Simon Stevin, (c. 1548–1620)

Simon Stevin (1548-1620), the country’s leading mathematician, was an important collaborator in Maurice’s army reforms. He introduced the decimal system, applied rigorous accountancy to the army’s bookkeeping, produced standard designs for camps and fortifications, and, to ensure reliable maps for the army, in 1600 he founded a chair for land-surveying at Leiden University. Stevin was also an avid inventor, though neither a folding spade-pickaxe that he devised for the infantry, nor the `sailing carts’ that Maurice enjoyed riding on flat beaches (his only known leisure pastime), were in fact adopted for the army.

In 1597, Maurice of Nassau advanced in the Lower Rhineland capturing a number of fortresses including Moers, west of Duisburg. His objective was to give the Dutch room for manoeuvre, create a buffer zone of fortified positions, and cut Spanish supply and communication links, particularly along the Rhine and with the north-eastern Low Countries. Dutch siege warfare, directed by Simon Stevin, who was the Quartermaster-General of the army, was both well-organised and successful.

Flemish scientist who, in physics, developed statics and hydrodynamics; he also introduced decimal notation into Western mathematics.

Stevinus was born in Bruges (now in Belgium). Until 1570 he worked as a merchant’s clerk in Antwerp before travelling extensively in Germany, Poland and Norway. He then settled in Holland and took up a teaching position at Leiden University; one of his students was Prince Maurice of Orange-Nassau, stadholder of the United Provinces after 1584. As a mathematician, Stevin helped to standardize the use of decimal fractions, ideas which he published in La Thiende (1585) and La Disme (1585). He made important contributions to the science of fluid mechanics and assisted in the refutation of the Aristotelian notion that heavier bodies fall faster than lighter bodies. After about 1590, Prince Maurice frequently consulted Stevin on matters relating to fortification and castramétation. He is mentioned as quartermaster-general and engineer of the Dutch army in 1592 and additionally held the post of commissioner of the public water works. Stevin planned entrenched camps and drew up instructions for the building of fortifications and the conduct of sieges. More importantly, Stevin designed the series of sluices and inundations which became the basis of Holland’s `Water Line’. His ideas were encapsulated in Sterctenbouwing (1594), in which he advocated a number of mathematical rules for the design of fortifications. This book was the theoretical expression of the `Old Netherlands’ System’ of fortification whose principal exponent was Adriaen Anthonisz. Stevin frequently attended at sieges to advise on the methods of attack.

On 9 January 1600 Maurice and Stevin set up a chair of surveying and fortification at Leyden University. The instruction to the university stipulated that each period of teaching in surveying is to last half an hour, and it is to be followed by a further half hour in which the lecturer will answer questions and elaborate on any points which were not understood in the first session. In their daily engineering business the pupils are to converse in the ordinary local speech, and speak little or no Latin. For that reason the lessons are to be held in Dutch, and not in Latin, French or any other foreign language (Duyck, 1862-6, II, lxxix). Aspirant engineers attended the Leyden school in some numbers until a pedantic professor reintroduced Latin in 1668 and drove them away. Lectures were delivered in Dutch rather than Latin. Stevin inspired many military engineers, especially A. Freitag and M. Dogen; the nineteenth-century Belgian engineer Henri Brialmont was profoundly influenced by Stevin’s work.

Field Engineering

The 80 Years’ War changed the craft of war into a science, and this is perhaps best illustrated by the development of field engineering. The problems facing commanders did not differ much between the beginning and the end of the war: rivers always had to be crossed, cities had to be secured, camps protected and fortifications overcome. Yet the early approach differed vastly from the later resources and techniques.

When William of Orange had to cross the Meuse in 1568, his opponents guarded all known bridges and forts. Eventually William found a suitable ford for his 8,000 cavalry, but the current was too strong for his 18,000 infantry. Instead of looking elsewhere or building a bridge, he improvised: he ordered a few hundred cavalry to wade into the river and form a living dam to break the water’s speed, so the infantry could cross safely in their lee.

Some 25 years later, when Maurice was seeking to impose order and control in his army, engineering offered him a perfect platform. Every engineer had his own ideas on how to lay a siege; to remedy this, in 1604 Maurice asked Simon Stevin, the leading mathematician, to design a `blue print’ for future fortifications and siege works. Stevin had also introduced bookkeeping to the army, allowing budgets to be set. Combining budgets, standardization and known attrition rates meant that the outcome of sieges could be more or less calculated.

