乔瓦尼·塞瓦Giovanni Ceva

直到最近，乔瓦尼·塞瓦的出生和死亡日期一直不确定（例如，在[1]撰写时它们还是未知的），但最近在教区记录中找到了正确的信息（例如参见Paola Landra的工作[2]）。塞瓦的父亲Carlo Francesco Ceva（1610-1690）是一个从事许多不同活动的人，例如买卖房屋和土地。他还以官方身份为米兰公爵工作，征收消费税。这意味着他是一个富有的人，能够为家人提供高质量的生活方式。他于1639年9月20日与Cristoforo Columbo和Elisabetta Caballina的女儿Paola Columbo结婚。他们有几个孩子：Laura Maria Francesca Elisabetta 塞瓦（生于1640年）、Clara Giustina Bonaventura Ceva（生于1642年）、Iginio Nicolò 塞瓦（生于1644年）、Francesco Ceva（生于1645年）、塞瓦 Benedetto Ceva（本传记的主角，生于1647年）、Tommaso Ceva（在本档案中也有传记，生于1648年）、Teresa 皮耶罗·德拉·弗朗西斯卡 塞瓦（生于1650年）和Cristoforo Vittore 塞瓦（生于1652年）。Laura、Iginio、Francesco、Tomasso、Teresa和Cristoforo都有教会职业生涯，其中Francesco、Tomasso、Teresa和Cristoforo成为耶稣会士，加入了耶稣会。塞瓦的表兄，也叫Carlo Francesco Ceva，是托尔托纳的主教。我们对塞瓦的青年时代一无所知，但他确实发表了一个耐人寻味的评论，说他的青年时代因“许多种不幸”而悲伤。他还暗示他的家庭反对他的学术追求。

塞瓦在米兰的耶稣会学院Collegio di Brera接受教育，在那里他表现出对科学，特别是数学的特殊才能。离开学院后，他跟随父亲的脚步，在米兰、热那亚和曼图亚从事商业活动和行政政治角色。但他也有兴趣从事科学活动，除了他正在进行的金融交易外，他还学习几何学和水力学。他于1670年进入比萨大学，在那里他师从Donato Rossetti（1633-1686），逻辑学教授，他是原子理论的坚定支持者。他还师从Alessandro Marchetti（1633-1714），后者于1679年接替他的老师吉奥万尼·阿方索·博雷利（1608-1679）成为比萨的数学教授。Marchetti：-

……是一个超越偏见的人，自由地宣布自己的观点，偏爱实验而非权威，理性而非亚里士多德。

在比萨学习期间，塞瓦还遇到了里奇，他和Rossetti一样，是罗马数学-物理学院的成员。因此，极有可能塞瓦在比萨居住的两年期间在罗马的学院度过了一些时间。他攻克的第一个数学问题是经典的化圆为方问题，他给出了几个不正确的解决方案。他放弃了这项工作，变得有些气馁。在比萨停留之后，塞瓦继续他的数学研究，这些研究将发表在他的著作De lineis rectis se invicem secantibus statica constructio（1678）中，同时，他继续从事与他父亲类似的活动。此时他住在曼图亚，在那里他被任命为曼图亚和蒙费拉托公爵Ferdinando Carlo Gonzaga的审计员和专员，接替了他父亲的职位。在这个行政职位上，塞瓦基本上负责曼图亚和蒙费拉托的经济。然而，主要的政府角色并没有阻止塞瓦找到时间从事他的科学研究，因为在此期间他进行了他在1682年Opuscula mathematica de potentiis obliquis, de pendulis, de vasis et de fluminibus 中写下的工作。1683年，曼图亚公爵授予塞瓦曼图亚公民身份，表明公爵认为塞瓦对国家的贡献有多么重要。尽管他非常忙于为公爵履行职责，塞瓦继续从事数学研究。他与当时许多领先的科学家通信，这使他保持在数学和其他科学发展的前沿。然而，他确实评论说，他的工作被“朋友和家人的严重忧虑和事务”所分散。

