罗贝瓦尔Gilles de Roberval

罗贝瓦尔的父母是Pierre Personne和Jeanne Le Dru。此时人们可能会问的明显问题是，为什么罗贝瓦尔的父亲不姓罗贝瓦尔。原因是罗贝瓦尔被命名为罗贝瓦尔 Personne，这至少在他生命的前二十五年里是他为人所知的名字，直到1628年之后才加上“罗贝瓦尔”。Pierre和Jeanne Personne出身卑微，住在罗贝瓦尔村，位于巴黎以北约50公里（略偏东）。他们务农，但可能相当富裕，足以过上舒适的生活。最近的研究（2003年）表明，罗贝瓦尔出生在Noël-Saint-Martin，Villeneuve-sur-Verberie的一块田地里，靠近罗贝瓦尔，当时他的母亲正在收割庄稼。他第二天接受了洗礼，这一记录已在瓦兹地区的档案中找到。我们知道罗贝瓦尔有一个庞大的大家庭，有兄弟姐妹，但只有一个妹妹Marie比他活得长。

罗贝瓦尔14岁开始学习数学，当时罗贝瓦尔以北仅2公里的村庄Rhuis的本堂神父意识到年轻的罗贝瓦尔非常聪明，便开始给他上课。这位本堂神父实际上是王后玛丽·德·美第奇的随行神父，他不仅教罗贝瓦尔 Personne数学，还教他拉丁语，可能还有希腊语。在某个阶段（没有记录表明具体何时），他离开了家乡，广泛游历，访问了法国的许多地方。此时他靠教数学谋生，同时与他所访问城镇的大学教师讨论高级课题。Auger写道[2]，他骑马从一个城镇到另一个城镇，马鞍上绑着一个墨水瓶。在旅途中，他去了波尔多，在那里遇到了皮埃尔·德·费马。1627年9月，他在拉罗谢尔，当时法国国王路易十三向胡格诺派宣战，围攻了这座法国最重要的胡格诺城市和胡格诺抵抗中心的城镇。当时仍被称为罗贝瓦尔 Personne的他，研究了这次围攻所产生的筑城和弹道学问题的实践和理论两个方面。

他于1628年抵达巴黎，并与马兰·梅森的圈子建立了联系，特别是与Claude Hardy、Claude Mydorge、埃蒂安·帕斯卡尔和布莱兹·帕斯卡。他成为该圈子的一员；事实上，他后来成为该群体中唯一的职业数学家。大约在这个时候，在获得罗贝瓦尔村长的许可后，他在自己的名字中加上了“罗贝瓦尔”，成为罗贝瓦尔 Personne 罗贝瓦尔。从现在起我们将称他为罗贝瓦尔。从1628年到1632年，他致力于积累数学知识和技能，目标是获得一个职业数学家的职位。他在1632年实现了这一目标，被任命为巴黎热尔韦学院的哲学教授。这是附属于巴黎大学的一个小型机构。它成立于14世纪，是为来自巴约的学生而设，但到罗贝瓦尔被任命时，它已不再有这一限制。在他被任命到热尔韦学院后，罗贝瓦尔在学院旁边租了住处[5]：-

罗贝瓦尔搬进了那里的房间，并一直居住到生命尽头；他从未在巴黎拥有房产。他的住所位于二楼，仅由两个房间组成，一个方向朝向学院庭院，另一个方向朝向Boutebrie街。在学院任教期间，他准备成为巴黎最负盛名的数学职位之一的候选人：皇家学院的彼得吕斯·拉米斯讲席，该职位于1634年空缺，将通过公开竞争填补。

在我们简要考虑罗贝瓦尔在这些房间里的生活是什么样子之前，我们需要稍微了解一点他的性格。Sturdy写道[5]：-

……他脾气暴躁、难以相处，这是出了名的。

与他的生活方式更相关的是他吝啬的名声[5]：——

他明显不愿花钱，这为他赢得了积习难改的守财奴的名声，他的贪婪在同事和同行中成了笑柄。这并不完全公平，因为他乐于为侄女和侄孙女慷慨地提供嫁妆。另一方面，用于个人便利和舒适的东西……数量很少，确实给人留下一种印象：他的生活方式极其简朴。

