菲利普·德拉伊尔Philippe de La Hire

菲利普·德拉伊尔的父亲是Laurent 德拉伊尔（1606年2月27日—1656年12月28日）。Laurent出生于巴黎，后来成为一位颇有成就的画家，从教会、政界人士以及希望为自己画肖像的富裕巴黎人那里获得委托。他成为绘画与雕塑学院的教授。德拉伊尔的母亲是Marguerite Coquin（卒于1669年），de la 德拉伊尔家对孩子们来说是一个令人兴奋的成长环境，因为Laurent和Marguerite招待艺术家、科学家和数学家。经常出入他们家的最著名的数学家是吉拉尔·笛沙格。德拉伊尔是他父母五个孩子中最大的一个，有一个弟弟Barthélemy和三个妹妹；Marie（出生在两个男孩之间）以及家中最小的两个成员Marguerite和Louise。这个家庭在巴黎有两处住所，一处在rue Montmartre，有四层楼和一个花园，另一处是位于rue Gravilliers的较小住宅。

德拉伊尔 接受的是艺术家教育，在素描和绘画方面变得技艺娴熟。尽管他既未在学校也未在大学接受过正规教育，但他的父亲仍期望儿子继承自己的职业，并据此对他进行训练。德拉伊尔 十六岁时父亲去世，那时他已完全投身于艺术家的生活。他成长过程中健康状况一直不佳，因此在父亲去世三年后，他计划前往意大利。此行有两个原因：他希望逗留意大利能使健康状况好转，而且尽管 Laurent 本人从未去过意大利，父亲却培养了他对意大利艺术的热爱。德拉伊尔 于 1660 年启程前往威尼斯，在那里度过了四年，发展艺术技巧并学习几何学。对几何学的兴趣源于他对艺术中透视法的研究，但很快他就发现数学课比绘画更有趣。

1664年回到巴黎时，德拉伊尔已是一个富有的人，能够追求自己的兴趣而无须寻求职业。Sturdy写道[8]：——

一个来自法国的聪明年轻人，在[威尼斯]度过了四年中的大部分时间，回国时不可能不比他离开时更加成熟、自信、老练和通晓世故。

他继续绘画，但他的严肃研究致力于几何学。他有一个朋友马克斯·亚伯拉罕 Bosse，他可以与之分享艺术和数学兴趣。Bosse是一位艺术家，比德拉伊尔年长得多，但从1641年起就参加了吉拉尔·笛沙格的几何课程。吉拉尔·笛沙格，德拉伊尔从小就认识，已于1661年去世。Bosse出版了一系列著作，发展了他从吉拉尔·笛沙格学到的几何思想，并于1661年建立了自己的艺术学校。德拉伊尔深受吉拉尔·笛沙格工作的影响，无论是直接还是通过他与Bosse的友谊，他研究了conic sections，并以射影方式处理它。他于1672年出版了他的第一部著作Observations sur les Points d'Attouchement de Trois Lignes Droites qui touchent la Section d'un Cone Ⓣ（《关于与圆锥截面相切的 three straight lines 的切点的观察》），随后于1673年出版了他著名的论著Nouvelle méthode en géometrie pour les sections des superficies coniques et cylindriques Ⓣ（《圆锥曲线和圆柱面几何的新方法》）。Taton [1]写道，Nouvelle méthode Ⓣ（《圆锥曲线和圆柱面几何的新方法》）：-

……是一部借助projective方法对圆锥截线进行的全面研究，基于一种射影对应，使得可以从一个特定的圆推导出所考察的圆锥截线。这部论著不久后由一篇题为“Les planiconiques”的补编完成，该补编以更直接的方式呈现了这一方法。《新方法》清楚地显示了吉拉尔·笛沙格的影响，尽管德拉伊尔在1679年写的一则注记中……断言，他直到自己的著作出版之后才知道后者的工作。然而，我们所知道的关于德拉伊尔训练的情况似乎与这一断言相矛盾。此外，他们的射影描述如此相似，以至于德拉伊尔的表述不可能不显得是对吉拉尔·笛沙格的改编。尽管如此，德拉伊尔的表述用的是古典语言，并且同时从空间和平面两方面来表述，要简单和清晰得多。因此，德拉伊尔理应被视为继布莱兹·帕斯卡之后射影几何中吉拉尔·笛沙格的直接弟子。

