德·维特Johan de Witt

德·维特在多达雷赫特就读于贝克曼的学校，然后于1641年进入莱顿大学学习法律。在大学里，他展现出非凡的才能，尤其是在数学和法律方面。1645年，扬和他的哥哥科内利斯访问了法国、意大利、瑞士和英国，之后扬于1647年至1650年作为律师居住在海牙。他于1645年获得昂热大学的法学博士学位。

德·维特是弗兰斯·范斯霍滕的伙伴，并曾在他家中住过一段时间。他最重要的著作Elementa curvarum linearumⓉ（曲线要义）（1659-61）于1649年完成，是直线和圆锥曲线的解析几何的首次系统发展。它由弗兰斯·范斯霍滕出版，作为他编辑的勒内·笛卡儿的Géometrie（1660）的一部分。下面我们简要考察这部著作以及弗兰斯·范斯霍滕在其最终出版中所起的作用。在此我们注意到，这一长期延迟的原因是德·维特在完成此书后的时期内在荷兰担任高级职务，他过于忙于政治工作，无法进行必要的编辑以准备出版。

1650年，德·维特被任命为多达雷赫特的议长，即多达雷赫特在荷兰政府中代表团的领袖。三年后，他被任命为荷兰大议长；这是政府律师（为荷兰权利辩护的顾问）的职位，实际上合并了首相和外交大臣的职务，使德·维特成为荷兰的政治领袖。作为荷兰的领袖，德·维特将他的数学知识应用于共和国的财政和预算问题。他写了The Worth of Life Annuities Compared to Redemption Bonds，将probability应用于国家财政问题。De Witt于1654年促成了与英国的和平，此后他在为荷兰带来繁荣方面极为成功。当1665年与英国再次爆发战争时，德·维特能够在布雷达条约（1667）中达成非常令人满意的解决方案。他的政治才能在荷兰共和国、英国和瑞典之间的三国同盟（1668）中进一步得到体现。

1672年法国入侵，出现了反对德·维特的示威活动。他的兄弟科内利斯于7月24日被捕，两周后扬德·维特辞去荷兰政治领袖职务。当扬来监狱探望科内利斯时，他们遭到一大群人的袭击并被杀害。引用[2]：-

科内利斯遭受酷刑，并于8月19日被判处剥夺职务和流放。他的兄弟来到海牙的盖万根普特监狱探望他。一大群人听闻此事，聚集在外，最终冲进来，抓住两兄弟，将他们撕成碎片。他那个时代和荷兰历史上最伟大的政治家之一就这样陨落了。

现在让我们来看德·维特的主要数学著作Elementa curvarum linearumⓉ（《曲线概要》）。在书中他解释了自己的意图。他感到恼火的是，众所周知的圆锥曲线明明是平面曲线，却由三维方法生成。他在著作中写道：-

当我更仔细地研究关于曲线的书籍——就古人所传、后世数学家所释者而言——我认为，到立体中去寻找这些曲线的起源，然后再把它们转移到平面上，这绝对违背了自然秩序，而我们在数学中应尽可能尊重这种秩序。

让我们指出，directrix一词最早由德·维特使用，并出现在这部著作中。

弗兰斯·范斯霍滕在促成此书出版方面起了重要作用。他在1658年写信给德·维特说：-

我非常喜欢它，因为我认为这些想法非常新颖，而且你表达的方式非常正确和清晰。

他提出帮助准备这部著作以供出版。1658年10月8日，德·维特写了一封信，在信中他表示，在主要著作（即现在的文本第二部分）之前，必须先出版一篇前面的“简短论著”（即现在的文本第一部分）。事实上，出版后第一部分占83页，而第二部分稍长，为97页。在同一封信中，德·维特批评了阿波罗尼奥斯，他认为后者把事情弄得过于复杂。他声称自己的方法要简单得多。弗兰斯·范斯霍滕通过编辑文本并以极高的精确度绘制图形来帮助准备文本。De Witt阅读了校样，并对弗兰斯·范斯霍滕所完成内容的修改拥有最终决定权。