那么他是如何布置他的两个房间的呢？房间里只有床、桌子和椅子，而且这些物品质量很差。墙上没有挂画，也没有装饰品。不过，他的房间里确实有一些书，作者包括欧几里得、阿基米德、弗朗索瓦·韦达、埃万杰利斯塔·托里拆利、皮埃尔·伽桑狄、勒内·笛卡儿、马兰·梅森、约翰内斯·开普勒、维特鲁威、希罗多德、西塞罗和昆体良。他有几本词典、语法书，还有一本拉丁文《圣经》（尽管他并非虔诚的教徒）。他去世时，房间里连一瓶酒都没有找到，却发现了大量现金，大约是他年薪的八倍。

1634年6月24日，他被宣布为拉米斯讲席竞争的获胜者，并被任命为皇家学院的该数学讲席。这是一个竞争性任命，罗贝瓦尔每三年都必须竞争连任。1655年，除了拉米斯讲席外，他还被任命为皇家学院皮埃尔·伽桑狄的数学讲席，并终身担任这两个讲席。1648年至1653年间，对于任何住在巴黎的人来说都是艰难的岁月，因为发生了被称为投石党运动的內战。1648年8月，巴黎发生起义，人们在街上设置路障。在军队围攻之后，叛乱于1649年春天逐渐平息，但内战再次爆发，1652年夏天在巴黎周边进行了一场战斗。到1653年，内战结束，尽管与西班牙的战争仍在继续。到1655年，罗贝瓦尔感到法国已在其人民之间实现了和平，并感到足够自信，进行了一次大规模的土地购买[5]：-

1655年，投石党运动平息后，他从库莱领主皮埃尔·德·布吕拉尔手中买下了位于梅内瓦尔的一座农场。

Sturdy在[5]中进行了一项计算，表明罗贝瓦尔为农场支付的价格高于人们的预期。也许这处特定的房产对他意义重大，而且可以肯定的是，到他生命尽头时，他大家庭的许多成员都住在该地区。农场是混合经营的，用于粮食生产，并有一群奶牛和一群肉牛。罗贝瓦尔通过将农场上的小块土地出租给个人来获得额外收入。他雇用了两名经理和若干劳工来经营农场。他的侄子路易·安托万 Personne住在农场，并管理了它多年。Menerval与罗贝瓦尔的出生地一样，位于巴黎以北，但更靠西，距巴黎约80公里。它的位置便于其农产品在巴黎销售，而且距离也足够近，使罗贝瓦尔能够前往农场。

现在让我们看看罗贝瓦尔对数学的贡献。评估他的重要性和影响相当困难，因为尽管他做出了具有根本重要性的杰出贡献，但他一生中只出版了两部著作。这两部是Traité de mécanique des poids soutenus par des puissances sur des plans inclinés à l'horizontale Ⓣ（《论斜面上由力支撑的重量的力学》）（1636年）和Le système du monde d'après Aristarque de Samos Ⓣ（《根据阿里斯塔克斯的世界体系》）（1644年）。人们可能会合理地问，既然他产生了如此大量的创新数学，为什么他出版得这么少。我们不确定这个问题的答案，但一种可能的理论是，他想让自己的发现不进入公共领域，以便他可以在每三年一次的拉米斯讲席[3]竞赛中使用这些材料：-

候选人不仅被要求讲课，还被要求证明定理并解决所有来者向他们提出的问题；结果，形成了一种做法，即现任者试图通过提出只有他才能解决的问题来确保自己再次被任命。

无论他一生中缺乏出版物的原因是什么，他的大量工作于1693年发表在Divers ouvrages de mathématique et de la physique par messieurs de l'Académie Royale des Sciences Ⓣ（皇家科学院绅士们的各种数学和物理学著作）中。罗贝瓦尔在这1693年出版物中的大部分材料至少已有五十年历史，因此它没有产生如果在写成后不久就出版本会产生的影响。其他文本在很久以后才出版，例如1996年的Eléments de géométrie Ⓣ（几何学基础），还有其他材料尚未出版（也许永远不会出版），例如他关于天文学、测量学、建筑学和自然地理学的课程。

罗贝瓦尔在早期的积分研究中发展了强大的方法，撰写了Traité des indivisibles Ⓣ（论不可分），他声称这是基于阿基米德而非博纳文图拉·卡瓦列里。它作为Divers ouvrages de mathématique et de la physique par messieurs de l'Académie Royale des Sciences Ⓣ（皇家科学院成员的各种数学结构和物理学）（1693年）的一部分出版。在其中，他计算了$x$的有理的次幂和$\sin x$的定积分。计算$\sin x$的积分使他能够解决这个问题：-