这一评价对德拉伊尔可能有点苛刻，他是一个极其诚实和一丝不苟的人。有可能他对吉拉尔·笛沙格这些思想的了解是通过Bosse而不是直接来自吉拉尔·笛沙格，因此他关于直到自己的著作出版之后才知道吉拉尔·笛沙格出版物的说法仍然可能是真的。但我们应该对Nouvelle méthode Ⓣ（《圆锥截线与圆柱面几何学的新方法》）[1]的内容再多了解一些：——

德拉伊尔阐述了圆锥曲线的性质。他从它们的焦点定义开始，并将笛卡尔解析几何应用于方程的研究和不定问题的求解；他还展示了通过曲线交点求解某些类型方程的笛卡尔方法。虽然这不是一部极具原创性的著作，但它总结了半个世纪以来解析几何所取得的进展，并包含了一些有趣的想法，其中包括将空间可能扩展到三维以上。

德拉伊尔的母亲于1669年去世，巴黎的两处住宅由五个孩子共同继承。母亲去世后不久，德拉伊尔买下了他的兄弟和三个姐妹的份额。他于1670年与Cathérine le Sage结婚，他们住进了蒙马特街的家中。他们在格拉维利耶街的第二处住宅则出租。德拉伊尔和Cathérine 德拉伊尔有四个孩子：Cathérine-Geneviève（生于1671年）、Marie-Ann（生于1673年）、Gabriel-德拉伊尔（生于1677年）和Anne-Julie（生于1680年）。

1678年1月26日，德拉伊尔当选为Académie des Sciences院士。相当令人意外的是，他当选的是天文学部。当时他并未对天文学做出任何贡献，但贝尔纳·勒布耶·德·丰特奈尔[3]表明，他的当选是凭借其在几何学方面的出色出版物。当然，常常有资格进入科学院的人会进入出现空缺的学部，而不是被迫等待——也许要等很多年——等待更合适学部的空缺。当选科学院对德拉伊尔来说是极大的荣誉，但这也意味着生活方式的改变。Academy是一个工作机构，因此当选意味着他不再是一个有闲之人。法国财政大臣让-巴蒂斯特·柯尔贝尔在1666年创建科学院时发挥了重要作用，他现在指派德拉伊尔协助让-费利克斯·皮卡德进行测量工作，其最终目标是绘制更精确的法国地图。1679年，德拉伊尔和让-费利克斯·皮卡德一起在布列塔尼进行测量工作，1880年又在吉耶讷进行测量工作。随后，德拉伊尔在没有让-费利克斯·皮卡德的情况下，于1681年前往加来和敦刻尔克周边进行测量，1682年又测量了普罗旺斯海岸。我们注意到，德拉伊尔的地球地图的投影中心不在极点，而在沿通过极点的半径延伸的$r/√2$处（其中$r$是地球半径）。

1681年4月1日，德拉伊尔的妻子Cathérine去世。他别无选择，只能迅速再婚，因为有四个孩子，最小的刚满一岁。他于1681年9月18日与公证人Jean Nonnet及其妻子Marie的女儿Cathérine Nonnet结婚。此时，德拉伊尔为科学院所做的工作与巴黎天文台密切相关，该天文台与科学院一样，在很大程度上是由于Colbert而建立的。台长是乔凡尼·多美尼科·卡西尼，天文台于1679年出版了Connaissance des temps Ⓣ（认识时间），这是世界上第一部航海历书。德拉伊尔选择与新婚妻子住在天文台，而不是住在蒙马特街的家中。Sturdy写道[8]：-

