SIMON STEVINUS (1548-1620). This great mathematician was born in 1548 at Bruges (where the Place Simon Stevin contains his statue by Eugen Simonis) and died in 1620 at The Hague or in Leyden. Of the circumstances of his life very little is recorded; the exact day of his birth and the day and place of his death are alike uncertain. It is known that he left a widow with two children; and one or two hints scattered throughout his works inform us that he began life as a merchant's clerk in Antwerp, that he travelled in Poland, Denmark, and other parts of northern Europe, and that he was intimate with Prince Maurice of Orange, who asked his advice on many occasions, and made him a public officer,—at first director of the so-called "waterstaet," and afterwards quartermaster-general. The question whether Stevinus, like most of the rest of the prince's followers, belonged to the Protestant creed hardly admits of a categorical answer. A Catholic, it may be said, would never in those times have risen to so high a position. A Catholic would perhaps not have been so ready as Stevinus to deny the value of all authority, whether of an Aristotle, of an Euclid, or of a Vitruvius. A Catholic could not well have boasted, as Stevinus in a political pamphlet did, that he had always been in harmony with the executive power. But against these considerations it might be urged that a Protestant had no occasion to boast of a harmony most natural to him, while his further remark, in the same pamphlet, to the effect that a state church is indispensable, and that those who cannot belong to it on conscientious grounds ought to leave the country rather than show any opposition to its rites, seems rather to indicate the crypto-Catholic, who wishes for reasons of his own to remain in the Netherlands. The same conclusion is supported by the ascertained fact that Stevinus, a year before his death, bequeathed a pious legacy to the church of Westkerke in Flanders, out of the revenues of which masses were to be said. But, however it may be answered, the question is fortunately of little importance to us, as Stevinus was neither a political personage nor did he engage in religious controversy. He was mainly, as already said, a great mathematician, and it is chiefly in this quality that we must try to get acquainted with him. His claims to fame are most varied. Some of them appealed strongly to the men of his time, but many were such as could not well be understood by most of his contemporaries, and have found due acknowledgment only in later times.
His contemporaries were most struck by his invention of a carriage with sails, a little model of which was preserved at Scheveningen till 1802. The carriage itself had been lost long before; but we know that about the year 1600 Stevinus, with Prince Maurice of Orange and twenty-six others, made use of it on the sea-shore between Scheveningen and Petten, that it was propelled solely by the force of the wind, and that it acquired a speed which exceeded that of horses. Another idea of Stevinus, for which even Grotius gave him great credit, was his notion of a bygone age of wisdom. Mankind once knew everything knowable, but gradually forgot most of it, till a time came when little by little the forgotten knowledge was reacquired; the goal to be aimed at is the bringing about of a second age of wisdom, in which mankind shall have recovered all its early knowledge. The fellow-countrymen of Stevinus were proud that he wrote in their own dialect, which he thought fitted for a universal language, as no other abounded like Dutch in monosyllabic radical words.
History has been much less enthusiastic than his contemporaries in admiring these claims to fame, but it has discovered in Stevinus's works various inventions which did not at once receive the notice they deserved. He was the first to show how to fashion regular and semiregular polyhedra by delineating their frames in a plane. Stevinus also distinguished stable from unstable equilibrium. He proved the law of the equilibrium on an inclined plane. He demonstrated before Varignon the resolution of forces, which, simple consequence of the law of their composition though it is, had not been previously remarked. He discovered the hydrostatic paradox that the downward pressure of a liquid is independent of the shape of the vessel, and depends only on its height and base. He also gave the measure of the pressure on any given portion of the side of a vessel. He had the idea of explaining the tides by the attraction of the moon.
It remains to enumerate those claims of Stevinus to immortality which were recognized from the first and which succeeding ages have not lessened,—his writings on military science, on book-keeping, and on decimal fractions.
That the man who was quartermaster-general to Maurice of Orange should have been possessed of more than ordinary merit, and have left behind him military papers of lasting value, is hardly more than might have been expected. This expectation, in the case of Stevinus at least, is fully borne out in the opinion of competent judges. Prince Maurice is known as the man who conquered the greatest number of fortresses in the shortest time, and fortification was the principal aim of his adviser. Stevinus seems to be the first who made it an axiom that strongholds are only to be defended by artillery, the defence before his time having relied mostly on small fire-arms. He wrote upon temporary fortifications, but the excellence of his system was only slowly discerned. He was the inventor of defence by a system of sluices, which proved of the highest importance for the Netherlands. His plea for the teaching of the science of fortification in universities, and the existence of such lectures in Leyden, have led to the impression that he himself filled this chair; but the belief is quite erroneous, as Stevinus, though living at Leyden, never had direct relations with its university.
Book-keeping by double entry may have been known to Stevinus as clerk at Antwerp either practically or through the medium of the works of Italian authors like Paccioli and Cardan. He, however, was the first to recommend the use of impersonal accounts in the national household. He practised it for Maurice, and recommended it in a small pamphlet to Sully the French statesman; and, if public book-keeping has grown more and more lucid by the introduction of impersonal accounts, it is certainly to Stevinus that the credit of the improvement is due.
His greatest success, however, was a small pamphlet, first published in Dutch in 1586, and not exceeding seven pages in the French translation (which alone we have seen). This translation is entitled La Disme, enseignant facilement expedier par Nombres Entiers sans rompuz, tous Comptes se rencontrans aux Affaires des Hommes. Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody before Stevinus established their daily use; and so well aware was he of the importance of his innovation that he declared the universal introduction of decimal coinage, measures, and weights to be only a question of time. His notation is rather unwieldy. The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) we have found it, and it was accepted by Napier in his logarithmic papers (1614 and 1619). Stevinus printed little circles round the exponents of the different powers of one-tenth. For instance, 237 578/1000 was printed
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; and the fact that Stevinus meant those encircled numerals to denote mere exponents is evident from his employing the very same sign for powers of algebraic quantities, e.g.,
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denote 9x4 - 14x3 + 6x - 5. He does not even avoid fractional exponents ("Racine cubique de
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serait 2/3 en circle"), and is ignorant only of negative exponents. Powers and exponents have also been carried back to a period several centuries earlier than Stevinus, and it is not here intended to give him any undue credit for having maintained them ; but we believe it ought to be recognized more than it generally is, that for our author there was a connexion between algebraic powers and decimal fractions, and that even here Stevinus the profound theorist is not lost to view behind Stevinus the man of brilliant practical talents. (M. CA.)
The above article was written by: Prof. Moritz Cantor, Ph.D., University of Heidelberg.