数学家传记
西蒙·斯蒂文是一位佛兰芒数学家，他首次对小数进行了初等而详尽的阐述，并将其引入数学。
西蒙·斯蒂文的父亲是Anthuenis (Anton) 斯蒂文，据信他是弗尔讷一位市长的幼子。他的母亲是Cathelijne（或Catelyne）van der Poort，她是伊珀尔一个市民家庭的女儿。Anthuenis和Cathelijne没有结婚，但斯蒂文的母亲Cathelijne后来嫁给了一个从事地毯销售和丝绸贸易的男人。通过婚姻，Cathelijne加入了一个加尔文主义家庭。关于斯蒂文的早年生活或教育一无所知，尽管人们推测他是在加尔文主义传统中长大的。
斯蒂文成为安特卫普一家公司的簿记员和出纳员。已知他在1571年至1577年间曾在波兰、普鲁士和挪威旅行过一段时间。然后在1577年，他在布鲁日的税务办公室找到了一份职员的工作。此后，他于1581年搬到莱顿，在那里他首先上了拉丁学校，然后于1583年（35岁时）进入莱顿大学。关于他为什么搬到莱顿，人们提出了各种理论。要理解这些，我们需要简要回顾一下这一时期的历史。
1579年1月23日的乌得勒支联盟旨在在低地国家的更大联盟内形成一个集团（称为三级会议），以抵抗西班牙统治。它在荷兰北部产生了一个联盟，名义上仍处于西班牙国王的统治之下，但与南部不同。大约从1567年开始，西班牙在南部占领区开始的恐怖统治引发了强烈的反抗。北部主要是加尔文主义者，实际上由奥兰治亲王威廉统治。1581年，三级会议宣布从西班牙独立，随后出现了复杂的局面，因为外国援助被引入。
斯蒂文搬到荷兰北部无疑与他们从西班牙国王统治下独立同时发生。然而，斯蒂文搬家的其他可能原因也存在，因为我们已经提到，斯蒂文在母亲再婚后是在加尔文主义家庭中长大的。当然，斯蒂文并不是唯一一个在这段时间逃离荷兰南部的人，许多人去了北部，但其他人逃往英国或德国。当斯蒂文在莱顿大学时，他遇到了杰森·约翰·拿骚伯爵毛里茨（莫里斯），他是奥兰治的威廉的次子。两人成为亲密的朋友，斯蒂文成为王子的数学导师以及亲密顾问。奥兰治的威廉于1584年7月10日在代尔夫特被一名罗马天主教徒暗杀，该教徒认为通过暗杀威廉，他将阻止对天主教西班牙的叛乱。威廉的长子菲利普·威廉忠于西班牙，因此毛里茨于1584年被任命为荷兰和泽兰，或荷兰联合省的总督。
由于毛里茨王子现在是共和国军队的首领，并且斯蒂文作为他的顾问服务，随后对西班牙军队取得了一系列军事胜利。毛里茨理解军事战略、战术和工程在军事成功中的重要性。1600年，他要求斯蒂文在莱顿大学内建立一所工程学校。坚持在那里用荷兰语授课是一个很好的政治举措。当然，毛里茨王子认为他的朋友斯蒂文在他的成功中具有重大重要性，最近在海牙公共记录办公室发现的一份记录斯蒂文1604年薪水为600荷兰盾的期刊证实了他的高位。
据信从1604年起，斯蒂文担任荷兰联省军队的军需总监。他发明了一种方法，通过打开堤坝上选定的水闸，淹没入侵军队所经之处的低地。他是一位杰出的工程师，为风车、船闸和港口的建造提供咨询。他就对抗西班牙的战争防御工事建设向毛里茨亲王提供建议，并详细描述了军队所采用的军事创新。这些创新后来被许多其他国家效仿。
联省军队从西班牙统治下收复的基本上就是今天的荷兰领土，联省共和国也获得了英格兰和法国的正式承认，成为一个独立国家。毛里茨亲王希望继续对西班牙作战，但当西班牙实际上承认联合省为独立主权国家后，继续战斗的热情便所剩无几。十二年停战协定于1609年开始。
斯蒂文于1612年以3800荷兰盾买下了海牙Raamstraat的一栋房子（这再次表明他地位高、财富多）。他结婚的日期，有些资料说是1610年，另一些资料说是1614年。他的妻子是Catherine Krai，他们有四个孩子，分别叫Frederic、Hendrik、Susanna和Levina。他们的第二个孩子Hendrik后来进入莱顿大学，并成为一位著名科学家，还担任了他父亲全集的编辑。
斯蒂文著有11本书，在三角学、力学、建筑学、音乐理论、地理学、筑城学和航海学方面都做出了重要贡献。他的第一本书是Tafelen van Interest Ⓣ（利息表），于1582年出版。在此之前，未出版的手稿利息表在欧洲各地的银行家中普遍使用，但一直被视为不得泄露的秘密信息。在给出数值表之前，斯蒂文给出了单利和复利的规则，并给出了许多使用示例。
