数学家传记
鲁杰尔·约瑟普·博斯科维奇的主要工作是在数学物理领域。他是第一个给出通过三次观测行星位置来计算其轨道程序的人。
首先让我们注意博斯科维奇Giuseppe Boscovich名字的不同版本。至少有三种常用形式:意大利语版本博斯科维奇Giuseppe Boscovich,克罗地亚语版本鲁杰尔·约瑟普·博斯科维奇,以及英语版本RogerJoseph Boscovich。两种不太常见的形式是法语版本Rogér Joseph Boskovic和拉丁语版本Rogerio Josepho博斯科维奇。博斯科维奇的父亲是Nikola博斯科维奇,一位来自杜布罗夫尼克的商人,他的母亲是Pavica Bettera,Baro Bettera的女儿,Baro Bettera也是一位商人。Baro Bettera来自意大利的贝加莫,因此本传记的主人公博斯科维奇有一半意大利血统;他一生中大部分时间生活在意大利,今天有些人认为他是意大利人。Nikola和Pavica受过良好教育,相当富裕。他们住在杜布罗夫尼克主街旁的一栋三层家族住宅中。当然,他们需要一栋大房子,因为博斯科维奇是家中九个孩子中的第八个,家中有六个男孩和三个女孩。
在博斯科维奇生命的最初几年,杜布罗夫尼克共和国与周围的战争和战斗隔绝。周边地区持续争夺,土耳其人占据了该地区的大部分。奥地利人与威尼斯人结盟,在这片领土上与土耳其人作战。土耳其人和俄罗斯人也在城市附近交战,1716年奥地利人试图包围杜布罗夫尼克。尽管看似处于战区中心,这座城市却十分平静,年幼的博斯科维奇是否意识到战斗的存在值得怀疑。然而,他肯定知道父亲身体不好,因为Nikola在博斯科维奇十岁时去世,此前十年一直卧床不起。博斯科维奇的母亲Pavica是一位非常活跃能干的女性,尽管丈夫健康有问题,她仍让家庭保持幸福。他们很虔诚,其中一个女孩成为修女,两个男孩成为耶稣会神父,另一个成为多明我会修士。在九个孩子中,只有博斯科维奇的大姐Mare结了婚。
博斯科维奇接受的最初教育来自当地的神父,神父教他读写的基础知识。大约九岁时,他进入当地的耶稣会拉古萨学院,在那里接受了正规教育[5]:-
在他十五岁那年……他离开了家人、朋友和故乡。在虔诚的信仰、雄心和对学问的热爱的驱使下,或是在选择未来职业时受到家人或拉古萨学院院长和教师的影响(他们察觉到他非凡的才智),或是独立地认识到自己的使命,他主动接受了在罗马由耶稣会士进行的长期而严格的宗教与智力训练。
博斯科维奇于1725年9月16日离开杜布罗夫尼克,渡过亚得里亚海,然后乘驿站马车前往罗马。他在弗拉泰的圣安德烈亚成为初学修士,在那里度过了两年,随后在罗马人民广场北侧的罗马学院学习[1]:-
他头脑异常敏锐,智力全面,勤奋不倦——简而言之,是一位杰出的学生。他以一种后来职业生涯中典型的方式学习科学,即通过独立研究数学、物理学、天文学和大地测量学。
他在1732年完成了学业,但随后被要求在耶稣会学校任教五年。由于他是一位如此杰出的学生,他不必在较小的学校任教,而是大部分时间都在罗马学院任教。这是一份严苛的日程安排,在这种压力下,他的健康多次崩溃。在这些年里,他继续学习,从1735年起阅读艾萨克·牛顿的Opticks和Principia。他还开始进行天文观测,并于1736年11月11日观测到水星的中天,将结果发表在De Mercurii novissimo infra solem transituⓉ(《论水星凌日》)(1737年)上。同样在1737年,他出版了一部关于球面三角学的数学著作Trigonometriae sphaericae constructioⓉ(《球面三角学构造》)。到1737年,他完成了初步训练,可以开始学习神学课程,这将引导他进入神职。然而,他留在罗马学院,继续在那里教授数学和逻辑,同时除了学习神学外还进行深入的科学研究。难怪他的健康状况变差,但他再次恢复过来,继续这种严苛的日程安排。