在直圆柱上，用圆规的一次运动，描绘出一个与给定正方形面积相等的曲面。

他（有理由地）为解决了这个问题而感到非常自豪，并且使用类似的技术，他在1644年第一个求出了斜锥面的面积。他在1636年之前研究摆线并计算了它的求积，他还计算了它绕其底边旋转所生成立体的体积。他比较了曲线的长度，这是一个自古希腊时代以来未被考虑的主题，他将普通形式的螺线和抛物线等同起来。在1648年8月之前，他已经发现了广义摆线和椭圆的长度相等。这意味着他在布莱兹·帕斯卡之前解决了这个问题，而后者因在1659年首次实现这一点而获得荣誉。他在1640年之前通过将问题归结为正弦的积分计算了摆线的弧长。因此他在埃万杰利斯塔·托里拆利之前解决了这个问题，后者在1644年之后找到了解法。他还计算了螺线的弧长。

除了在平面曲线上的发现之外，罗贝瓦尔还因他绘制曲线切线的方法而重要，这一方法已由埃万杰利斯塔·托里拆利提出。这种绘制切线的方法使罗贝瓦尔成为运动几何学的创始人。他写道：-

借助曲线自身的特定性质，考察描述它的点在你想绘制切线处所作的各种运动：从所有这些运动中合成一个单一运动；画出合成运动的方向线，你就得到了曲线的切线。

他在1636年之前的某个时候研究摆线时发展出了这种计算切线的方法。起初他将这一发现保密，但他在1639年至1644年间教授了这一方法。罗贝瓦尔写了一篇关于代数的论文和一篇关于解析几何的论文，后者出现在他1693年的遗作中。他确实在勒内·笛卡儿之前将代数方法引入解决几何问题，但尽管他因此值得称赞，他并没有产生笛卡尔几何。

然而，他的一些最重要的贡献是在力学领域。这里最令人印象深刻的工作是1636年发现力的合成定律。他在研究一个由两根绳子悬挂的物体时发现了这一普遍原理。1647年他写信给埃万杰利斯塔·托里拆利谈论他在力学中的发现（例如见[1]）：-

我们已经建造了从地基到屋顶都是新的力学，除了少数之外，拒绝了用来建造它的古老石头。

随后，他继续向埃万杰利斯塔·托里拆利概述了一部计划中的八卷本力学新著。内容规划如下：第一卷，论一般力的作用中心；第二卷，论平衡；第三卷，论特殊力的作用中心；第四卷，论弦；第五卷，论仪器与机械；第六卷，论在某些介质内作用的力；第七卷，论复合运动；第八卷，论运动力的撞击中心。该论著从未被发现，可能从未写成，但八卷中每一卷的部分内容存在于罗贝瓦尔的手稿中。

我们在上文提到，Le système du monde d'après Aristarque de Samos Ⓣ（根据阿里斯塔克斯的世界体系）（1644年）是罗贝瓦尔一生中仅有的两部出版物之一。在这部著作中，他赞扬了阿里斯塔克斯的日心体系，但他并未完全否定克劳狄乌斯·托勒密的以地球为中心、太阳和行星围绕地球运转的体系，也未完全否定第谷·布拉赫的体系——该体系以地球为中心，但行星围绕一个绕地球运转的太阳运行。罗贝瓦尔在序言中写道：-

也许这三种体系全都是错误的，而正确的体系尚不为人知。尽管如此，阿里斯塔克斯的体系在我看来似乎是最简单、最符合自然定律的。

有趣的是，罗贝瓦尔早在艾萨克·牛顿提出万有引力之前就相信它：-

在所有这些世俗物质中，以及在其每一个部分中，都存在着某种特性，凭借这种特性的力量，该物质收缩为一个连续的单一物体。

1666年，罗贝瓦尔是一群在让-巴蒂斯特·柯尔贝尔的巴黎住所进行天文观测的科学家中的一员。除罗贝瓦尔外，其他参与者还有克里斯蒂安·惠更斯、皮埃尔·德·卡克维、阿德里安·奥祖、福兰尼可和雅克·比奥。在许多方面，这可以被视为Académie Royale des Sciences正式成立之前的一次会议。柯尔贝尔是法国财政大臣，他挑选了这个小型团体于1666年12月22日在国王图书馆聚会，这正是Académie Royale des Sciences的成立会议。罗贝瓦尔是这些创始成员之一，并在早期作为科学院一位热情而精力充沛的成员发挥了重要作用[5]：-

