——卢卡·帕西奥利
评论文章作者:
Dr. Daniele Struppa
教授，澳门威尼斯人app下载大学校长
Schmid College of Science and Technology; Mathematics
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卢卡·帕乔利先生 (1447-1517) was a Franciscan friar born in Borgo Santo Sepolcro (now Borgo Sansepolcro) in Tuscany. Early in his life he moved to Venezia as a tutor in the house of the merchant Antonio Rompiasi. 以他的身份, he accompanied the merchant in his travels and developed significant knowledge in the practice of commercial accounting. In those years he also attended the lecture on commercial mathematics given at the Rialto School by Domenico Bragadin, 威尼斯共和国的数学家. In 1468 Pacioli became a lecturer of mathematics and priest in San Marco.
Fra Pacioli is now best remembered for two very important books: the 总结 de arithmetica, geometria, proportioni et proportionalita (威尼斯，1494) 长诗Proportione (威尼斯,1509).
的 总结, 就像帕乔利自己写的那样, 难道不是原创作品吗, but rather offers a summary of the state of the art in Renaissance mathematics and stresses the importance of mathematics in a variety of professions and arts, 包括画家, 这位音乐家, 占星家的, 宇宙学家的, 架构师, 律师和医生. 但可能最重要的应用是商业. 在他的著作中，Pacioli描述了投资规则, 销售, profits and the necessity of being able to translate different weights and currencies when commerce takes place across borders. 整个部分(计算机和圣经的特殊性) is dedicated to a complete and detailed description of the accounting methodology that we now call 复式簿记 (or 变奏曲摘得 这是意大利语的叫法). Pacioli承认，在他之前就有人知道这个想法了, 他认为这是威尼斯商人所为, 从哪个, 他告诉我们, 他掌握了所谓的威尼斯方法. 这是, 不过, the first time that the methodology is explained in detail and formalized so that it could be used by a larger audience.
的 basic idea is to record every transaction in two sections (for debits and for credits) in order to satisfy the fundamental accounting equation that states that the assets of a company are the sum of the liabilities plus the owner’s equity. In 复式簿记 every transaction is therefore recorded both in the debits and in the credits column, and the sum of all debits must equal the sum of all credits. 的 main advantage of this system is the simplicity that it brings and the ability for the merchant to reconcile all the transactions and identify possible errors. 的 system also provided a means to deal with possible disputes, and it quickly became adopted throughout the mercantile system.
It is because of this contribution that 卢卡·帕乔利先生 is often called the father of accounting, and this motivates why his bust was chosen to commemorate the establishment of the 杰一个. 会计与经济学玻璃椅.
这是帕乔利的另一个方面, which is the reason for the specific quote that was chosen 为了他的胸围, 在他的 长诗Proportione, a book he wrote in Milano around 1498 while working at the court of the Duke of Milano, 卢多维科·莫罗. 它最终于1509年在威尼斯出版. This book is dedicated to the way in which geometry is present in various aspects of the visible world and how it can be applied to art and architecture. 的re are many interesting observations one could make on this book, and on its illustrations. 实际上有两部分的插图, 第一个包含23个大写字母, Pacioli自己写的, 用尺子和指南针. 的 modern reader may be surprised at the inclusion of letters as geometrical objects, but this is in fact a tradition that has been kept alive even in modern times by Donald Knuth in his continuing work on the font creation software Metafont. 第二组插图更有趣, 因为它由六十幅木刻插图组成, originally drawn by Leonardo da Vinci while taking mathematics lessons from Pacioli himself, 当时他们都在米兰.
的 book has, 然而, great interest independently of the illustrations. 它分为三个部分. 的 first is dedicated to the so-called golden ratio (or divine ratio), 无理数是x的正解2-x-1=0, and whose interesting properties were first studied by Euclid. 这个数字出现在各种不同的情况下. It is for example the ratio between the diagonal and the side in a regular pentagon; it is also the ratio of the sides of the rectangle with the property that it can be cut into a square and a smaller rectangle with the same aspect ratio. Finally, the golden ratio is the limit of the quotient of two consecutive Fibonacci numbers. 对于Pacioli, 然而, this number had an interest beyond its mathematical properties, 它代表了神圣的三位一体, 上帝的无所不在和精髓, the fifth element that in medieval cosmogony filled the region of the universe above the earth. 的 second part of the book is devoted to the application of mathematics to architecture, and the third part deals with the five regular solids (also known as Platonic solids), 这似乎是一种翻译, 没有信用, 另一位伟大的意大利艺术家兼数学家的作品, 皮耶罗·德拉·弗朗西斯卡.
因为这第二本书, and the interest that Pacioli devoted to the intersection between art and mathematics, 我们决定选择, 为了他的胸围, “没有数学就没有艺术。,” a sentence that captures the essential role of mathematics for painters learning the (at the time new) ideas of perspective.
参考文献
Donald E. 《威尼斯人app》， http://s3-us-west-2.amazonaws.com/visiblelanguage/pdf/16.1 / the-concept-of-a-meta-font.pdf
Mario Livio, 的 Golden Ratio; 的 Story of Phi, the World’s Most Astonishing Number, New York, 2002.
卢卡·帕西奥利，《澳门威尼斯人app下载》， http://issuu.com/s.c.williams-library/docs/de_divina_proportione
卢卡·帕西奥利先生，《澳门威尼斯人app下载》， http://aura.abdn.ac.uk/bitstream/handle/2164/18994/Sangster_etal_AH_Lost_in_Translation_VOR.pdf?sequence=2
