The whole book evolves around the topic of geometry, more precisely the so called “arithmetische Linien” or arithmetic lines as foundation and layout for the fortifications. Following sort of a prologue to the book, Alexander introduces the reader within the first 15 pages in the “Bericht” to the different tools and rules of fortification buildings. In the main part, the tasks of the arithmetic lines are described in 27 separate points. These geometric principles and methods are key to understand the basis of fortification and the ability to construct effective and competitive defensive structures. It is obvious that Alexanders main goal was to create a manual that can be used on building sites. The short texts, tables with important numbers and the simple visualisations of key angles and lengths in fortification building are clear indications for this statement.
In the first so called “Aufgaben”, Alexander describes basic arithmetic knowledge as lengths and proportions. He adds annotations and summaries here and there at the end of chapters as a follow up to definitions and mostly examples. After the 6th Chapter, where multiplication and division are explained, the geometry finally comes in and Alexander makes examples with triangles and polygons.
The concept of geometry is beautifully visualized in the book’s appendix. Following different drawings and examples of the discussed angles, Alexander attached various tables containing norms of angles used to build different parts of the fortifications. All the measurements are marked with a letter which can be found again in the drawings and ground plans. This part of the book is probably the most used one in praxis while the main part contains the theory and basics which are used to properly understand the drawings and normed measurements.
In conclusion one could argue that the theory behind it is of geometrical or mathematical nature. Most part of the manual is dedicated to defining and explaining these sciences to the reader, in this case usually to engineers and masons who need to have all this knowledge of leading such a massive construction. With the huge number of tables listing every to that time known to be useful angle attached to different lengths, it points out why this book was used as a manual. These numbers couldn’t just be calculated on construction site by anyone but instead, the book was used as a mass fabricated guide across the country in times of war.