他在1667年宣读了四篇关于各种主题的论文，1668年十九次，1669年两次；这些年里还记录了另外九次贡献。再次，当一位德国发明家于1668年向Colbert提出一种能解决经度计算问题的秘密机器时，罗贝瓦尔是Colbert任命来审查该主张的小委员会成员之一（其他人是阿德里安·奥祖、皮埃尔·德·卡克维、克里斯蒂安·惠更斯、让-费利克斯·皮卡德和一位资深海军军官）。作为Académie des Sciences的资深成员，他对其早期活动做出了杰出贡献，为它的审议带来了热情和力度……

1669年，他发明了“罗贝瓦尔天平”，这种天平现在几乎普遍用于天平类型的称重。他于同年8月21日向科学院提交了细节。他还与让-费利克斯·皮卡德合作进行地图绘制，并撰写了关于绘制法国的文章。他研究了当时的一个重大问题，即真空是否存在，并设计了被布莱兹·帕斯卡用于其实验的仪器。在1647年9月20日写的一份报告中，他证实了布莱兹·帕斯卡关于管中倒置水银柱上方真空的实验。他通过外部水银上的空气压力解释了管中水银的悬停。

布莱兹·帕斯卡的姐妹Jacqueline Pascal在1647年9月25日写了一封信，其中描述了罗贝瓦尔和勒内·笛卡儿之间的一次会面。后者不相信真空的存在[4]：-

……他们开始讨论真空问题。勒内·笛卡儿先生对这个问题变得特别严肃。其他人向他解释了一个最近的实验，并问他认为什么进入了被抽空的管子的空间。他说那是他的“微妙物质”。我的兄弟[布莱兹·帕斯卡]尽其所能回应了这个理论。认为我的兄弟在表达自己方面有些困难，罗贝瓦尔先生带着不小的激情与勒内·笛卡儿先生交锋——尽管他保持礼貌。勒内·笛卡儿先生相当尖刻地回应说，他可以随心所欲地与我的兄弟交谈，因为我的兄弟说话合理，但他不会继续与罗贝瓦尔先生交谈，因为后者说话出于太多偏见。说完，他看了一眼手表，看到已是中午。他站了起来，因为他在圣索菲·热尔曼郊区有一个晚餐约会。罗贝瓦尔先生也在同一个街区有一个约会。于是勒内·笛卡儿先生领他到一辆马车旁，两人单独在一起。他们似乎在互相开玩笑，但他们的幽默中带有一点锋芒，正如罗贝瓦尔先生晚餐回来后所证实的那样……

从这封信中，我们看到了罗贝瓦尔和勒内·笛卡儿之间的摩擦。他们不仅在科学问题上争论，而且还表现出强烈的相互厌恶。除了在巴黎与其他科学家会面外，罗贝瓦尔还定期与皮埃尔·德·费马和埃万杰利斯塔·托里拆利通信，直到后者于1647年去世。他有一些亲密的朋友，如Abbé Gallois，他从1665年到1674年担任Le Journal des Sçavans的编辑，1668年和1669年担任科学院的秘书，后来担任法兰西公学院的数学和希腊语教授。其他亲密的朋友包括皮埃尔·德·卡克维和Desnoyers，即太后秘书。

Gilles Roberval's parents were Pierre Personne and Jeanne Le Dru. The obvious question one might ask at this point is why Gilles Roberval's father was not named Roberval. The reason is that Gilles Roberval was named Gilles Personne and this was the name under which he was known for at least the first twenty-five years of his life, only adding the "de Roberval" after 1628. Pierre and Jeanne Personne were of humble origins, living in the village of Roberval, about 50 km north (and a bit east) of Paris. They worked on the land but probably were well enough off to lead a comfortable life. Recent research (in 2003) has shown that Gilles was born in a field at Noël-Saint-Martin, Villeneuve-sur-Verberie, close to Roberval, where his mother was bringing in the harvest. He was baptised the next day and the record of this has been found in the archives of the Oise region. We know that Gilles had a large extended family, had brothers and sisters but only one sister, Marie, outlived him.

