莱昂·巴蒂斯塔·阿尔伯蒂Leon Battista Alberti

莱昂·巴蒂斯塔·阿尔伯蒂的父亲是Lorenzo Alberti。我们不知道他的母亲是谁，有理由相信他是一个私生子。他父亲的家族很富有，14世纪时曾在佛罗伦萨从事银行业和商业业务。事实上，佛罗伦萨城在这一时期的成功在很大程度上是阿尔伯蒂家族成功的结果，其公司在意大利北部广泛设有分支机构。然而，家族成员并不满足于他们主要的金融成就，还涉足政治。这最终成了一场灾难，在通过流放他们的法令后，家族被逐出佛罗伦萨。正是因为这个原因，Lorenzo Alberti在他儿子出生时住在热那亚，因为在那里他既安全，又能继续在家族公司当地分支机构中维持富裕的生活方式。

作为孩子，阿尔伯蒂阿尔伯蒂从父亲洛伦佐那里接受数学教育。然而，当瘟疫袭击热那亚时，洛伦佐迅速带着他的孩子们前往威尼斯，那里该公司也有一个由阿尔伯蒂家族成员经营的主要分号。然而，洛伦佐在抵达威尼斯后不久就去世了，阿尔伯蒂阿尔伯蒂开始与他的一个叔叔住在一起。这种安排很短暂，因为这位叔叔很快就消失了。很可能到这时，家族成员正试图通过不择手段的方式获取家族财富。阿尔伯蒂阿尔伯蒂在帕多瓦的一所学校就读，然后从1421年起，他进入博洛尼亚大学学习法律，但并不喜欢这个科目。他因过度劳累而生病，但仍设法获得了教会法学位。大约在这个时候，他开始对从事数学研究产生兴趣，这多少是作为一种在因法律学习而感到压力时放松的方式，他发现法律学习对记忆的要求实在太大。也大约在这个时候，他写了一部喜剧Philodoxius（《荣耀爱好者》，1424年），用拉丁文诗歌写成。

此时，迫使他的家人逃离佛罗伦萨的法令已被撤销，阿尔伯蒂 前往这座城市居住，在那里他遇到了 菲利波·布鲁内莱斯基，两人成为好友。他们对数学有共同的兴趣，并且通过 菲利波·布鲁内莱斯基，阿尔伯蒂 对建筑产生了兴趣。然而，在这个阶段，他的兴趣纯粹是理论上的，他并没有将理论付诸实践。1430年，阿尔伯蒂 开始为罗马天主教会的一位红衣主教工作。这个职位意味着他经常旅行，特别是去法国、比利时和德国。1432年，他开始了文学事业，在罗马教廷担任秘书，用优雅的拉丁文撰写圣徒传记。去罗马对 阿尔伯蒂 来说意义重大，因为在那里他爱上了周围所见的古代古典建筑。这促使他不仅研究古典建筑，还研究绘画和雕塑。阿尔伯蒂 曾为教皇尤金四世服务，但这是教廷相当虚弱的时期，针对教皇的军事行动迫使尤金四世多次离开罗马。阿尔伯蒂 在这些时候随教皇离开罗马，并在里米尼的宫廷中度过时光。尼古拉五世，从1447年到1455年担任教皇，是古典研究的热衷者，并营造了一个非常适合 阿尔伯蒂 的环境，后者于1452年向他呈献了自己的建筑著作 De re aedificatoria。阿尔伯蒂 以 维特鲁威 的古典著作为蓝本，模仿其格式，将文本分为十卷。维特鲁威（公元前1世纪）是著名论著 De architectura（《论建筑》）的作者。阿尔伯蒂 在文本中提出的防御工事方法极具影响力，并在数百年的城镇防御工事中被使用。1447年，即尼古拉五世成为教皇的那一年，阿尔伯蒂 成为佛罗伦萨大都会教堂的教士和比萨圣埃雷米塔的修道院长。教皇尼古拉五世雇用他进行一些重大建筑项目，我们下面描述他的一些杰出建筑。

阿尔伯蒂研究了三维物体的表示，并于1435年撰写了第一部关于透视法则的通用论著De Pictura。该书最初以拉丁文出版，但次年阿尔伯蒂以Della pittura为标题出版了意大利文版本。这本书献给了菲利波·布鲁内莱斯基，后者确实给了他极大的启发。该书于1511年印刷。Simon在[13]中写道：-