无论居住在天文台能带来怎样的声望，从家庭角度来看，它有许多缺点。住所极其狭窄。La Hire一家只有两间卧室、一间德拉伊尔工作的房间、一间厨房和一个可用的地窖。不仅要照顾德拉伊尔第一次婚姻的孩子：德拉伊尔和Cathérine又生了四个孩子。到1680年代末和1690年代初，德拉伊尔一家有十口人，一定感受到了过度拥挤带来的巨大压力……

在某种程度上，过度拥挤有所缓解，因为至少在他们婚姻的早期，德拉伊尔经常外出为科学院工作。他继续为法国地图进行测量工作，但在1683年Colbert去世后，他受其继任者François Michel le Tellier，Marquis de Louvois的指挥。皇家宫廷于1682年迁入凡尔赛宫，德拉伊尔被分配了与新宫殿供水相关的测量项目。以下引自贝尔纳·勒布耶·德·丰特奈尔 [3]的话告诉我们很多关于德拉伊尔的性格：-

德拉伊尔一丝不苟，几乎到了迷信的程度，他常常向de Louvois先生提交逐日列出的开支清单，其中连分数也不忽略。这位大臣习惯性地不看就撕掉它们，并让人按四舍五入后的数字寄出款项。

1682年12月，他被任命为皇家学院的数学讲席，该职位自1675年10月罗贝瓦尔去世后一直空缺。他讲授的课程包括天文学、力学、流体静力学、屈光学和航海学。被任命为教授四年后，他又被任命为皇家建筑学院的建筑学讲席[8]：-

德拉伊尔认真对待他在皇家学院和建筑学院的职责，认真备课并尽可能定期授课。如果他的其他事务妨碍了他，他的长子加布里埃尔-德拉伊尔会代他授课。

事实上，正如德拉伊尔自己的父亲训练他继承其艺术家职业一样，德拉伊尔也训练自己的长子继承自己的事业。德拉伊尔的目标是让儿子当选为科学院院士，而加布里埃尔-德拉伊尔德拉伊尔确实在一系列科学活动中协助了父亲，并于1694年十七岁时当选为科学院的'élève'；由此他成为十七世纪科学院最年轻的成员。

尽管德拉伊尔的兴趣横跨整个科学学科领域，他仍然对几何学着迷。1685年，他出版了一部关于圆锥曲线的综合性著作Sectiones conicaeⓉ（圆锥曲线），其中描述了吉拉尔·笛沙格的射影几何。1708年，他计算了心脏线的长度。他还撰写了关于摆线、外摆线、蚌线和求积法的论文。然而他还有其他数学兴趣，也撰写了关于magic squares的著作。他于1695年出版了Traité de mécaniqueⓉ（力学论著）。塔顿写道[1]：-

尽管被大多数力学史家所忽略，这部著作标志着向编写一部适合各学科工程师的现代实用力学手册迈出了重要一步。

他做出重要贡献的其他主题包括天文学、物理学和大地测量学。在天文学方面，他在巴黎天文台安装了第一台中天仪器。他还制作了给出太阳、月球和行星运动的表格，于1687年出版，并于1702年出版了更多此类表格。

德拉伊尔参与了许多不同科学领域的实验工作。例如，他做了关于落体的实验（例如1683年与Mariotte一起），关于磁性的实验，关于月球反射热的实验，关于声音传播的实验，关于水的物理性质的实验，关于静电学的实验，关于呼吸的实验，以及关于生理光学的实验。他还研究了实验工作中涉及的仪器。例如，对于测量——他的主要任务之一——他设计了一种仪器来测定场地的水平，并研究了计算坡度和高程的仪器。他还研究了测量温度、气压和风速等气候条件的仪器，并在巴黎天文台用这些仪器进行测量。其他实验涉及精确计时，因此他研究了时钟以及用于其他实验工作的磁体和静电机器。