Gilles began to study mathematics at the age of 14 years when the parish priest of Rhuis, a village just 2 km to the north of Roberval, realised that young Gilles was highly intelligent and began to give him lessons. The parish priest was actually the chaplain to the queen, Marie de Médici, and he not only instructed Gilles Personne in mathematics but also in Latin and probably Greek. At some stage (no record exists to indicate exactly when) he left his home district and travelled widely visiting many places in France. At this time he earned his living teaching mathematics while he discussed advanced topics with university teachers in the towns he visited. Auger writes [2] that he rode from town to town with an ink bottle strapped to the saddle of his horse. On his travels he went to Bordeaux where he met Pierre de Fermat. In September 1627 he was at La Rochelle when King Louis XIII of France, who had declared war on the Huguenots, besieged the town which was the most important of the Huguenot cities of France, and the centre of Huguenot resistance. Gilles Personne, as he was still known at the time, studied both practical and theoretical aspects of the problems of fortifications and ballistics which resulted from this siege.

He arrived in Paris in 1628 and made contact with Marin Mersenne's circle, particularly with Claude Hardy, Claude Mydorge, Étienne Pascal and Blaise Pascal. He became a member of the circle; in fact he later become the only professional mathematician in the group. At around this time, having received permission from the head of the village of Roberval, he added "de Roberval" to his name becoming Gilles Personne de Roberval. We will refer to him as Roberval from this point on. He spent the years from 1628 to 1632 building up his knowledge and skills in mathematics with the aim of getting a position as a professional mathematician. He achieved this in 1632 when he was appointed professor of philosophy in the Collège Gervais in Paris. This was a small institution attached to the university of Paris. It had been founded in the 14th century for students from Bayeux but by the time Roberval was appointed it no longer had that restriction. After he was appointed to the Collège Gervais, Roberval rented accommodation next to the College [5]:-

Roberval moved into rooms there where he resided until the end of his life; he never became a property owner in Paris. He had second floor accommodation comprising simply two rooms which looked into the college courtyard in one direction and the rue Boutebrie in the other. While teaching at the college he prepared himself as a candidate for one of the most prestigious mathematical positions in Paris: the Ramus Chair at the College Royal which fell vacant in 1634 and was to be filled through public competition.

Before we consider briefly what Roberval's life in these rooms was like, we need to understand a little of his character. Sturdy writes that [5]:-

... he was of notoriously difficult and irascible temper.

More relevant to his life style was his reputation for being mean [5]:-

His apparent reluctance to spend money earned him a reputation as an inveterate miser whose avarice was a by-word among his associates and colleagues. This is not entirely fair, for he was ready to contribute generously to the dowries of his niece and great-niece. On the other hand the items devoted to personal convenience and comfort ... [were] few in number and do convey the impression of somebody whose lifestyle was exceedingly austere.

So how did he furnish his two rooms? They had only beds, tables and chairs, and these items were of poor quality. No pictures hung on the walls, and there were no ornaments. However, he did have some books in his rooms by authors such as Euclid, Archimedes, Viète, Torricelli, Gassendi, Descartes, Mersenne, Kepler, Vitruvius, Herodotus, Cicero and Quintillian. He had several dictionaries, books on grammar, and (despite not being a religious man) a Latin Bible. When he died not even a bottle of wine was found in his rooms but a large amount of cash was found, something of the order of eight times his annual salary.

On 24 June 1634 he was declared the winner of the competition for the Ramus Chair, and was appointed to that chair of mathematics in the Collège Royale. This was a competitive appointment and Roberval had to compete for reappointment every three years. In 1655 he was appointed to Gassendi's chair of mathematics at the Collège Royale, in addition to the Ramus chair, and he held both chairs for the rest of his life. The years between 1648 and 1653 were difficult ones for anyone living in Paris with civil wars known as the Frondes. In August 1648 there was insurrection in Paris and the people barricaded the streets. After a siege by the army, the rebellion faded away by the spring of 1649 but civil war erupted again with a battle being fought around Paris in the summer of 1652. By 1653 the civil war ended although a continuing war with the Spanish was still going on. By 1655 Roberval felt that France had achieved peace between its own people and felt confident enough to make a major purchase of land [5]:-

In 1655, when the Frondes had died down, he bought from Pierre de Brûlart, sieur de Coullet, a farm situated at Menerval.

