The book “The Principles of Architecture” by Peter Nicholson covers three main fields, of which one is geometry. A select set of problems are drawn up, many of which are entirely new, and all intimately connected with the subject in hand. They are arranged in methodical order, and are preceded by the necessary definitions. Geometry as to be found in this book is the science which treats of the descriptions and properties of magnitudes in general. Different types of points, lines, angles, superficies, figures and a lot more are closely looked at. Exact illustrations accompany the descriptions.
At the beginning, the content seems still very familiar. Speaking of triangles, circles, parallelograms, polygons et cetera. But very soon, complex geometry, mathematical terms and figures enter the table. There, the illustrations play a decisive role in easily understanding the content correctly. But on the other hand, only looking at the drawings you can totally not figure out what they are supposed to show. Some of them are huge, covering an entire page. The drawings are generally labelled with capital letters, starting from “A” and reaching up to “Y” at least. According to what the illustration is about, there are also lower case letters and numbers. The title consists of the word “problem”, either fully written-out or abbreviated as “prob.” and the corresponding number in Roman numerals behind it. Furthermore, the drawings are mainly made of dotted, dashed, thin and thick solid lines. Some of them also feature hatching and shading. In the section of solids, one page is dedicated to perspective drawings of cylinders, cones, spheroids and spheres, divided into sections. This kind of illustration of geometrical figures is rather an exception in this chapter and thus stands out.
The rules, guidelines and information that are written down are not only supposed to be used by architects and those wanting to become architects, but by any person involved in the building and design sector. So to say it should be seen as a general guide also for masons, carpenters, carvers, designers, draftsmen and many more. This is because, for example, to draw shadows correctly, you need to know the geometrical rules involved in representing them.
Geometry does though not only appear in the chapter that is named after it, but of course also in the fields of arithmetic and mensuration. There are moreover various examples of geometrical components shown on Grecian and Roman antiquities.