在Problemata geometrica Ⓣ（几何问题）（1583年）中，斯蒂文呈现的几何学主要基于欧几里得和阿基米德，但他所研究的问题表明，他也受到了阿尔布雷希特·丢勒的影响。斯蒂文在这部著作中对与多边形和多面体有关的作图作了有趣的叙述，使用了相似性的概念，并研究了正多面体和半正多面体。这本书用拉丁文写成，是他唯一一本首次以拉丁文出版的著作。他后来成为用荷兰语撰写科学著作的坚定倡导者，并在1586年撰写的一篇文章中明确说明了这一选择的理由。
1585 年，他出版了 La Thiende Ⓣ（第十），这是一本二十九页的小册子，其中他对小数给出了初等而详尽的论述。他写这本小书是为了以下人群的利益：-
…… 占星家、测量员、地毯制造商、酒类计量员、铸币师以及各类商人。
尽管他没有发明小数（早在 斯蒂文 的时代之前，阿拉伯人和中国人就已经使用小数），但他确实将小数的使用引入了欧洲数学。斯蒂文 指出，十进制硬币、度量衡的普遍引入只是时间问题（但他若知道 21 世纪仍有一些国家抵制采用十进制，大概会感到惊讶）。Robert Norton 于 1608 年在伦敦出版了 La Thie
同年（1585年），他出版了La pratique d'arithmétique Ⓣ（算术实践）和L'arithmétique Ⓣ（算术），这是他最早用法语写成的仅有的两部著作。在后一部中，斯蒂文给出了求解二次方程的统一处理方法和求任意次代数方程近似解的方法。他还强烈呼吁，诸如平方根、无理数数、不尽根、负数等一切数都应作为数来对待，而不应被区分为性质不同。斯蒂文的实数概念基本上被后来所有科学家所接受。尤为重要的是斯蒂文接受了负数，但他不接受“新的”虚数，这阻碍了虚数的发展。
受阿基米德启发，斯蒂文撰写了重要的力学著作。他的论述主要涉及静力学，见于他1586年出版的De Beghinselen der Weeghconst Ⓣ（称重技艺原理）一书。该书以包含力的三角形定理而闻名，这一定理推动了静力学的发展。同年，他关于流体静力学的论著De Beghinselen des Waterwichts Ⓣ（流体静力学原理）对阿基米德在这一主题上的工作作出了显著改进。许多人认为，他通过这部著作表明液体施加于给定表面上的压强取决于液体的高度和表面的面积，从而创立了流体静力学这门科学。
同样在1586年（比伽利略早3年），他报告说不同重量的物体在相同时间内下落给定距离。他的实验使用两个铅球，一个的重量是另一个的十倍，他从代尔夫特教堂塔楼上让它们下落三十英尺。
在1608年出版的De Hemelloop Ⓣ（天空漫步）中，他撰写了天文学内容，并大力捍卫尼古拉·哥白尼的日心体系。尽管斯蒂文的数学工作是在其生涯较早时期进行的，但他将自己的一些数学著作收集起来，加以编辑，并于1605年至1608年间在Wiskonstighe Ghedachtenissen Ⓣ（数学文集）（数学文集）中出版。该文集包括De Driehouckhandel Ⓣ（三角学）、De Meetdaet Ⓣ（测量实践）和De Deursichtighe Ⓣ（透视法）。关于透视法的著作考察了若干创新，例如为在不垂直于地面的画布上作图而计算透视的情形，以及逆透视的情形。逆透视计算的是，如果给定一个物体和该物体的透视图，观察者的眼睛应置于何处。斯蒂文在其著作Stelreghel Ⓣ（代数）中使用了记号+、-和√。
他的其他著作包括1590年出版的Vita Politica. Het Burgherlick leven Ⓣ（公民生活）、1594年出版的De Sterktenbouwing Ⓣ（防御工事的建造）、1599年出版的De Havenvinding Ⓣ（定位），以及1617年出版的双重著作Castrametatio, dat is legermeting Ⓣ（军事测量）和Nieuwe Maniere van Stercktebou door Spilsluysen Ⓣ（建造水闸的新方法）。