1740年,他被任命为罗马公学数学教授,尽管此时他仍在接受神学训练。事实上,1740年也标志着新教皇本笃十四世的登基,他很快将让博斯科维奇担任重要角色。1742年,博斯科维奇被要求就圣彼得大教堂穹顶多年来明显的裂缝发表意见。他建议在穹顶周围放置铁环,这确实在1743年8月至1744年9月间完成了。(Poleni也曾被咨询此问题并给出了相同的建议。)教皇对博斯科维奇的建议非常满意,他还被赋予了各种其他建筑任务。他成为神父的训练在1744年以他的授职圆满结束。然而,他的兴趣不在于神职,而在于他作为数学教授的角色[5]:-
他从一个有些忧郁、外表谦逊、怀有抱负的年轻人,一个前途光明的新手,为人胆怯,但在思辨飞跃上大胆,成长为一个成熟的男人,自信,具有威严的个性。他越来越被认为是一位原创的知识分子,能够雄辩地捍卫自己的思想。他是一位在罗马众多杰出知识分子中享有相当声誉的学者。他甚至在国外也为人所知。他是一位令人羡慕的年轻专家,前途光明。
他是欧洲大陆最早接受艾萨克·牛顿引力理论的人之一,并撰写了70篇关于光学、天文学、引力、气象学和三角学的论文。他的主要工作是在数学物理领域。在他对地球形状的研究中,他使用了最小化偏差绝对值之和的思想,从而对统计学做出了重要的早期贡献。他对这个最小化问题的解决方案采取了几何形式。博斯科维奇是第一个给出从三次位置观测计算行星轨道的程序的人,他还给出了从三次表面特征观测确定行星赤道的程序。
博斯科维奇于1758年出版了Theoria philosophiae naturalis reducta ad unicam legem virium in natura existentium。他批评了艾萨克·牛顿的绝对空间和时间、绝对运动、超距作用和原子论的概念。他自己关于原子论的思想在[36]中有详细描述,作者写道:-
他的原子观念与较古老的卢克莱修理论相对立,后者认为原子是延展的、坚硬且弹性的物体。他打算通过假设非延展的原子和原子间的力定律来解释所有自然现象。博斯科维奇理论的影响在18和19世纪广泛,尤其是在英国。博斯科维奇假设点原子,与坚硬、延展的原子相对立。他还假设原子间的力在非常小的距离上是排斥的,随着距离增加交替吸引和排斥,在宏观距离上遵循引力定律是吸引的。基于这些假设,他打算解释物质的性质。他的思想在18和19世纪传播。他的原子从不同的角度被考虑,即,在距离上相互作用的点原子和作为力场中的奇点的那些。他的思想在原子论历史中的意义被陈述。
在[19]中,Manara写到了博斯科维奇关于连续性和空间性质的工作:-
我们认为,这位达尔马提亚物理学家和数学家的伟大天才、多才多艺的才智和独创性,值得人们铭记并研究他的著作和思想。……在一篇[藏于布雷西亚天主教大学的]论文中,博斯科维奇提出了他自己关于连续性的观点,连续性被视为通常所谓的几何空间的一种属性。此前,我们曾从这一角度分析过他的论文,试图阐明博斯科维奇关于当时备受争议的所谓“几何连续统的性质与构造”这一问题的观点,该问题与几何不可分量的问题相关联,后者起源于博纳文图拉·卡瓦列里的著作并引发了长时间的争论。让我们简要总结一下我们认为博斯科维奇关于这些主题的思想的基本要点:
- 博斯科维奇接受亚里士多德关于连续量的定义;根据该定义,连续统的特征在于其各部分有一个共同的端点。
- 在这一观念中,点被视为线的“端点”,因此是不可分的,且其性质与线段不同。
- 几何连续统是无限可分的;无论多小或多大的线段都可以产生。
- 不存在真正的无穷小线段。
