ABSTRACT

The article has as its main purpose the detailed investigation of the geometric methods of tracing historical structures, using a variety of examples. The design and construction of historic buildings has long been the subject of extensive research. However, the application of geometry to the constructional tracing of basic building elements is a relatively unknown field of science.

The methodology is primarily concerned with presenting the broader scientific context and analysing the design and tracing of structures. Through examples covering a wide range of times — from ancient Egypt, ancient Greece, Roman times, Byzantium, Islamic architecture, to the western Middle Ages and the Renaissance — it is proven that two distinct methods are historically used in design and construction: the first relates to geometrical constructions based on the use of circles, squares and equilateral triangles (ad quadratum and ad triangulum), while the second relates to pure modular systems with the help of pythagorean triangles for the rectangular tracing of building elements. For the understanding of the two methods, basic tracing and construction control tools are presented and different historical metric systems are analysed.

Through the analysis of the examples the basic design principles of historical architecture are revealed and the geometrical methods used by building guilds are inscribed. In this way, the importance of architectural models and the role of particular knowledge of geometry in the construction and the final form of historical structures are crystallised.

摘要

本文的主要目的是通过各种例子详细研究追溯历史结构的几何方法。历史建筑的设计和建造长期以来一直是广泛研究的主题。然而，几何学在基本建筑元素的构造追踪中的应用是一个相对未知的科学领域。

该方法主要涉及呈现更广泛的科学背景并分析结构的设计和追踪。通过涵盖广泛时代的例子——从古埃及、古希腊、罗马时代、拜占庭、伊斯兰建筑，到西方中世纪和文艺复兴——证明了两种不同的方法在历史上被用于设计和建造：第一种涉及基于使用圆形、正方形和等边三角形（ad quadratum 和 ad triangulum）的几何结构，而第二个涉及借助毕达哥拉斯三角形的纯模块化系统，用于矩形跟踪建筑元素。为了理解这两种方法，介绍了基本的跟踪和施工控制工具，并分析了不同的历史度量系统。

通过对实例的分析，揭示了历史建筑的基本设计原则，铭刻了建筑行会所使用的几何方法。通过这种方式，建筑模型的重要性以及特定几何知识在建筑和历史结构的最终形式中的作用得到了体现。