阿尔伯蒂通过使用一扇向世界敞开的窗户的隐喻，解释并论证了他的透视构造方法。画面被设想为与视觉金字塔相交而不改变它。

阿尔伯蒂写到他如何喜欢将数学应用于艺术事业：-

没有什么比数学研究和论证更令我高兴的了，尤其是当我能够将它们用于某些有用的实践，从数学中汲取绘画透视的原理以及一些关于重物移动的惊人命题时。

阿尔伯蒂 的著作 9 也评论了数学如何通过 阿尔伯蒂 及同期其他人的贡献影响艺术：-

在十六世纪透视学向应用艺术发展的过程中，我们似乎看到的是数学作为工匠（一般而言）和建筑师（尤其如此）训练与实践中日益重要组成部分的进步。

阿尔伯蒂 还从事地图工作（同样涉及他在几何映射方面的技能），并与 Paolo Toscanelli 合作，后者为哥伦布的首次航行提供了地图。他还写了第一本关于密码学的书，其中包含第一个频率表的例子。在这一领域，他引入了多表替换 10。这是一种密码方法，其中文本的第 $k$ 个字母（即字母表中的第 $i$ 个字母）被字母表中的第 $j$ 个字母替换，其中 $j = f (i, k)$ 对于某个函数 $f$。多表替换由 阿尔伯蒂 引入外交实践，他还发明了一种简单的机械装置来加速编码和解码，由一个固定环和一个可移动环组成。

然而，阿尔伯蒂 最为人所知的是作为建筑师。我们上面提到 阿尔伯蒂 在里米尼度过时光，正是在那里他设计了马拉泰斯塔神庙的立面，这是他首次尝试将关于建筑的理论思想付诸实践。它的设计风格仿照里米尼的奥古斯都拱门，是艺术史上古典建筑成为文艺复兴建筑范本的第一个例子。

Gombrich 写道 [4]：-

菲利波·布鲁内莱斯基 的想法是引入古典建筑的形式，即他从罗马废墟中复制的柱子、山花和檐口。他在他的教堂中使用了这些形式。他的后继者渴望在这方面效仿他。[曼图亚的圣安德烈亚教堂] 是一座由佛罗伦萨建筑师 阿尔伯蒂 阿尔伯蒂 设计的教堂，他将教堂的立面构思为罗马风格的巨大凯旋门。但是，这个新方案如何应用于城市街道上的普通住宅呢？罗马时代没有私人住宅留存下来，即使有，需求和习俗也发生了很大变化，它们可能提供不了什么指导。因此，问题在于在带有墙壁和窗户的传统房屋与 菲利波·布鲁内莱斯基 教给建筑师使用的古典形式之间找到折衷。又是 阿尔伯蒂 找到了这个直到我们今天仍有影响的解决方案。当他为富有的佛罗伦萨商人家庭 Rucellai 建造宫殿时，他设计了一座普通的三层建筑。这个立面与古典废墟几乎没有相似之处。然而 阿尔伯蒂 坚持 菲利波·布鲁内莱斯基 的方案，并使用古典形式来装饰立面。他没有建造柱子或半柱，而是用扁平的壁柱和柱顶横梁网络覆盖房屋，暗示古典柱式而不改变建筑的结构。... 阿尔伯蒂 ... 仅仅通过平滑掉“野蛮的”尖拱并在传统语境中使用古典柱式的元素，将哥特式设计“翻译”成古典形式。

曼图亚的圣安德烈亚教堂，贡布里希在上述引文中对其有所评论，由阿尔伯蒂于1470年设计，两年后动工。阿尔伯蒂未能亲眼见到自己的设计成形，因为他在建筑动工那年去世，而当立面和门廊就位时，他已去世18年。该教堂在[5]中有所讨论，作者写道，阿尔伯蒂的：-

……公开宣称的建筑目标，即以教堂的空间形式图式化世界内在的和谐秩序，在[他]自己的曼图亚圣安德烈亚教堂中得到了宏伟的实现。这是他最后的建筑作品……并以完美的艺术清晰性实现了这些理论思想。

阿尔伯蒂在其设计中做出了众多创新，摒弃了传统的中殿与侧廊之分，转而提供连续的空间。阿尔伯蒂让大小礼拜堂沿主空间两侧交替排列的方式，确实带有数学意味。

除了曼图亚的圣安德烈亚教堂，阿尔伯蒂早先还设计了佛罗伦萨新圣母大殿的立面，他于1447年开始这项工作，以及上文贡布里希引文中提到的鲁切拉伊宫。这两项工程都是为佛罗伦萨商人乔瓦尼·迪·保罗·鲁切拉伊进行的。鲁切拉伊宫设计于1446年至1451年间，位于维尼亚街。广场右侧是阿尔伯蒂于1460年为鲁切拉伊家族建造的正式大厅——鲁切拉伊凉廊。