- 连续性定律在几何曲线的一切情况下都成立,几何曲线不可能有停止点或不连续点。
因此,博斯科维奇能够设想物质由非广延的质点组成,这些质点受到力的作用,这些力不仅如艾萨克·牛顿的引力定律所确定的那样是吸引的,而且在短距离上也可以变为排斥的;这既解释了内聚现象,也解释了物质不可入性和坚固性的现象。
在一篇相关的论文[17]中,Homann写道:-
博斯科维奇隐含的、或工作性的数学哲学集中于一种几何学,这种几何学在公理上是欧几里得的,从现象经验中抽象出来,并且能够以近似的方式描述宏观层次上的现象。这种几何学允许通过诸如理想点之类的元素进行扩展,而这些元素在现象经验中没有对应物。在适当的情况下,连续统的几何学可以描述在微观层次上不连续且有限的物理实在。
对于深入思考科学的人来说,在教会内工作总是被证明是困难的。尽管博斯科维奇是一位坚定的基督徒,但他发现自己在罗马的处境变得相当不舒服。他请求允许旅行,并获得了批准。他于1759年动身前往巴黎;他访问的细节见[35]。他已经与科学院成员如夏尔·马里·德·拉孔达米纳和拉朗德建立了良好关系,后者在意大利旅行期间遇到了博斯科维奇(见[21])。博斯科维奇于1752年提交了一篇关于他对土星和木星研究的论文,参加科学院的大奖赛。奖金授予了莱昂哈德·欧拉,但博斯科维奇获得了荣誉奖。
博斯科维奇在巴黎逗留期间参加了科学院的会议,他在法国以关于天文学、北极光以及他于1739年进行的罗马至里米尼子午线弧测量的研究而闻名。他与亚历克西斯·克劳德·克莱罗成为朋友,后者钦佩他广博的文化修养和充满活力的个性;在他离开巴黎后,他们于1760年5月至1764年7月之间通信。在巴黎待了六个月后,博斯科维奇前往伦敦,并于1761年1月15日被选入皇家学会。在英国期间,他于1760年见到了托马斯·辛普森,并向托马斯·辛普森提出了一个关于最小偏差回归的问题(见[33])。他还鼓励皇家学会派遣探险队去观测定于1761年6月发生的金星凌日。
博斯科维奇计划在伊斯坦布尔亲自观测凌日,但由于他的旅行同伴是威尼斯驻伊斯坦布尔大使,他到达得太晚,未能观测到这一重要的天文事件。他于1764年成为帕维亚的数学教授,并担任布雷拉天文台台长。他为天文台改进光学设备做了大量工作,并在消色差透镜方面取得了重要进展。Proverbio写道[27]:-
1769年11月,博斯科维奇被从帕维亚召到米兰的帕拉蒂尼学校教授天文学和光学。在1769年至1771年期间,他在自己设计的布雷拉天文台加强了在天文学和光学领域的研究活动。1771年底,维也纳政府在对帕维亚和米兰的大学研究进行总体重组时,对布雷拉天文台的运作提出了一些意见。这一批评在科学界引起了不止一些困惑,特别是在拉朗德中,拉朗德是博斯科维奇的勤奋通信者之一。博斯科维奇在一份长篇纪念文[Risposta]中回应了这些意见,该文直到1927年实际上一直不为人知。
1769年,他应皇家学会之邀,率领一支探险队前往加利福尼亚,以观测下一次金星凌日。然而,政治因素使他未能成行。此时情况变得更糟。他失去了同事们的欢心,并于1772年被免去布雷拉天文台台长的职务。他辞去教授职位以示抗议。身为耶稣会士意味着他失宠,因为一段时间以来,反对耶稣会的势力一直很强。葡萄牙王室已于1759年驱逐耶稣会士,而博斯科维奇曾公开批评罗马对其修会支持不足。葡萄牙国王若泽一世认为耶稣会士过于政治化,并干扰了他的野心。法国于1764年宣布耶稣会为非法,1767年西班牙和两西西里王国也相继效仿。克莱门特十四世由耶稣会士教育,对他们友好,于1769年5月18日当选教皇。他不得不面对耶稣会问题,为了挽救罗马天主教会的分裂,他于1773年7月21日解散了耶稣会。博斯科维奇该怎么办?