在Het Burgherlick leven Ⓣ（一个公民的生活）中，斯蒂文讨论了国家公民应如何遵守当局的规则（即使这些规则显得不公正），并特别建议公民在内乱时期应如何行事。在De Sterktenbouwing Ⓣ（堡垒建造）中，斯蒂文采用了一种意大利的筑城方法，并加以修改以供荷兰使用。他在这部论著中提出的想法很巧妙，但实施起来过于昂贵。著作De Havenvinding Ⓣ（寻找港口）字面意思是“寻找港口”，提出了一种通过利用罗盘针的磁差确定经度来找到船只位置的方法。尽管理论上合理，但该方法不切实际。在我们上面提到的最后一部双重著作的第一部分中，斯蒂文描述了军营的建立、布局和设置。特别引人入胜的是他对毛里茨亲王军营的描述，该军营是他在1610年于利希战役前设立的。两部著作中的第二部论述了斯蒂文为放入防御工事以使护城河保持正确深度而设计的水闸。
他对音乐的贡献包含在 De Spiegheling der Singconst Ⓣ（歌唱艺术理论）中，该书以手稿形式保存到 1884 年才出版。这通常被视为将八度分成十二个相等音程的第一个正确理论，例如见 [1]。Cohen 在 [13] 中解释了这个问题对当时科学家的重要性：-
科学革命的许多先驱，如伽利略、约翰内斯·开普勒、斯蒂文、勒内·笛卡儿、马兰·梅森等，都撰写了大量关于音乐理论的著作。这并非少数个别科学家的偶然兴趣。相反，它反映了自毕达哥拉斯时代以来科学家们对解决音乐理论中某些可量化问题的持续关注。其中一个问题在专业上被称为“八度的划分”，即用哪些音来创作音乐的问题。
科恩认为，这并非如人们通常所认为的那样（见[1]），是斯蒂文论文的目的：-
对1600年前后音乐科学中问题状况的仔细分析表明，斯蒂文的论文突出了音乐科学核心问题——即协和问题——历史上的一个特定阶段。这就是依据科学原理为毕达哥拉斯定律寻求解释：为什么那些为数不多的、以甜美悦耳的方式影响我们耳朵的音程，对应于最初几个整数的比？
Simon Stevin's father was Anthuenis (Anton) Stevin who, it is believed, was a cadet son of a mayor of Veurne. His mother was Cathelijne (or Catelyne) van der Poort who was the daughter of a burgher family of Ypres. Anthuenis and Cathelijne were not married but Simon's mother Cathelijne later married a man who was involved in selling carpets and in the silk trade. By marriage Cathelijne joined a family who were Calvinists. Nothing is known of Simon's early years or of his education although one assumes he was brought up in the Calvinist tradition.
Stevin became a bookkeeper and cashier with a firm in Antwerp. It is known that he spent some time between the years 1571 to 1577 travelling in Poland, Prussia and Norway. Then in 1577 he took a job as a clerk in the tax office at Brugge. After this he moved to Leiden in 1581 where he first attended the Latin school, then he entered the University of Leiden in 1583 (at the age of 35). Various theories have been put forward as to why he moved to Leiden. To understand these we need to look briefly at the history of the period.