1685年1月15日，塞瓦与塞西莉亚·韦基结婚；他们有几个孩子，多米蒂拉弗朗西斯卡（生于1687年），卡洛·弗朗切斯科（生于1688年，但三岁时去世），马西莫·克里斯托弗罗（生于1689年），彼得罗·安东尼奥（生于1690年），玛丽亚·多米蒂拉（生于1692年，同年去世），卡洛·弗朗切斯科（生于1693年），和科斯坦蒂诺·因诺琴佐（生于1694年）。曼图亚公爵将他已经给予塞瓦的公民身份扩展到了他的孩子。他于1686年被任命为曼图亚大学的数学教授，他终身担任这个职位。然而，到18世纪初，贡扎加家族陷入危机，哈布斯堡王朝开始威胁曼图亚。费迪南多·卡洛于1701年逃离，留下安娜·伊莎贝拉·贡扎加作为摄政。塞瓦继续从事几何问题的研究并致力于经济问题，他的研究结果分别发表在下面提到的1710年和1711年的两部著作中。1707年，奥地利吞并了曼图亚公国并开始建造重型防御工事。塞瓦迅速转向支持新的奥地利政权，事实上，他被城市一个地区的人民选为他们的提名人，宣誓效忠他们的新政治主人。

在他一生的大部分时间里，塞瓦从事几何学研究。他发现了希腊时代和19世纪之间关于三角形综合几何的最重要结果之一。该定理指出，从三角形的顶点到对边的线共点，当且仅当边被分割的比率的乘积为1。他在De lineis rectis（1678）中发表了这一点，他将此书献给了曼图亚公爵，这本书分为两部分，并附有一个重要的附录。塞瓦也在这部著作中重新发现并发表了梅涅劳斯的定理。这本书在出版时没有得到充分赏识，这一点可以从只有一个版本出现以及书中的许多结果后来被不知道塞瓦工作的人重新发现这一事实中看出。塞瓦发现的重要性直到19世纪被米歇尔·沙勒指出时才被充分赏识。

你可以在THIS LINK看到塞瓦的定理，在THIS LINK看到梅涅劳斯定理。

除了几何学的工作外，塞瓦还研究了力学和静力学在几何系统中的应用。尽管他错误地得出结论，两个摆的振荡周期与它们的长度成正比，但他后来纠正了这个错误。我们现在简要地看一下他的其他著作。

如上所述，塞瓦于1682年发表了Opuscula mathematica 。这部献给里奇的著作分为四部分。它既探讨纯几何问题，也探讨数学的应用，特别是流体动力学方面的应用。在Geometria motus, opusculum geometricum in gratiam aquarum excogitatum（1692年）中，他在研究抛物线和双曲线等曲线时，使用博纳文图拉·卡瓦列里引入的那类无穷小方法，在一定程度上预见了无穷小的微积分。从1685年他与温琴佐·维维亚尼以及安东尼奥·马利亚贝基（托斯卡纳大公的图书馆员）的通信中可以清楚看出，在这一阶段，受水力学研究的推动，他已经在进行研究，这些研究最终出现在1692年的这部出版物中。他将Geometria motus 献给曼图亚公爵费迪南多·卡洛。1710年，他发表了一部关于其几何研究的小著作Tria problemata geometris proposita。次年，他发表了De re nummeraria quod fieri potuit, geometrice tractata，这是数学经济学最早的著作之一；在书中，塞瓦试图解决像曼图亚这样的国家的货币体系的均衡条件。正如我们多次提到的，塞瓦在水力学方面做了重要工作。关于这一主题，他发表了Opus hydrostaticum（1728年），除De lineis rectis外，这是他最重要的贡献。

在曼图亚政府任职期间，他得以运用自己的水力学知识，成功反对了一项提议将雷诺河引入波河的工程。塞瓦在小册子Conseguenze del Reno, se coll'aderire al progetto de' Signori Bolognesi, si permettesse in Po grande（1716年）中提出了自己的观点，但这些观点遭到Eustachio Manfredi的反对，后者以小册子Ragioni del Signor G. C. ... e del Signor D. M. Battaglia ... contra l'introduzione del Reno nel Po grandeⓉ（G. C.……和D. M. Battaglia……反对将雷诺河引入波河的理由）（1716年）作为回应。争论随着塞瓦的Replica ... in difesa delle sue dimostrazioni, e ragioni, per le quali non debbasi introdurre Reno in PoⓉ（答复……为其论证辩护，以及不应将雷诺河引入波河的理由）（1717年）而继续，曼弗雷迪以Osservationi alla replica di G. C. Ⓣ（对G. C.答复的观察）（1717年）作答。这场争论最终以塞瓦的胜利告终，他关于该主题的最后一份小册子是Risposta alle osservazioni del Sig. Dott. E. M. contro la di lui replica in proposito dell'immissione di Reno in Po grande, pretesa da' Signori BolognesiⓉ（对自称来自博洛尼亚的E. M.博士的评论的回应，该评论反对他将雷诺河引入波河的论证）（1721年）。