Sturdy carries out a calculation in [5] which suggests that Roberval paid a higher price for the farm than one would expect. Perhaps this particular property meant a lot to him and certainly by the end of his life many members of his extended family were living in the area. The farm was mixed, set up for grain production, and had a dairy herd of cattle as well as a beef herd. Roberval brought in extra income by leasing out small plots on his farm to individuals. He employed two managers to run the farm together with a number of labourers. His nephew Antoine Personne lived on the farm and managed it for a number of years. Menerval is, like Roberval's birthplace, north of Paris, but it is further to the west about 80 km from Paris. It was well situated for its produce to be sold in Paris, and also near enough for Roberval to be able to make trips to the farm.

Let us now look at Roberval's contributions to mathematics. It is rather difficult to assess his importance and influence for, although he made outstanding contributions of fundamental importance, he only published two works during his lifetime. These were Traité de mécanique des poids soutenus par des puissances sur des plans inclinés à l'horizontale Ⓣ (1636) and Le système du monde d'après Aristarque de Samos Ⓣ (1644). One might reasonably ask why, given that he produced such a large quantity of innovative mathematics, he published so little. We do not know the answer to this question for certain, but one likely theory is that he wanted to keep his discoveries out of the public domain so that he could use the material in the three-yearly competitions for the Ramus Chair [3]:-

Candidates were required not only to lecture, but also to demonstrate theorems and solve problems put to them by all comers; as result, the practice grew up of the incumbent trying to ensure his re-appointment by proposing problems which only he could solve.

Whatever the reason for the lack of publications during his lifetime, quite a lot of his work was published in Divers ouvrages de mathématique et de la physique par messieurs de l'Académie Royale des Sciences Ⓣ in 1693. Most of Roberval's material in this 1693 publication was at least fifty years old, so it did not have the impact that it would have done had it been published shortly after being written. Other texts have been published much later, for example Eléments de géométrie Ⓣ in 1996, and other material has not yet been published (and perhaps never will be published) such as his courses on astronomy, surveying, architecture and physical geography.

Roberval developed powerful methods in an early study of integration, writing Traité des indivisibles Ⓣ which he claimed was based on Archimedes and not Cavalieri. It was published as part of Divers ouvrages de mathématique et de la physique par messieurs de l'Académie Royale des Sciences Ⓣ (1693). In it he computed the definite integral of a rational power of $x$ and of $\sin x$. Computing the integral of $\sin x$ allowed him to solve the problem:-

Trace on a right cylinder, with a single motion of the compass, a surface equal to that of a given square.

He was (rightly) very proud of having solved this problem and, using similar techniques, he was the first to square the surface of the oblique cone in 1644. He worked on the cycloid computing its quadrature before 1636 and he also computed the cubature of the solid it generates by rotating it about its base. He compared the lengths of curves, a topic not considered since the times of the ancient Greeks, equating the spiral and parabola in their ordinary forms. Before August 1648 he had discovered the equality of the length of the generalised cycloid and the ellipse. This means that he solved the problem before Blaise Pascal, who receives the credit for achieving this first in 1659. He computed the arc of the cycloid before 1640 by reducing the problem to the integration of the sine. He therefore solved this problem before Torricelli who found a solution after 1644. He also computed the arc length of a spiral.

In addition to his discoveries on plane curves, Roberval is important for his method of drawing the tangent to a curve, already suggested by Torricelli. This method of drawing tangents makes Roberval the founder of kinematic geometry. He writes:-

By means of the specific properties of the curved line, examine the various movements made by the point which describes it at the location where you wish to draw the tangent: from all these movements compose a single one; draw the line of direction of the composed movement, and you will have the tangent of the curved line.

He developed this method of computing tangents while working on the cycloid some time before 1636. At first he kept this discovery a secret, but he taught the method between 1639 and 1644. Roberval wrote a treatise on algebra and one of analytic geometry which appeared in his posthumous 1693 publication. He certainly introduced algebraic methods into solving geometric problems before René Descartes did, but although he deserves credit for this nevertheless he did not produce Cartesian geometry.

However, some of his most important contributions were in the area of mechanics. Here is most impressive work was the discovery of the law of composition of forces in 1636. He discovered this general principle while studying a body suspended by two strings. In 1647 he wrote to Torricelli about his discoveries in mechanics (see for example [1]):-

We have constructed mechanics which is new from its foundation to its roof, having rejected, save for a small number, the ancient stones with which it had been built.

He then went on to give Torricelli an overview of an intended new eight-volume work on mechanics. The content was planned as follows: Book I, On the centre of action of forces in general; Book II, On the balance, Book III, On the centre of action of particular forces; Book IV, On the chord; Book V, On instruments and machines; Book VI, On the forces which act within certain media; Book VII, On compound movements; Book VIII, On the centre of percussion of moving forces. The treatise has never been found and probably was never written, but parts of each of the eight books exists in Roberval's manuscripts.