巴黎是他以前为逃避问题而前往的地方,他再次寻求这样做。1773年,他前往巴黎担任法国海军光学主任。当然,这不是法国人乐意看到由外国人担任的职位,所以博斯科维奇成为了法国公民。然而他发现法国并不像他希望的那样愉快,因为他卷入了一些纠纷。早在1746年,他就设计了一种通过三次观测彗星位置来确定其轨道的方法。现在年轻而雄心勃勃的皮埃尔·西蒙·拉普拉斯攻击了他的方法。他还卷入了一场关于他设计的一些测量仪器的优先权纠纷。他试图在乡下享受平静的生活,但决定在1782年返回意大利准备出版他的著作。他于1785年出版了一部五卷本的贡献论著,但编辑和校正这部著作的工作对他的健康产生了负面影响。他开始失去智力,但也许幸运的是,在这些能力恶化太多之前,他死于肺病。
最后,让我们看看博斯科维奇的科学方法论。这在[15]中有所讨论,格梅克写道:-
在关于方法论的陈述中,他坚持所有人类知识的局限性和相对性;他描述了知识的三个来源;他定义了陈述科学可靠性的标准;最后,他以批判的方式处理归纳问题,并提出了一种特殊的启发式程序(“解读法”)。博斯科维奇清晰地描述了他构建“新世界”的逻辑程序。尽管这一程序非常清晰,但它只部分对应于他的实际方法。如果博斯科维奇在其关于科学方法论的陈述中既不接受纯粹理性主义,也不接受培根式归纳,并表现为实验方法的追随者,那么他很少求助于这种方法。
First let us note different versions of Ruggero Giuseppe Boscovich's name. There are at least three commonly used: the Italian version Ruggero Giuseppe Boscovich, the Croatian version Ruđer Josip Bošković, and the English version Roger Joseph Boscovich. Two less common forms are the French version Rogér Joseph Boskovic and the Latin version Rogerio Josepho Boscovich. Ruggero's father was Nikola Boscovich, a merchant from Dubrovnik, and his mother was Pavica Bettera, the daughter of Baro Bettera who was also a merchant. Baro Bettera came from Bergamo in Italy, so Boscovich, the subject of this biography, was half Italian; he lived for a large part of his life in Italy and some today consider him an Italian. Nikola and Pavica were well educated and fairly well off. They lived in a three-storeyed family house just off the main street of Dubrovnik. Certainly they needed a large house for Ruggero was the eighth of the nine children in the family which consisted of six boys and three girls.
The Dubrovnik Republic was, in the first few years of Boscovich's life, isolated from the wars and fighting which went on around it. The surrounding area was continually fought over with Turks holding much of the district. Austrians, in alliance with Venetians, fought the Turks over the territory. The Turks and the Russians also fought close to the city and in 1716 the Austrians tried to surround Dubrovnik. Despite appearing in the middle of a war zone, the city was peaceful and it is doubtful whether the young Boscovich was aware of the fighting. He certainly was aware, however, of his father's ill health for Nikola died when Boscovich was ten years old having been confined to bed during these ten years. Boscovich's mother Pavica was a very active and able woman who continued to keep the family happy despite the health problems of her husband. They were religious with one of the girls becoming a nun, two of the boys Jesuit priests, and another a Dominican friar. Of the nine children, only Boscovich's eldest sister Mare married.
The first education that Boscovich received was from the local priest who taught him the basics of reading and writing. At the age of around nine he attended the local Jesuit Collegium Ragusinum where he received formal education [5]:-
In his fifteenth year ... he left his family and friends and native town. Driven by fervent piety, ambition and a love of learning and either influenced in the choice of his future career by his family or by his Rector and teachers at the Ragusinum, who were aware of the exceptional qualities of his mind, or independently realizing his vocation, he offered himself for the protracted and severe religious and intellectual training by the Jesuits in Rome.
Boscovich left Dubrovnik on 16 September 1725, crossed the Adriatic, then travelled by stage-coach to Rome. He became a novice in S Andrea delle Fratte where he spent two years, then studied at the Collegium Romanum on the north side of the Piazza del Popolo in Rome [1]:-
He was extraordinarily sharp of mind, comprehensive in intelligence, and tireless in application - in short, an outstanding student. He learnt science in a way characteristic of his later career, through independent study of mathematics, physics, astronomy, and geodesy.
He had completed his course by 1732 but then was required to teach in Jesuit schools for five years. Because he was such an outstanding student he did not have to teach in smaller schools, but spent most of this time teaching in the Collegium Romanum. It was a punishing schedule and under the pressure his health broke down on several occasions. He continued studying during these years reading Newton's Opticks and Principia from 1735 onwards. He also began making astronomical observations and observed the transit of Mercury on 11 November 1736, publishing his results in De Mercurii novissimo infra solem transitu Ⓣ (1737). Also in 1737 he published a mathematical work on spherical trigonometry Trigonometriae sphaericae constructio Ⓣ. By 1737 he had completed his initial training and could embark on a course in theology which would lead to entry into the priesthood. He remained at the Collegium Romanum, however, and continued to teach mathematics and logic there while undertaking deep scientific research in addition to studying theology. Little wonder that his health became poor, but again he recovered to continue with the punishing schedule.