我们还应当提到德拉伊尔在编辑让-费利克斯·皮卡德、Edme Mariotte、罗贝瓦尔和福兰尼可的著作方面所做的贡献。

最后我们引用德拉伊尔对1贡献的评价[1]：-

对像德拉伊尔这样多样的著作整体作出评判是困难的。他是一位精确而规律的观察者，为巴黎天文台的顺利运行以及各项大地测量事业的成做出了贡献。然而，他并未负责任何重要的创新。他在物理学、气象学和自然科学方面的各种观察，仅仅证明了他极高的求知欲。尽管他对微积分的排斥可能使他的一部分数学工作变得贫瘠，但他在射影几何、解析几何和应用几何方面的早期著作，使他跻身于吉拉尔·笛沙格和勒内·笛卡儿最优秀的追随者之列。最后，他多样的知识以及艺术、技术和科学方面的经验，是技术思想成长、实用力学进步和图形技术完善的因素。

Philippe de la Hire's father was Laurent de La Hire (27 February 1606 - 28 December 1656). Laurent was born in Paris and became a painter of some distinction, getting commissions from the church, from politicians, and from wealthy Parisians who wished their portrait painted. He became a professor at the Academy of Painting and Sculpture. Philippe's mother was Marguerite Coquin (died 1669) and the de la Hire home was a stimulating place for children to grow up in, for Laurent and Marguerite entertained artists, scientists and mathematicians. The most notable mathematician who was frequently in their home was Girard Desargues. Philippe was the oldest of his parents five children having a younger brother Barthélemy and three younger sisters; Marie (who was born between the two boys) and the two youngest members of the family Marguerite and Louise. The family had two homes in Paris, one in the rue Montmartre with four floors and a garden, and the other, a smaller dwelling, in the rue Gravilliers.

La Hire was educated as an artist and became skilled in drawing and painting. Although he received no formal education either in a school or in a university, nevertheless his father expected his son to follow his profession and trained him accordingly. La Hire was sixteen years old when his father died and at that time he was fully committed to a life as an artist. His health had been poor as he grew up so, three years after his father's death, he made plans to visit Italy. There were two reasons for the visit: he hoped that a stay in Italy would see his health improve, and also his father had given him a love of Italian art despite Laurent never having himself been to Italy. La Hire set off for Venice in 1660 and there spent four years developing his artistic skills and learning geometry. The interest in geometry arose from his study of perspective in art, but soon he was finding his mathematics classes more enjoyable than painting.

Returning to Paris in 1664, La Hire was a wealthy man and able to pursue his interests without the need to seek employment. Sturdy writes [8]:-

An intelligent young man from France who had spent the best part of four years [in Venice] could not fail to return home a more mature, self-confident, sophisticated, and worldly-wise person than when he left.

He continued to paint but his serious studies were devoted to geometry. He had a friend, Abraham Bosse, with whom he could share both artistic and mathematical interests. Bosse was an artist who was much older than La Hire, but had attended classes on geometry by Girard Desargues from 1641. Desargues, who La Hire had known from childhood, had died in 1661. Bosse had published a series of works developing the geometric ideas that he had learnt from Desargues and had established his own school of art in 1661. Much influenced by the work of Desargues, both directly and through his friendship with Bosse, La Hire worked on conic sections which he treated projectively. He published his first work Observations sur les Points d'Attouchement de Trois Lignes Droites qui touchent la Section d'un Cone Ⓣ in 1672, followed by his famous treatise Nouvelle méthode en géometrie pour les sections des superficies coniques et cylindriques Ⓣ in 1673. Taton [1] writes that the Nouvelle méthode Ⓣ:-

... is a comprehensive study of conic sections by means of the projective approach, based on a homology which permits the deduction of the conic sections under examination from a particular circle. This treatise was completed shortly afterwards by a supplement entitled 'Les planiconiques' which presented this method in a more direct fashion. The 'Nouvelle méthode' clearly displayed Desargues' influence, even though La Hire, in a note written in 1679 ..., affirmed that he did not become aware of the latter's work until after publication of his own. Yet what we know about La Hire's training seems to contradict this assertion. Furthermore, the resemblance of their projective descriptions is too obvious for La Hire's not to appear to have been an adaption of Desargues'. Nevertheless, La Hire's presentation, which was in classical language and in terms of both space and the plane, was much simpler and clearer. Thus La Hire deserves to be considered, after Pascal, a direct disciple of Desargues in projective geometry.

