Arithmetic

De Thiende, and the hydrostatic paradox

1585 – 1600s · Leiden · The Hague

*De Thiende* — The Tenth — appeared in 1585 and runs to about twenty-nine pages. It introduced decimal fractions to a European readership.

Before it, fractional quantities in commerce and surveying were handled with vulgar fractions and a chaos of subdivisions: halves, thirds, twelfths, sixtieths, and units subdivided differently in every trade. Stevin proposed that everything be expressed in tenths, hundredths and thousandths, so that calculation with fractions becomes exactly the same operation as calculation with whole numbers.

His notation is clumsy — he wrote small circled numerals after each digit to mark its place rather than using a single point — and it was quickly improved. The idea underneath it was not improved because it did not need to be. He also proposed, in the same pamphlet, that coinage, weights and measures should be decimalised throughout, which took most of Europe another two hundred years and Britain until 1971.

His hydrostatics is equally striking. He established the *hydrostatic paradox*: the pressure a liquid exerts on the base of a vessel depends only on the depth and the area of the base, not on the shape of the vessel or the total amount of liquid in it. A narrow tall vessel and a wide flaring one with the same base area and depth press equally, even though one contains far more water.

He also worked out the pressure on a submerged wall, which mattered enormously to a country holding back the sea.

Why this matters

Decimal fractions made calculation with parts of a unit identical to calculation with whole numbers, which changed commercial and scientific arithmetic outright.

You have the decimals and the paradox in the vessel. What is your question?

Ask Stevin

• “Why does a wide vessel not press harder on its base than a narrow one?”
• “What was arithmetic like before decimal fractions?”
• “Why propose decimalising money and measures as well?”
• “How much pressure is a sea wall actually holding back?”
• “Were you sorry your notation was replaced?”

Chapter 5 · Sluices, Fortifications and a Chariot That Beat Horses

Engineering for a country that had to be built

1590 – 1620 · The Hague · Scheveningen · The Dutch Republic

Stevin's day job was engineering for a state at war and below sea level.

He designed sluices and drainage systems, and worked on the mills that pumped water out of the polders — the reclaimed land on which much of the Netherlands exists. He improved the design of the windmills used for drainage and patented several arrangements. He wrote on fortification, and in particular on the bastioned trace and the use of water as a defensive obstacle, which suited Dutch ground perfectly and which Maurice of Nassau used in a series of successful sieges.

He set up an engineering school at Leiden, teaching in Dutch, to train surveyors and military engineers. He wrote on double-entry bookkeeping and persuaded Maurice to apply it to the state's accounts — arguably the first application of proper accounting to public finance.

And around 1600 he built the *zeilwagen*, a sailing chariot, which carried a party of about twenty-eight — including Maurice and several foreign guests — along the beach from Scheveningen toward Petten at a speed reported to exceed that of galloping horses. It became famous across Europe and was engraved and reproduced for a century.

He married late, had four children, and died at The Hague in 1620. His son Hendrick edited and published the remaining papers.

Why this matters

Stevin's mathematics and his engineering were the same activity: the physics of pressure and force was worked out by a man responsible for keeping the sea out.

You have the sluices, the bastions and the chariot on the sand. What would you ask?

Ask Stevin

• “How does a country below sea level stay dry?”
• “How fast did the sailing chariot actually go?”
• “Why use water as a defence rather than higher walls?”
• “What changed when the state kept double-entry accounts?”
• “Are engineering and mathematics really the same subject?”

What Stevin changed

The wreath of balls is one of the most admired proofs in physics — Ernst Mach called it a stroke of genius — and the composition of forces it establishes underlies every free-body diagram since. De Thiende gave Europe the decimal fraction and changed commercial and scientific arithmetic outright. His hydrostatics, sluices and fortifications helped make a country that sits below the sea possible.

A debate that continues

Stevin's Delft tower experiment predates Galileo's work on falling bodies, but he reported a single observation rather than developing a law, and how much priority that earns him is genuinely arguable.

Keep exploring — ask Stevin

• “What would you decimalise next?”
• “Can a proof be beautiful and still be a proof?”
• “Which of your machines are you proudest of?”

Related lives

• Archimedes — Give Me a Place to Stand
• Nicole Oresme — Who Drew Change Itself
• John Napier — Who Spared The World Its Multiplying
• Blaise Pascal — Who Carried A Barometer Up A Mountain

Related themes

Forces and equilibrium · Pressure in fluids · Decimals