Giovanni Ceva's dates of birth and death have, until recently, been uncertain (for example they were unknown when [1] was written) but recently the correct information has been found in the parish records (see for example Paola Landra's work [2]). Ceva's father, Carlo Francesco Ceva (1610-1690), was a man who undertook many different activities such as buying and selling houses and land. He also worked for the duke of Milan in an official capacity, collecting excise duty. This meant that he was a wealthy man, able to provide a high quality lifestyle for his family. He married Paola Columbo, the daughter of Cristoforo Columbo and Elisabetta Caballina, on 20 September 1639. They had several children: Laura Maria Francesca Elisabetta Ceva (born 1640), Clara Giustina Bonaventura Ceva (born 1642), Iginio Nicolò Ceva (born 1644), Francesco Ceva (born 1645), Giovanni Benedetto Ceva (the subject of this biography, born 1647), Tommaso Ceva (who also has a biography in this archive, born 1648), Teresa Francesca Ceva (born 1650), and Cristoforo Vittore Ceva (born 1652). Laura, Iginio, Francesco, Tomasso, Teresa and Cristoforo all had ecclesiastical careers, with Francesco, Tomasso, Teresa and Cristoforo becoming Jesuits, joining the Society of Jesus. Giovanni Ceva's cousin, also named Carlo Francesco Ceva, was the Bishop of Tortona. We know no details of Ceva's youth, but he does make an intriguing comment that his youth was saddened by "many kinds of misfortune". He also suggests that his family opposed his academic pursuits.

Giovanni Ceva was educated at the Collegio di Brera, a Jesuit college in Milan, where he showed a particular aptitude for science, particularly for mathematics. After leaving the College, he followed the same path as his father, engaging in business activities and in administrative political roles in Milan, Genoa and Mantua. But he was also interested in undertaking scientific activities and, in addition to the financial dealing he was doing, he studied geometry and hydraulics. He entered the university of Pisa in 1670 and there he studied under Donato Rossetti (1633-1686), the professor of logic, who was a strong supporter of atomic theories. He also studied under Alessandro Marchetti (1633-1714), who succeeded his teacher Giovanni Alfonso Borelli (1608-1679) as professor of mathematics at Pisa in 1679. Marchetti:-

... was a man above prejudices, free to declare his sentiments, preferring experiment to authority, and reason to Aristotle.

While studying in Pisa, Ceva also met Michelangelo Ricci who, like Rossetti, was a member of the Mathematics-Physics Academy of Rome. It is highly likely, therefore, that Ceva spent some time at the Academy in Rome during his two years of residence in Pisa. The first mathematical problem he attacked was the classic problem of squaring the circle and he produced several incorrect solutions to it. He gave up this work, becoming somewhat discouraged. Following his stay in Pisa, Ceva carried on with his mathematical studies which he would publish in his work De lineis rectis se invicem secantibus statica constructio (1678), and, at the same time, he continued with similar activities to those of his father. He was at this time living in Mantua where he was appointed as Auditor and Commissioner to Ferdinando Carlo Gonzaga, the Duke of Mantua and Montferrat, taking over the role from his father. In this administrative position, Ceva was essentially responsible for the economy of Mantua and Montferrat. Major government roles did not stop Ceva finding time to pursue his scientific studies, however, for during this period he undertook the work that he wrote up in Opuscula mathematica de potentiis obliquis, de pendulis, de vasis et de fluminibus in 1682. In 1683 the Duke of Mantua granted Ceva citizenship of Mantua, showing how important the Duke considered Ceva's contributions to the state. Although he was very busy with his duties for the Duke, Ceva continued to undertake mathematical research. He corresponded with many of the leading scientists of the day which kept him in the forefront of mathematical and other scientific developments. He does comment, however, that his work was distracted by "serious cares and affairs of his friends and family."