We mentioned above that Le système du monde d'après Aristarque de Samos Ⓣ (1644) was one of only two publications by Roberval in his lifetime. In this work he praises Aristarchus's heliocentric system but he did not totally reject Ptolemy's earth centered system with the sun and planets circling the earth, or Tycho Brahe's system which has the earth at the centre, but has the planets circling a sun which circles the earth. Roberval writes in the Preface:-

Perhaps all three of these systems are false and the true one unknown. Still, that of Aristarchus seemed to me to be the simplest and the best adapted to the laws of nature.

It is interesting to see that Roberval believes in universal attraction well before it was proposed by Isaac Newton:-

In all this worldly matter, and in each of its parts, resides a certain property by the force of which this matter contracts into a single continuous body.

In 1666 Roberval was one of a group of scientists making astronomical observations from Jean-Baptiste Colbert's Paris residence. In addition to Roberval the others involved were Christiaan Huygens, Pierre de Carcavi, Adrien Auzout, Bernard Frénicle de Bessy and Jacques Buot. In many ways this can be seen as a meeting of the Académie Royale des Sciences before its official foundation. Colbert, who was the French Minister of Finance, chose the small group who met in the King's Library on 22 December 1666, which was the founding meeting of the Académie Royale des Sciences. Roberval was one of these founding members and went on to play an important role as an enthusiastic and energetic member of the Academy in is early years [5]:-

He read papers on various subjects four times in 1667, nineteen times in 1668 and twice in 1669; nine other contributions are recorder during these years. Again, when a German inventor approached Colbert in 1668 with the offer of a secret machine which would solve the problem of calculating the longitude, Roberval was one of a small committee appointed by Colbert to examine the claim (the others were Auzout, Carcavi, Huygens, Picard and a senior naval officer). As a senior member of the Académie des Sciences he made an outstanding contribution to its early activities, bringing to its deliberations an enthusiasm and forcefulness ...

In 1669 he invented the 'Roberval balance' which is now almost universally used for weighing scales of the balance type. He presented details to the Academy on 21 August of that year. He also worked with Jean Picard in cartography and wrote on mapping France. He worked on one of the big questions of the day, whether a vacuum could exist, and designed apparatus which was used by Blaise Pascal in his experiments. In a report written on 20 September 1647 he confirmed Pascal's experiments on the vacuum above an inverted column of mercury in a tube. He explained the suspension of mercury in the tube by the pressure of air on the exterior mercury.

Jacqueline Pascal, the sister of Blaise Pascal, wrote a letter on 25 September 1647 in which she describes a meeting between Roberval and Descartes. The latter did not believe in the existence of a vacuum [4]:-

... they began to discuss the problem of the vacuum. Monsieur Descartes became particularly serious on the subject. The others explained a recent experiment to him and asked him what he thought entered into the space of the emptied tube. He said that it was his "subtle matter". My brother [Blaise Pascal] responded to this theory as best he could. Believing that my brother was having some difficulty expressing himself, Monsieur de Roberval took on Monsieur Descartes with not a little passion - although he remained civil. Monsieur Descartes responded rather bitterly that he could speak to my brother as long as he desired because my brother spoke reasonably but that he wouldn't continue to talk with Monsieur de Roberval, because the latter spoke out of too many prejudices. With that, he glanced at his watch and saw that it was noon. He stood up, because he had a dinner date in the Faubourg Saint-Germain. Monsieur de Roberval also had a date in the same neighbourhood. So Monsieur Descartes led him over to a carriage where the two of them were alone. They appeared to be joking with each other, but there was a bit of an edge to their humour, as Monsieur de Roberval confirmed after he returned from dinner ...

We see from this letter the friction between Roberval and Descartes. Not only did they argue over scientific issues, but they also showed a strong mutual dislike of each other. As well as meeting with other scientists in Paris, Roberval also corresponded regularly with Pierre de Fermat and with Evangelista Torricelli until his death in 1647. He had some close friends such as Abbé Gallois who was the editor of Le Journal des Sçavans from 1665 to 1674, secretary of the Academy in 1668 and 1669 and later professor of Mathematics and Greek at the Collège de France. Other close friends included Pierre de Carcavi and Desnoyers, the Queen Mother's Secretary.