关于阿尔伯蒂的性格与外貌，吉勒在[1]中写道：-

我们得知，阿尔伯蒂和蔼可亲、非常英俊且机智风趣。他擅长引导讨论，并乐于组织小型谈话聚会。

事实上，阿尔伯蒂写有一些留存下来的自传笔记，其中他夸耀自己的体能。他声称自己能够：-

……双脚并拢站立，一跃跳过一个人的头顶。

同样地，他还声称自己：-

……擅长各种身体锻炼；能够双脚被绑的情况下跃过一个站立的人；能在大教堂里将一枚硬币高高抛起，使其撞击拱顶发出声响；以驯服野马和攀登高山为乐。

即使这些说法不实，这些有趣的引述也向我们透露了许多关于阿尔伯蒂个性的信息。

Leone Battista Alberti's father was Lorenzo Alberti. We do not know who his mother was, and there is reason to believe that he was an illegitimate child. His father's family were wealthy and had been involved in banking and commercial business in Florence during the 14th century. In fact the success of the city of Florence during this period is to a large extent a consequence of the success of the Alberti family, whose firm had branches spread widely through north Italy. Not content with their major financial achievements, however, members of the family became involved in politics. This turned out to be a disaster and the family was driven out of Florence after decrees were passed to exile them. It was for this reason that Lorenzo Alberti came to be living in Genoa at the time his son was born, for there he was safe yet still able to continue his wealthy life style within a local branch of the family firm.

As a child Leone Battista received his mathematical education from his father Lorenzo. However, when the plague struck Genoa, Lorenzo rapidly went with his children to Venice where the firm also had a major branch run by members of the Alberti family. However, Lorenzo died shortly after arriving in Venice and Leone Battista began living with one of his uncles. This arrangement was short-lived for the uncle soon vanished. It is likely that by this time members of the family were attempting by unscrupulous means to gain access to the family fortune. Leone Battista attended a school in Padua then, from 1421, he attended the University of Bologna where he studied law but did not enjoy this topic. He became ill through overwork but still managed to gain a degree in canon law. It was around this time that he became interested in pursuing his mathematical studies, rather as a way to relax when stressed out by his law studies which he found made far too large demands on memory. Also around this time he wrote a comedy Philodoxius (Lover of Glory, 1424), composed in Latin verse.

By this time the decrees which had forced his family to flee from Florence had been revoked and Alberti went to live in the city where he met Brunelleschi and the two became good friends. They shared an interest in mathematics and, through Brunelleschi, Alberti became interested in architecture. At this stage, however, his interest was purely theoretical and he did not put his theories into practice. In 1430 Alberti began working for a cardinal of the Roman Catholic Church. This post meant that he travelled a lot, in particular to France, Belgium and Germany. In 1432 he began following a literary career as a secretary in the Papal Chancery in Rome writing biographies of the saints in elegant Latin. Going to Rome was highly significant for Alberti, for there he fell in love with the ancient classical architecture which he saw all around. This led him to study not only classical architecture but also painting and sculpture. Alberti served Pope Eugene IV but this was a period of considerable weakness for the Papacy and military action against the Pope forced Eugene IV out of Rome on several occasions. Alberti left Rome with the Pope at such times and spent time at the court in Rimini. Nicholas V, who was Pope from 1447 to 1455, was an enthusiast for classical studies and produced an environment much suited to Alberti who presented him with his book on architecture De re aedificatoria in 1452. Alberti modelled the book on the classical work by Vitruvius and copied his format by dividing his text into ten books. Vitruvius (1st century BC) was the author of the famous treatise De architectura (On Architecture). The methods of fortification which Alberti set out in the text were highly influential and were used in the fortification of towns for several hundred years. In 1447, the year Nicholas V became Pope, Alberti became a canon of the Metropolitan Church of Florence and Abbot of Sant' Eremita of Pisa. Pope Nicholas V employed him on a number of major architectural projects and we describe below some of his remarkable buildings.

Alberti studied the representation of 3-dimensional objects and, in 1435, wrote the first general treatise De Pictura on the laws of perspective. This was first published in Latin but in the following year Alberti published an Italian version under the title Della pittura. The book was dedicated to Brunelleschi who had indeed been a great inspiration to him. It was printed in 1511. Simon writes in [13]:-

Alberti explained and justified his method of perspective construction by using the metaphor of a window opening onto the world. The picture surface is conceived as intersecting the pyramid of vision without altering it.