On 15 January 1685 Ceva married Cecilia Vecchi; they had several children, Domitilla Francesca (born 1687), Carlo Francesco (born 1688 but died at the age of three), Massimo Cristoforo (born 1689), Pietro Antonio (born 1690), Maria Domitilla (born 1692 and died in the same year), Carlo Francesco (born 1693), and Costantino Innocenzo (born 1694). The Duke of Mantua extended the citizenship, which he had already given to Ceva, to his children. He was appointed Professor of mathematics at the University of Mantua in 1686, a post he held for the rest of his life. By the beginning of the 18th century, however, the Gonzaga family were in crisis and the Habsburgs began to threaten Mantua. Ferdinando Carlo fled in 1701 leaving Anna Isabella Gonzaga as a regent. Ceva continued to undertake research on geometric problems and to work on economic issues, the results of his research being published in the two works of 1710 and 1711, respectively, mentioned below. In 1707 Austria annexed the duchy of Mantua and began to construct heavy fortifications. Giovanni Ceva quickly moved to support the new Austrian regime and in fact he was chosen by the people of a district of the city as their nominee to swear allegiance to their new political masters.

For most of his life Giovanni Ceva worked on geometry. He discovered one of the most important results on the synthetic geometry of the triangle between Greek times and the 19th Century. The theorem states that lines from the vertices of a triangle to the opposite sides are concurrent precisely when the product of the ratio the sides are divided is 1. He published this in De lineis rectis (1678), which he dedicated to the Duke of Mantua, a book in two parts together with an important appendix. Ceva also rediscovered and published Menelaus's theorem in this work. That the book was not fully appreciated at the time of its publication is suggested by the fact that only one edition appeared and also by the fact that many of the results in the book were later rediscovered by others who were unaware of Ceva's work. The importance of Ceva's discoveries was only fully appreciated when pointed out by Michel Chasles in the 19th century.

You can see Ceva's theorem at THIS LINK and Menelaus's theorem at THIS LINK.

In addition to his work on geometry, Ceva studied applications of mechanics and statics to geometric systems. Although he wrongly concluded that the periods of oscillation of two pendulums were in the same ratio as their lengths, he later corrected the error. We now look briefly at his other works.

As we mentioned above, Ceva published Opuscula mathematica in 1682. This work, dedicated to Michelangelo Ricci, is in four parts. It investigates questions of pure geometry as well as applications of mathematics, particularly to hydrodynamics. In Geometria motus, opusculum geometricum in gratiam aquarum excogitatum (1692) he, to some extent, anticipated the infinitesimal calculus in his study of curves such as parabolas and hyperbolas using infinitesimal methods of the type introduced by Bonaventura Cavalieri. It is clear from his correspondence with Vicenzo Viviani and Antonio Magliabechi (the librarian to the Duke of Tuscany) in 1685 that at this stage he was already undertaking research, motivated by his study of hydraulics, which eventually appeared in this 1692 publication. He dedicated Geometria motus to Ferdinando Carlo, the Duke of Mantua. He published a small work on his geometric researches, Tria problemata geometris proposita in 1710. In the following year he published De re nummeraria quod fieri potuit, geometrice tractata, one of the first works in mathematical economics; in it Ceva attempted to solve the conditions of equilibrium for the monetary system of a state like Mantua. As we have mentioned a number of times, Ceva did important work on hydraulics. On this topic he published Opus hydrostaticum (1728) which, other than De lineis rectis, is his most important contribution.

In his role in the government of Mantua he was able to use his knowledge of hydraulics and argue successfully against a project which proposed to divert the river Reno into the river Po. Ceva put forward his views in the pamphlet Conseguenze del Reno, se coll'aderire al progetto de' Signori Bolognesi, si permettesse in Po grande (1716) but these views were opposed by Eustachio Manfredi who replied with the pamphlet Ragioni del Signor G. C. ... e del Signor D. M. Battaglia ... contra l'introduzione del Reno nel Po grande Ⓣ (1716). The controversy continued with Ceva's Replica ... in difesa delle sue dimostrazioni, e ragioni, per le quali non debbasi introdurre Reno in Po Ⓣ (1717) to which Manfredi replied with Osservationi alla replica di G. C. Ⓣ(1717). The argument was finally settled in Ceva's favour with his final pamphlet on the topic Risposta alle osservazioni del Sig. Dott. E. M. contro la di lui replica in proposito dell'immissione di Reno in Po grande, pretesa da' Signori Bolognesi Ⓣ (1721).