He was appointed professor of mathematics at the Collegium Romanum in 1740, although at this stage he was still undertaking theology training. In fact the year 1740 also marked the advent of a new Pope, Benedict XIV, and he would soon involve Boscovich in important roles. In 1742 Boscovich was asked to give an opinion on the cracks which had been evident in the dome of St Peter's for many years. He recommended that iron rings be placed round the dome and indeed this was done between August 1743 and September 1744. (Poleni was also consulted about the problem and gave the same advice.) The Pope was well pleased with Boscovich's advice and he was given various other architectural tasks. His training to be a priest achieved a successful conclusion in 1744 with his ordination. However his interests did not lie in the priesthood but rather in his role as professor of mathematics [5]:-
He had developed from a somewhat melancholy, outwardly modest young man with ambitions, a novice of promise, timid in person, but bold in speculative flights, into a mature man, sure of himself, with a commanding personality. He was being increasingly considered as an original intellectual who could eloquently defend his ideas. He was a scholar with a considerable reputation among the many brilliant intellects of Rome. He had even been heard of abroad. He was an enviable young expert with a distinguished career before him.
He was one of the first in continental Europe to accept Newton's gravitational theories and he wrote 70 papers on optics, astronomy, gravitation, meteorology and trigonometry. His main work was in mathematical physics. In his study of the shape of the Earth he used the idea of minimising the sum of the absolute values of the deviations so making an important early contribution to statistics. His solution to this minimising problem took a geometric form. Boscovich was the first to give a procedure to compute a planet's orbit from three observations of its position and he also gave a procedure for determining the equator of a planet from three observations of a surface feature.
Boscovich published Theoria philosophiae naturalis reducta ad unicam legem virium in natura existentium in 1758. He criticised Newton's concepts of absolute space and time, absolute motion, action-at-a-distance, and atomism. His own ideas on atomism are described in detail in [36] where the author writes:-
His idea of atoms is opposed against the older Lucretian theory that atom is an extended, hard and elastic body. He intended to explain all natural phenomena by postulating nonextended atom and the law of force between atoms. The influence of Boscovich's theory was wide in the eighteenth and nineteenth centuries especially in Britain. Boscovich assumed point-atoms in opposition to hard, extended atoms. He also postulated the force between atoms to be repulsive at very small distances, attractive and repulsive alternately with increasing distance and attractive, following the law of gravitation, at macroscopic distances. Based on these assumptions he intended to account for the properties of matter. His ideas spread in the eighteenth and nineteenth centuries. His atoms were considered from the different points of view, namely, the point-atoms interacting at a distance and those as singular points in the field of force. The meaning of his ideas in the history of atomism is stated.
In [19] Manara writes about Boscovich's work on continuity and the nature of space:-
In our opinion the great genius, versatile intelligence, and originality of this Dalmatian physicist and mathematician warrant the remembrance and the study of his works and thought. ... In a treatise [held in the Catholic University at Brescia] Boscovich presents his own ideas concerning continuity, which is seen as a property of what is usually called geometric space. Earlier we analysed his treatise from this point of view in an attempt to cast light upon Boscovich's ideas concerning the question, much debated at the time, of what one might call 'the nature and constitution of the geometric continuum', a problem associated with the question of geometric indivisibles, which originated with the works of Bonaventura Cavalieri and was debated at length. Let us briefly summarize what we feel to be the fundamental points of Boscovich's thoughts concerning these topics:
- Boscovich accepts the Aristotelian definition of continuous quantity; according to that definition, the continuum is characterized by the fact that the parts have a common end.
- In this conception, the point is considered an 'end' of the line, and is therefore indivisible and of a nature different from that of the segment.
- The geometric continuum is infinitely divisible; segments, no matter how small or how large, can arise.
- There do not exist true infinitesimal segments.
- The law of continuity holds in all cases for geometric curves, which cannot have stopping points or discontinuities.
Boscovich was therefore able to conceive of matter as made up of nonextensive material points acted upon by forces that not only are attractive, as determined by Newton's law of gravitation, but can also become repulsive at short distances; this explains the phenomenon of cohesion no less than that of the impenetrability and solidity of matter.
In a related paper [17] Homann writes:-
Boscovich's implicit, or working, philosophy of mathematics centred on a geometry that was axiomatically Euclidean, abstracted from phenomenal experience, and able to describe, in an approximate manner, phenomena on a macroscopic level. This geometry admitted extension by elements, such as ideal points, with no correspondent in phenomenal experience. In appropriate circumstances, the geometry of the continuum can describe physical reality that, on the microscopic level, is discontinuous and finite.