The Union of Utrecht on 23 January 1579 was designed to form a block (known as the States-General) within the larger union of the Low Countries which would resist Spanish rule. It produced a union in the north Netherlands, still officially under the rule of the King of Spain, but distinct from the south. The strong reaction against the Spanish followed the start of a reign of terror by the Spanish occupation in the south beginning around 1567. The north was predominantly Calvinist and effectively ruled by William, Prince of Orange. In 1581 the States-General declared independence from Spain and a complex situation followed as foreign help was enlisted.
Stevin's move to the north Netherlands certainly coincided with their move to independence from the King of Spain. There were other possible reasons for Stevin to move, however, for we have already mentioned that Stevin was brought up in a Calvinist family after his mother remarried. Certainly Stevin was not alone in fleeing from the south Netherlands around this time, with many going to the north, but others fleeing to England or Germany. While Stevin was at the University of Leiden he met Maurits (Maurice), the Count Of Nassau, who was William of Orange's second son. The two became close friends and Stevin became mathematics tutor to the Prince as well as a close advisor. William of Orange was assassinated on 10 July 1584 at Delft by a Roman Catholic who believed that by assassinating William he would prevent the rebellion against Catholic Spain. William's eldest son Philip William was loyal to Spain so it was Maurits who was appointed stadholder of Holland and Zeeland, or the United Provinces of the Netherlands, in 1584.
With Prince Maurits now head of the army of the republic, and with Stevin as an advisor in his service, a series of military triumphs over the Spanish forces followed. Maurits understood the importance of military strategy, tactics, and engineering in military success. In 1600 he asked Stevin to set up an engineering school within the University of Leiden. It was a good political move to insist that the courses were taught there in the Dutch language. Certainly Prince Maurits saw his friend Stevin as having major importance in his success and the recent discovery of a journal in the Public Record Office of The Hague recording Stevin's salary as 600 Dutch guilders in 1604 confirms his high position.
It is believed that from 1604 Stevin was quartermaster-general of the army of the States-General. He invented a way of flooding the lowlands in the path of an invading army by opening selected sluices in dikes. He was an outstanding engineer who advised on building windmills, locks and ports. He advised Prince Maurits on building fortifications for the war against Spain and wrote detailed descriptions of the military innovations adopted by the army. These innovations would be copied by many other countries.
The army of the States-General reclaimed from Spanish rule essentially the territory which is today The Netherlands, and the States-General became officially recognized by England and France as an independent state. Prince Maurits wished to continue the war against Spain but, when Spain effectively recognised the United Provinces as independent and sovereign, there was little enthusiasm to continue the fight. The Twelve Years' Truce began in 1609.
Stevin bought a house at the Raamstraat in The Hague in 1612 for 3800 Dutch guilders (another sign of his high status and wealth). He married at a date given as 1610 by some sources and as 1614 by other sources. His wife was Catherine Krai, and they had four children named Frederic, Hendrik, Susanna and Levina. Hendrik, their second child, went on to attend the University of Leiden and, becoming a famous scientist in his own right, was the editor of his father's collected works.
The author of 11 books, Simon Stevin made significant contributions to trigonometry, mechanics, architecture, musical theory, geography, fortification, and navigation. His first book was Tafelen van Interest Ⓣ which he published in 1582. Prior to this, unpublished manuscript interest tables were in common use with bankers throughout Europe but had been treated as secret information not to be divulged. Before presenting the numerical tables, Stevin gave rules for simple and compound interest and also gave many examples of their use.
In Problemata geometrica Ⓣ (1583) Stevin presented geometry based largely on Euclid and Archimedes but the problems which he studied show that he was also influenced by Dürer. Stevin gave an interesting account in this work of constructions related to polygons and polyhedra, using the concept of similarity, and a study of regular and semi-regular polyhedra. It was written in Latin, and is the only one of his books to be first published in that language. He became a strong advocate of writing his scientific works in Dutch and he gives clear reasons for this choice in a text written in 1586.
In 1585 he published La Thiende Ⓣ, a twenty-nine page booklet in which he presented an elementary and thorough account of decimal fractions. He wrote this small book for the benefit of:-
... stargazers, surveyors, carpet-makers, wine-gaugers, mint-masters and all kind of merchants.