Maurice set up a new hierarchy of officials to supervise the progress of all engineering works. The commies van de fortijicatien stood at the bottom of the ladder, and the successive rungs were represented by ingenieurs (who received 300 florins per year) and controlleurs (who got one hundred more).

The whole machine was directed by Simon Stevin of Bruges, who had once been Maurice’s tutor in mathematics and fortification, and was now appointed Quartermaster-General of the army. Stevin originated and directed the attacks in all the sieges at which he was present. Otherwise, as ‘even Master Stevin cannot be everywhere’ (quoted in Ten Raa, 191 I, 11,284), the siege projects were put forward by the engineers on the spot and the most suitable scheme selected by the commanding general.

Stevin’s work was not confined to the field. As well as composing valuable textbooks, he helped Maurice to draw up the engineer regulations of 1599 and 1606, and he worked out the exact and permanent dimensions of the Rhineland foot, a unit of measurement which remained in wide currency in northern European fortification well into the nineteenth century.

Many a stretch of ground, which seemed eminently suitable for siege approaches, could be flooded without warning when the defenders cut a dyke or opened a sluice, as happened to Mondragon’s battery when he was attacking Fort Lillo at Antwerp in 1584. Stevin, defined two categories of sites which were particularly suitable for ‘water manoeuvres’ of this kind. The first embraced towns which stood beside the sea or on rivers which had a large tidal variation (Ostend, Sluis, Ijzendijk, Antwerp, Veere, Zierikzee, Willemstad, Geertruydenberg, Enkhuizen, etc.). The second consisted of places that stood on non-tidal stretches of river, but owned a tributary which flowed through or close by the walls (Doesburg, Zutphen, Deventer, Zwolle).

Armies would try to situate their camp or battlefield position with flanks protected by terrain or wagons. Under Maurice these aspects also became regulated and standardized, and with good reason: on several occasions camps of both sides had been overrun by unexpected attacks. In 1600 Maurice appointed the mathematician Stevin to direct the construction of army camps. After reaching a new location, a regiment would be shown where to start digging and setting up huts according to Stevin’s plans, and drummers had a special signal to summon the men for this task. Even an overnight camp had to have a ditch 3ft (1m) wide and 4ft (1.2m) deep, preferably with a palisade (a clear echo of the ancient Roman marching camp). In the 1630s the army train carried 60,000 pointed stakes for this purpose, each around 4ins (10cm) thick and 6ft (2m) long. Another quick defence were Xs of spears stuck in the ground, called Friese ruiter (`Frisian riders’, chevaux de frise). As a ready-to-use alternative, two-wheeled carts fitted with six spears could march with the army and be swiftly deployed; in 1644, 800 of these carts were sent to assist the French army on its coastal campaign in the Spanish Netherlands. When these standard means were not available local commanders continued to improvise, as on Sao Tome in 1641; there six big anchors were hauled ashore and put in front of the artillery to shield it from enemy fire.

Accounting Debates and Accounting Practices in the Dutch Republic

No transition in the history of accounting has drawn so much attention among historians as the introduction and spread of double-entry bookkeeping (DEB) with separate capital accounts. This, of course, is due to the special place this system of accounting holds in the grand narrative of modernization, ever since Werner Sombart and Max Weber singled out DEB as the hallmark of capitalist rationality. At first glance, the Dutch case bears out the theory. In the highly commercialized context of the Low Countries, instructive texts on the use of DEB aimed at merchants were already circulating in the first half of the sixteenth century. At the turn of the seventeenth century, Simon Stevin held a famous discussion with Stadtholder Maurice on the applicability of `merchant style accounting’ to the princely domains, as well as state accounting more generally. After this, he wrote an innovative treatise on accounting, including a model DEB-based account for Maurice’ domains. This text is considered the most advanced treatise on bookkeeping of its time, and DEB instructions such as this were very popular in the Dutch Republic. No doubt, the spread of knowledge on bookkeeping infused the minds of the Dutch ruling classes and political elites. As Jacob Soll pointed out: `The ars mercatoria was a rich part of everyday urban life and an essential element of state government. The Dutch ruling elite was familiar with the minutiae of finance, industry, and trade.’

For example, in his Nieuwe inventie van rekeninghe van compagnie (New invention of company accounts), Simon Stevin himself recommended DEB accounting explicitly for the aim of facilitating the closing of accounts in order to divide profits and losses over participants in a single, short-term venture.