This assessment may be a little harsh on La Hire who was an extremely honest and meticulous person. It is possible that he knowledge these ideas of Desargues came through Bosse rather than directly from Desargues, so his statement that he did not know of Desargues' publications until after his own had been published could still be true. But we should understand a little more about the contents of the Nouvelle méthode Ⓣ [1] :-

La Hire provided an exposition of the properties of conic sections. He began with their focal definitions and applied Cartesian analytic geometry t the study of equations and the solution of indeterminate problems; he also displayed the Cartesian method for solving certain types of equations by intersections of curves. Although not a work of great originality, it summarises the progress achieved in analytical geometry during half a century and contained some interesting ideas, among them the possible extension of space to more than three dimensions.

La Hire's mother died in 1669 and the two Paris homes were left jointly to the five children. La Hire bought out the shares of his brother and three sisters shortly after his mother's death. He married Cathérine le Sage in 1670 and they took up residence in their home in rue Montmartre. Their second home in rue Gravilliers was let out to rent. Philippe and Cathérine La Hire had four children; Cathérine-Geneviève (born 1671), Marie-Ann (born 1673), Gabriel-Philippe (born 1677) and Anne-Julie (born 1680).

On 26 January 1678 La Hire was elected to the Académie des Sciences. Rather surprisingly, his election was to the astronomy section. He had, at that time, made no contributions to astronomy but Fontenelle [3] suggests that his election was on the strength of his excellent publications in geometry. Of course, often someone deserving of admission to the Academy would enter the section in which a vacancy occurred rather than be forced to wait, perhaps for many years, for a vacancy in a more appropriate section. Election to the Academy was a great honour for La Hire, but it also meant a change in life style. The Academy was a working organisation so election meant that be was no longer a man of leisure. Jean-Baptiste Colbert, the French Minister of Finance, had been instrumental in founding the Academy in 1666 and he now assigned La Hire to assist Jean Picard in the surveying work he was undertaking with the ultimate aim of producing more accurate maps of France. Together La Hire and Picard undertook surveying work in Brittany in 1679 and in Guyenne in 1880. La Hire then went, without Picard, to survey around Calais and Dunkirk in 1681 and the coast of Provence in 1682. We note that La Hire's maps of the Earth were made with the centre of projection, not at the pole, but at $r/√2$ along a radius produced through the pole (where $r$ is the radius of the Earth).

On 1 April 1681 La Hire's wife Cathérine died. He had little option than to remarry quickly, having four children the youngest being just over one year old. He married Cathérine Nonnet, the daughter of notary Jean Nonnet and his wife Marie, on 18 September 1681. By this time La Hire's work for the Academy was closely linked to the Paris Observatory which, like the Academy, had been founded largely due to Colbert. The director was Giovanni Cassini, and the Observatory had published the Connaissance des temps Ⓣ in 1679 which was the world's first nautical almanac. La Hire chose to live with his new wife at the Observatory rather than in his house on rue Montmartre. Sturdy writes [8]:-

Whatever the prestige attached to residence in the Observatory, from a domestic point of view it had many drawbacks. The accommodation was extremely cramped. The La Hires had only two bedrooms, a room where Philippe worked, a kitchen and the use of a cellar. Not only were there the children of Philippe's first marriage to be catered for: four more children were born to Philippe and Cathérine. The La Hire family by the late 1680s and early 1690s numbered ten and must have felt intense pressure from overcrowding ...