Although he did not invent decimals (they had been used by the Arabs and the Chinese long before Stevin's time) he did introduce their use in mathematics in Europe. Stevin states that the universal introduction of decimal coinage, measures and weights would only be a matter of time (but he probably would be amazed to know that in the 21st century some countries still resist adopting decimal systems). Robert Norton published an English translation of La Thie
In the same year (1585) he published La pratique d'arithmétique Ⓣ and L'arithmétique Ⓣ which were the only texts he wrote first in French. In the latter Stevin presented a unified treatment for solving quadratic equations and a method for finding approximate solutions to algebraic equations of all degrees. He also made a strong plea that all numbers such as square roots, irrational numbers, surds, negative numbers etc should all be treated as numbers and not distinguished as being different in nature. Stevin's notion of a real number was accepted by essentially all later scientists. Particularly important was Stevin's acceptance of negative numbers but he did not accept the 'new' imaginary numbers and this was to hold back their development.
Inspired by Archimedes, Stevin wrote important works on mechanics. Mainly dealing with statics, his treatment appears in his book De Beghinselen der Weeghconst Ⓣ published in 1586. It is famous for containing the theorem of the triangle of forces which gave impetus to statics. In the same year his treatise De Beghinselen des Waterwichts Ⓣ on hydrostatics contained notable improvements to the work of Archimedes on this topic. Many consider that he founded the science of hydrostatics with this work by showing that the pressure exerted by a liquid upon a given surface depends on the height of the liquid and the area of the surface.
Also in 1586 (3 years before Galileo) he reported that different weights fell a given distance in the same time. His experiments were conducted using two lead balls, one being ten times the weight of the other, which he dropped thirty feet from the church tower in Delft.
In De Hemelloop Ⓣ, published in 1608, he wrote on astronomy and strongly defended the sun centred system of Copernicus. Although he undertook his mathematical work earlier in his life, Stevin collected together some of his mathematical writings which he edited and published during the years 1605 to 1608 in Wiskonstighe Ghedachtenissen Ⓣ (Mathematical Memoirs). The collection included De Driehouckhandel Ⓣ, De Meetdaet Ⓣ, and De Deursichtighe Ⓣ. The work on perspective looks at a number of innovations such as the case of calculating the perspective for making a drawing on a canvas which is not perpendicular to the ground, and the case of inverse perspective. This calculates where the eye of the observer should be placed if an object and a perspective drawing of that object are given. Stevin, in his book Stelreghel Ⓣ used the notation +, - and √.
His other works included Vita Politica. Het Burgherlick leven Ⓣ published in 1590, De Sterktenbouwing Ⓣ published in 1594, De Havenvinding Ⓣ published in 1599, and the double work Castrametatio, dat is legermeting Ⓣ and Nieuwe Maniere van Stercktebou door Spilsluysen Ⓣ published in 1617.
In Het Burgherlick leven Ⓣ Stevin discusses how a citizen of a state should comply with the rules of the authorities (even when they appear unjust) and, in particular, he advises citizens how to behave in times of civil unrest. In De Sterktenbouwing Ⓣ Stevin takes an Italian method of fortification and modifies it for Dutch use. The ideas that he put forward in this treatise were clever but too expensive to implement. The work De Havenvinding Ⓣ literally means 'finding the harbour' and presents a method of finding the position of a ship by determining its longitude using the magnetic variation of the compass needle. Although theoretically sound, the method is impractical. In the first of the final double work that we mentioned above, Stevin describes the establishment, layout and setting up of a military camp. Particularly fascinating is his description of Prince Maurits camp which he set up prior to the Battle of Juliers in 1610. The second of the two works deals with sluices Stevin had designed to put into fortifications to keep a moat at the correct depth.
His contributions to music are contained in De Spiegheling der Singconst Ⓣ which survived in manuscript until 1884 when it was published. This is usually seen as the first correct theory of the division of the octave into twelve equal intervals, see for example [1]. Cohen in [13] explains the importance of the problem to scientists of the period:-
Many pioneers of the Scientific Revolution, such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about music theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in music theory. One of the issues involved was technically known as 'the division of the octave', the problem, that is, with which notes to make music.
Cohen argues that this was not, as is commonly believed (see [1]), the purpose of Stevin's treatise:-
A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras's law: Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?.
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