最后，让我们引用克里斯蒂安·惠更斯在1659年6月6日写给约翰·沃利斯的一封信中对德·维特的赞扬：-

在我看来，没有哪个世纪像我们这个世纪一样数学家辈出，而在这些人中，此人甚至可能达到首位，如果他不是那么忙于公务的话。

Jan de Witt attended Beeckman's school in Dordrecht, then in 1641 he entered the University of Leiden to study law. At university he showed remarkable talents, especially in mathematics and law. In 1645 Jan and his elder brother Cornelius visited France, Italy, Switzerland and England, then on his return Jan lived at The Hague as an advocate from 1647 to 1650. He had received a doctorate in law from University of Angers in 1645.

De Witt was an associate of van Schooten and lived for a while in his house. His most important work Elementa curvarum linearum Ⓣ (1659-61) was finished in 1649, and was the first systematic development of the analytic geometry of the straight line and conic. It was published by van Schooten as part of his edition of Descartes' Géometrie (1660). We look briefly at the work and the part played by van Schooten in its eventual publication below. At this point we note that the reason for this long delay was that de Witt held high office in Holland during the period following completion of the book and he was too occupied with his political work to do the necessary editing to prepare it for publication.

In 1650 de Witt was appointed Pensionary of Dordrecht, the leader of Dordrecht's deputation in the government of Holland. Three years later he was appointed Grand Pensionary of Holland; this was the office of the Government Attorney (counsel for the defence of the rights of Holland) which effectively combined the offices of Prime Minister and Foriegn Secretary making de Witt the political leader of Holland. As leader of Holland, de Witt applied his mathematical knowledge to the financial and budgetary problems of the republic. He wrote The Worth of Life Annuities Compared to Redemption Bonds which applied probability to questions of state finance. De Witt brought about peace with England in 1654 and after this he was extremely successful in bringing prosperity to Holland. When war broke out again with England in 1665 de Witt was able to bring about a very satisfactory settlement at the Treaty of Breda (1667). His political skills were further seen in the Triple Alliance (1668) between the Dutch Republic, England and Sweden.

In 1672 France invaded and there were demonstrations against de Witt. His brother Cornelius was arrested on July 24 and two weeks later Jan de Witt resigned as political leader of Holland. When Jan came to visit Cornelius in prison they were attacked and killed by a large crowd. Quoting [2]:-

Cornelius was put to the torture and on August 19 sentenced to deprivation of his offices and banishment. His brother came to visit him in the Gevangenpoort at The Hague. A vast crowd, hearing this, collected outside and finally burst in, seized the two brothers, and tore them to pieces. Thus perished one of the greatest statesmen of his age and of Dutch history.

Let us look now at de Witt's major mathematical work, the Elementa curvarum linearum Ⓣ. In the book he explains his intentions. He was annoyed that well known conic sections, which are clearly plane curves, were generated by three dimensional means. He wrote in the work:-

When I studied more carefully the books on the curved lines - as far as they have been transmitted by the Ancients and explained by later mathematicians - I thought it absolutely against the natural order, which in mathematics one should respect as much as possible, to seek the origin of these curves in a solid and then transfer them to the plane.

Let us point out that the word directrix was first used by de Witt and appears in this work.

Van Schooten played a major role in getting the book published. He wrote to de Witt in 1658:-

I like it very much, as I think the ideas are very original and the way in which you express yourself is very correct and clear.

He offered to help prepare the work for publication. On 8 October 1658 de Witt wrote a letter in which he expressed the view that before the main work (which is now part II of the text), a preceding "brief treatise" must be published (now part I of the text). In fact in the published part I occupies 83 pages while part II is not much longer at 97 pages. In the same letter Witt criticises Apollonius who, in his opinion, had made things much too complicated. His own methods he claims are much simpler. Van Schooten helped prepare the text by editing it and drawing the figures with great precision. De Witt read the proofs and had the final say regarding changes to what van Schooten produced.

Let us end by quoting the praise that Huygens gave to de Witt in a letter written to Wallis 6 June 1659:-

In my opinion no century has been so abounding in mathematicians as ours, amongst whom this man even might have reached the first place, if he had been less occupied by his official duties.