Simon Stevin and the Aims of State Accounting Stevin’s 1604 tract is a stylized rendering of discussions between himself and Maurice around the turn of the seventeenth century. Positing himself (realistically) as Maurice’ teacher in matters concerning mathematics and bookkeeping, Stevin in a rather schoolmasterly fashion explains the advantages of replacing the traditional system of accounting for the princely domains with Italian-style double-entry bookkeeping. Up to that time, bailiffs of the domains had put income and expenditure in a single column, determining the balance by a simple process of adding and deducting. At the start of the fictitious conversation, Stevin gives the reasons why a merchant would prefer the double-entry system over the system commonly used in state administration:

First, so that he always knows how much money his treasurer has, or ought to have, in his cash register, which is now unknown to the Prince and his treasurer (.). Further, the merchant has a handy certainty of all goods handed over by him to the control of his factors, whereas the Prince in all commodities supplied to him must rely on the information of his officers. Third, the merchant always has a clear view, not only of the remainders on the accounts of his debtors and creditors, but also of the stock of all goods that he should have in his possession, the profits or damages incurred on every category of goods. And he obtains all of this with such short shrift that can be held for impossible if the ordinary method of accounting of the bailiffs would be applied to a large trade.

Stevin did not make clear why these advantages could only be reached by the use of a particular style of DEB. Overall, he concentrated on the greater ease provided by DEB in surveying. This emphasis is consistent with Stevin’s main contribution to DEB: the introduction of periodic balancing. Stevin thus laid much stress on the connections between commercial accounting, orderly management of stocks and the possibility of gaining a separate overview of costs and profits for the discrete elements of business brought on the accounts. As an ideal for managing people and goods, this cut two ways. Not only did proper accounting enable administrators to make far more precise economic judgements. It also increased state control over the administrators themselves, diminishing the possibilities for fraud. According to Stevin, `bookkeeping is a well-known means to force unjust people with violence to behave justly, out of shame and fear of what might follow’.

According to his own rendering, Stevin managed to convince Maurice of the usefulness of his suggestions, and, with the help of `an experienced accountant in trade’, he wrote an annotated model account for the princely domains. In 1604 his system of accounting was put into practice for the first time. In 1608, Stevin published his model account, and later he also prepared a second version, including substantial corrections for printing. His own stated reasons for doing so show his concern for the continuation, spreading and further development of DEB practices:

First, because it can serve as an example for those who might be willing to follow its example. Second, to make sure that its improvement – if any is found and made public – could serve to our common enlightenment. Third, and most importantly, to make sure that when some officers who act as auditor or clerk would come to pass away or leave their posts, there could always be found another person who understands this practice.

Contrary to the supposition in much of the older literature, the `modern’ form of DEB with a separate capital account advocated by Simon Stevin in his Vorstelicke bouckhouding op de Italiaensche Wyse was rarely fully applied in practice. Nevertheless, many of the underlying assumptions of the merits of commercial bookkeeping expressed by him did inform state administrators. They left a strong imprint on the attitudes of Dutch naval administrators.

On Religion

The conventional attitude of the Dutch political leadership at the close of the sixteenth century on Religion was summed up by the Flemish immigrant Simon Stevin in his book Het Burgherlick Leven (1590), where he urged those citizens of the United Provinces who privately did not accept the teachings of the Reformed Church to recognize it as their obligation, and as their own interest, to conform outwardly. This was partly for moral and educational reasons, for if the authority of the public Church is undermined, or seen not to be respected, then children will not be in awe of the Church and will grow up without discipline, morality, and respect. But it was also for political reasons, to curb internal dissension. He argues that the pious individual who rejects the theology of the public Church and insists on the practice of another religion should move to another state where his own religion is that of the State Church. If the individual, for whatever reasons, does not move, then it his clear duty to conform outwardly and not to criticize the established Church.

In statics Stevinus made use of the parallelogram of forces and in dynamics he made a scientific study of pulley systems. In hydrostatics he noted that the pressure exerted by a liquid depends only on its height and is independent of the shape of the vessel containing it. He is supposed to have carried out an experiment (later attributed to Italian physicist Galileo) in which he dropped two unequal weights from a tall building to demonstrate that they fell at the same rate.

Stevinus wrote in the vernacular (a principle he advocated for all scientists). His book on mechanics is De Beghinselen der Weeghcoust (1586).


R. Depau, Simon Stevin (Brussels, 1942); Eduard Jan Dijsterhuis, Simon Stevin: science in the Netherlands around 1600 (The Hague, 1970); The Principal Works of Simon Stevin, ed. W. H. Schukking (Amsterdam, 1964), iv, The Art of War.

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