It has always proved difficult for deep thinkers about science to work within the Church. Although Boscovich was a staunch Christian, he found his position in Rome becoming rather uncomfortable. He requested permission to travel and this was granted. He set off for Paris in 1759; details of his visit are given in [35]. He had already established good relations with members of the Academy such as La Condamine and Lalande who had met Boscovich during their travels around Italy (see [21]). Boscovich had submitted a memoir for the Grand Prix of the Academy of Sciences in 1752 on his study of Saturn and Jupiter. The prize was given to Euler but Boscovich had received an honourable mention.
Boscovich, who attended meetings of the Academy of Sciences during his stay in Paris, was known in France for his studies on astronomy, the aurora borealis, and the measurement of the arch of the meridian through Rome and Rimini which he had carried out in 1739. He became friendly with Clairaut who admired his vast culture and his dynamic personality; they corresponded between May 1760 and July 1764 after he left Paris. After six months in Paris, Boscovich went to London where he was elected to the Royal Society on 15 January 1761. While in England he met Thomas Simpson in 1760, and he posed a problem in least deviations regression to Simpson (see [33]). He also encouraged the Royal Society to send an expedition to observe the transit of Venus which was to take place in June 1761.
Boscovich planned to be in Istanbul to observe the transit himself, but due to the Venetian ambassador to Istanbul who was his travelling companion, he arrived too late to observe this important astronomical event. He became professor of mathematics at Pavia in 1764 and was director of Brera Observatory. He did much work on improved optical devices for the Observatory and made important advances on achromatic lenses. Proverbio writes [27]:-
In November of 1769, Boscovich was called from Pavia to teach astronomy and optics at the Palatine Schools in Milan. In the period between 1769 and 1771, he intensified his research activities in the fields of astronomy and optics at the Brera Observatory, which he himself had designed. Towards the end of 1771, the Vienna government, while carrying out its general reorganization of university studies in Pavia and Milan, advanced certain observations regarding the operation of the Brera Observatory. This criticism aroused more than a few perplexities in scientific circles, particularly in Lalande, one of Boscovich's assiduous correspondents. Boscovich replied to these observations in a long memorial [Risposta] that remained to all intents and purposes unknown until 1927.
He was invited by the Royal Society to lead an expedition to California in 1769 to observe the next transit of Venus. However politics prevented him from carrying this out. Things now took a turn for the worse. He was out of favour with his colleagues and in 1772 he was removed from his post as director of Brera Observatory. He resigned his professorship in protest. Being a Jesuit meant that he was out of favour since there had been strong moves against the Jesuits for some time. The Portuguese crown had expelled the Jesuits in 1759 and Boscovich had been openly critical of the lack of support given by Rome for his Order. King Joseph I of Portugal considered the Jesuits to be too political and to be interfering with his ambitions. France had made the Jesuits illegal in 1764, and in 1767 Spain and the Kingdom of the Two Sicilies had followed suit. Clement XIV, educated by the Jesuits and friendly towards them, was elected Pope on 18 May 1769. He had to face up to the Jesuit issue and to try to save the break-up of the Roman Catholic Church he dissolved the Jesuits on 21 July 1773. What was Boscovich to do?
Paris was where he had travelled to before to escape from problems and he sought to do so again. In 1773 he went to Paris to take up the post of Director of Optics for the French Navy. Of course this was not the sort of post that the French would be happy to see held by a foreigner, so Boscovich became a French citizen. However he did not find France as pleasant as he had hoped, for he became involved in a number of disputes. As long before as 1746 he had devised a method of determining the orbit of a comet from three observations of its position. Now the young ambitious Laplace attacked his methods. He was also involved in a priority dispute over some of the surveying instruments he had devised. He tried to enjoy a quiet life in the country but decided to return to Italy in 1782 to prepare his works for publication. He published a five volume treatise of his contributions in 1785 but the work involved in editing and correcting this had a negative affect on his health. He began to lose his mental faculties but, perhaps fortunately, died of a lung disease before these had deteriorated too much.
Finally let us look at Boscovich's scientific methodology. This is discussed in [15] in which Grmek writes:-
In statements pertaining to methodology he insists on the limits and the relativity of all human knowledge; he describes three sources of knowledge; he defines criteria of the scientific soundness of statements; finally, he deals with the problem of induction in a critical manner and sets out a particular heuristic procedure (the 'method of decipherment'). Boscovich describes with clarity the logical procedure by means of which he constructs his 'new world'. Although this procedure is perfectly clear, it corresponds only in part to his actual approach. If Boscovich accepts in his statements on scientific methodology neither pure rationalism, nor Baconian induction, and appears as an adept of the experimental method, he has only slight recourse to this method.
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