“The Principles of Architecture” is divided into three sections: geometry, arithmetic and mensuration. Each of these topics can be regarded as a key concept.
dealt with extensively on p.57-147
Nicholson’s presentation is clearly structured. We progress from the general and abstract to the specific. The explanations accompanying the numerical problems almost have a conversational tone, as if we are receiving a private tutorial from Nicholson himself. This style seems to arise naturally from his previous teaching experience at an evening school* and perhaps inspired his publications.
With regard to the theoretical presentation of the notions, the subtitles: “DEFINITION”, “NOTATION”, “AXIOM” and “COROLLARY” allow the reader to fluidly navigate the various arithmetic rules, their conventional shorthand representation as well as their underlying axioms. These sections are followed by a brief, enlightening sentence or short paragraph. While remaining formally correct Nicholson does not overload the non-mathematician with unnecessary detail/terminology, rather he is cautious to take the reader by the hand. He does not assume any prerequisite knowledge and thus ensures a legibility to a wide audience. For instance, he omits the introduction of the notions that addition is commutative and associative instead he provides an intuitive access via direct computations.
Putting theory into practice. Each theoretical notion, say “Simple Subtraction” p. 62, is followed by a set of general problems that one may face, such as “PROBLEM II. ‘to subtract one number from another’”. Nicholson proceeds to list a set of instructions of how to methodologically solve this problem. Then we see a quantitative and specific “EXAMPLE” along with a model solution which is extended by an “EXPLANATION” that draws the reader’s attention to potential pitfalls. It appears that Nicholson’s years as a teacher* have elevated his awareness for the concepts his pupils find challenging.
Nicholson is also keen to embed his problems into an architectural setting. We see that he enjoys to exploit all possible areas that mathematical reasoning can be used to solve problems that an architect may encounter, ranging from questions concerning financial aspects, e.g. building material costs on p.91 to questions dealing with the conversion of units of measure (see the section on duodecimals which is intrinsically linked to the imperial units: feet and inches) as well as questions concerning how to extract square roots. For the latter Nicholson does not go to the extent to present a problem in an architectural context. We must of course remember how crucial such cumbersome computational methods would have been in a time without calculators. Once more we see that the relevance of knowledge remains linked to a geographical and historical setting.
Overall Nicholson himself states his motivation and intentions for his treatment of arithmetic in the Preface vii and viii:
“Number as well as Magnitude being concerned in Architecture, ARITHMETIC follows next. The importance of this in forming estimates, both materials and expense, igniting rules for measuring, and fixing a price work &c. is sufficiently obvious. Here I have endeavoured to be as concise and clear as the nature of the subject will admit. All operations purely arithmetical being either an application singly of the four primary rules (via. Addition, Subtraction, Multiplication and Division,) or else compound of them, care has been taken to define the terms clearly, and to give the proper axioms under their respective heads.”
The book intends to educate the reader, students in architecture or associated professions such as engineering, masonry, carpentry or design, in three fundamental mathematical fields. Central to the treatment is a practical approach.
*Redgrave, Samuel (1878). A Dictionary of Artists of the English School: Painters, Sculptors, Architects, Engravers and Ornamentists: with Notices of Their Lives and Work. London: G. Bell and sons, 310.
Accessed 21 March 2021.