To some extent the overcrowding was eased by the fact that, at least in the early years of their marriage, La Hire was often absent undertaking work for the Academy. He continued the surveying work for the French atlas, but after the death of Colbert in 1683, he was directed by his successor François Michel le Tellier, Marquis de Louvois. The Royal Court had moved into the Palace of Versailles in 1682 and La Hire was given surveying projects relating to the supply of water to the new Palace. The following quote from Fontenelle [3] tells us a lot about La Hire's character:-

La Hire, scrupulously exact almost to the point of superstition, used to present to M de Louvois lists of expenses drawn up day by day, in which even fractions were not neglected. The minister habitually used to tear them up without looking at them, and have the sums sent in rounded up figures.

In December 1682 he was appointed to the chair of mathematics at the Collège Royale which had remained vacant following the death of Gilles Roberval in October 1675. Courses he lectured included astronomy, mechanics, hydrostatics, dioptrics, and navigation. Four years after being named professor, he was appointed, in addition, to the chair of architecture at the Académie Royale d'Architecture [8]:-

La Hire took his duties in the Collège Royale and Académie d'Architecture seriously, preparing his courses conscientiously and lecturing as regularly as possible. If his other commitments stood in his way, his eldest son, Gabriel-Philippe, lectured on his behalf.

In fact, in exactly the same way as La Hire's own father had trained him to follow in his profession as an artist, La Hire had trained his own eldest son to follow his own career. La Hire's aim was to have his son elected to the Academy and indeed Gabriel-Philippe La Hire assisted his father in a while range of scientific activities and was elected an 'élève' of the Academy in 1694 at the age of seventeen; in so doing he became the youngest member of the Academy in the seventeenth century.

Despite his interests across a whole range of scientific disciplines, La Hire remained fascinated by geometry. In 1685 he published a comprehensive work on conic sections Sectiones conicae Ⓣ which contained a description of Desargues' projective geometry. In 1708 he calculated the length of the cardioid. He also wrote memoirs on the cycloid, the epicycloid, the conchoid and quatratures. However he had other mathematical interests and also wrote on magic squares. He published Traité de mécanique Ⓣ in 1695. Taton writes [1]:-

Although passed over by the majority of the historians of mechanics, this work marks a significant step towards the elaboration of a modern manual of practical mechanics, suitable for engineers of various disciplines.

Other topics to which he made important contributions included astronomy, physics and geodesy. In astronomy he installed the first transit instrument in the Paris Observatory. He also produced tables giving the movements of the Sun, Moon and the planets which he published in 1687, publishing further such tables in 1702.

La Hire became involved in experimental work in many different scientific areas. For example he did experiments on falling bodies (for example with Mariotte in 1683), on magnetism, on the heat reflected by the moon, on the transmission of sound, on the physical properties of water, on electrostatics, on respiration, and on physiological optics. He also studied the instruments involved in experimental work. For example for surveying, which one of his major tasks, he designed an instrument to find the level at a site and studied instruments to compute slopes and elevations. He also studied instruments to measure climatic conditions such as temperature, pressure and wind speed, making measurements with such instruments at the Paris Observatory. Other experiments involved accurate time keeping so he studied clocks as well as magnets and electrostatic machines used in other experimental work.

We should also mention La Hire's contributions in editing the works of Jean Picard, Edme Mariotte, Gilles Roberval, and Frenicle de Bessy.

Finally we quote Taton's evaluation of La Hire's contributions [1]:-

It is difficult to make an overall judgement on a body of work as varied as La Hire's. A precise and regular observer, he contributed to the smooth running of the Paris Observatory and to the success of the different geodesic undertakings. Yet he was not responsible for any important innovation. His diverse observations in physics, meteorology, and the natural sciences simply attest to the high level of his intellectual curiosity. Although his rejection of the infinitesimal calculus may have rendered a part of his mathematical work sterile, his early works in projective, analytic, and applied geometry place him among the best of the followers of Desargues and Descartes. Finally, his diverse knowledge and artistic, technical, and scientific experience were factors in the growth of technological thought, the advances of practical mechanics, and the perfecting of graphic techniques.