Alberti wrote about how he enjoyed applying mathematics to artistic undertakings:-

Nothing pleases me so much as mathematical investigations and demonstrations, especially when I can turn them to some useful practice drawing from mathematics the principles of painting perspective and some amazing propositions on the moving of weights .

Field [9] also comments on how mathematics influenced the arts through the contributons of Alberti and others around the same period:-

What we seem to be seeing in this progress of perspective towards the applied arts in the sixteenth century is the progress of mathematics as an increasingly important component in the training and practice of craftsmen in general, and of architects in particular.

Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Paolo Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table. In this area he introduced polyalphabetic substitution [10]. This is the method of cipher in which the $k$th letter of a text which is the $i$th letter in the alphabet is replaced by the $j$th letter of the alphabet where $j = f (i, k)$ for some function $f$. Polyalphabetic substitution was introduced into diplomatic practice by Alberti, who also invented a simple mechanical device to speed up coding and decoding, consisting of a fixed and a movable ring.

Alberti is best known, however, as an architect. We mentioned above that Alberti spent time in Rimini and it was there that he designed the facade of the Tempio Malatestiano, his first attempt to put his theoretical ideas about architecture into practice. It was designed in the style of the Arch of Augustus in Rimini and is the first example in the history of art of a classical building becoming the model for a Renaissance one.

Gombrich writes [4]:-

Brunelleschi's idea had been to introduce the forms of classical buildings, the columns, pediments and cornices which he had copied from Roman ruins. He had used these forms in his churches. His successors were eager to emulate him in this. [The Church of S Andrea, Mantua, is] a church planned by the Florentine architect Leone Battista Alberti, who conceived its facade as a gigantic triumphal arch in the Roman manner. But how was this new programme to be applied to an ordinary dwelling-house in a city street? No private houses had survived from Roman times, and even if they had, needs and customs had changed so much that they might have offered little guidance. The problem, then, was to find a compromise between the traditional house, with walls and windows, and the classical forms which Brunelleschi had taught the architects to use. It was again Alberti who found the solution that remained influential up to our own days. When he built a palace for the rich Florentine merchant family Rucellai, he designed an ordinary three-storeyed building. There is little similarity between this facade and a classical ruin. And yet Alberti stuck to Brunelleschi's programme and used classical forms for the decoration of the facade. Instead of building columns or half-columns, he covered the house with a network of flat pilasters and entablatures which suggest a classical order without changing the structure of the building. ... Alberti ... merely 'translated' a Gothic design into classical forms by smoothing out the 'barbaric' pointed arch and using the elements of the classical order in a traditional context.

The Church of S Andrea, Mantua, which Gombrich comments on in the above quote, was designed by Alberti in 1470 and work on it began two years later. Alberti did not live to see his design take shape for he died in the year in which building started and by the time the facade and portico were in position he had been dead for 18 years. The church is discussed in [5] where the author writes that Alberti's:-

... avowed architectural aim, to schematise in the spatial form of the church the immanent, harmonious order of the world, found majestic realization in [his] own church of Sant' Andrea in Mantua. This was his final architectural work ... and it carries out these theoretical ideas with perfect artistic clarity.

Alberti made numerous innovations in his design with the traditional division into nave and aisles discarded in favour of providing a continuous space. There is certainly a mathematical flavour to the way that Alberti has sequences of small and large chapels alternating along the sides of the main space.

In addition to the Church of S Andrea, Mantua, Alberti had earlier articulated the facade of the Santa Maria Novella in Florence, which he began work on in 1447, and the Palazzo Rucellai, mentioned in the quote of Gombrich above. Both works were undertaken for the Florence merchant Giovanni di Paolo Rucellai. The Palazzo Rucellai was designed between 1446 and 1451 and stands in the Via della Vigna. In the square, on the right, is the Loggia dei Rucellai built by Alberti in 1460 as a formal hall for the Rucellai family.

As to Alberti's character and appearance, Gille writes in [1]:-

Alberti was, we are told, amiable, very handsome, and witty. He was adept at directing discussions and took pleasure in organising small conversational groups.

In fact Alberti wrote some autobiographical notes which survive in which he boasts of his physical abilities. He claimed he was capable of:-

... standing with his feet together, and springing over a man's head.

In a similar vein he also claimed that he:-

... excelled in all bodily exercises; could, with feet tied, leap over a standing man; could in the great cathedral, throw a coin far up to ring against the vault; amused himself by taming wild horses and climbing mountains.

Even if untrue, these delightful quotes tell us much of Alberti's personality.