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New introduction to the 2009 edition of

Geometry of Construction

T. B. Nicholls and Norman Keep

Geometry of Construction, first published in 1947 by Cleaver-Hume Press of London, remains the most concise and instructive guide to the technical geometry of the construction industry. Specifically written to develop the skills of students and apprentices, whether architects, carpenters, stonemasons, engineers or other crafts, this book covers all aspects of two and three dimensional geometry found in technical drawing and constructional practice.

Trafalgar Bertram Nichols A.I.O.B., M.I.P.H.E., A.I.Struct.E, was born in 1908 at Orsett, Essex. He progressed through industry into teaching and by the early 1930s had become Head of the Building Department at Guildford County Technical College (now Guildford College of Further and Higher Education). It was during this time that Nichols began to write technical books about the construction industry. The first, An Introduction to Masonry, was published in 1936 by English University Press of London, and was closely followed by Stonework published in 1938 by Crosby Lockwood of London. Nicholls later wrote Building Craft Certificate Series, published in 1961 by Cleaver–Hume Press Ltd of London.

Norman Presto Keep F.R.I.B.A, was born in 1894 at Wandsworth, London. He was an experienced member of RIBA (Royal Institute of British Architects) and taught Construction at Willesden Technical College (now The College of North West London) where he was Head of the Building Department. He also became the chief examiner in Building for Surrey County Council.

When Nichols and Keep collaborated to write Geometry of Construction, the combination of their vast practical experience and their lecturing skill produced what many consider to be the best geometry book ever written for the construction industry.

Beginning with the most basic principles in technical drawing and moving on to more complex and intricate details, Nichols and Keep demonstrate their wide experience of architectural drawing. This combines with their teaching skills to give clear, detailed, yet straightforward instructions by which readers can quickly grasp the fundamental principles behind construction geometry. A feature of the book is its layout, a model of clarity, linking concise instructions with extremely clear diagrams.

The contents are delivered to the reader in a progressive series of exercises that will develop their skills as they work through its pages. The more experienced can turn to an appropriate page to be reminded of the method to tackle a particular project.

The first part examines topics such as lettering, bisectors, angles, chords, the circle and the construction of scales. These are essential basics for students before they can advance to drawing skills. It is necessary to master the methods in this area as the following chapter provides examples of projected drawings and mouldings, which are more challenging to draught correctly, demanding a higher level of technique using projection methods. It explains how to use orthographic, isometric, oblique and axonometric drawings, while giving detailed examples of each.

The next part then looks at the circle and how to create mouldings and arch components, using arcs and bisection methods. Once again Nichols and Keep show that much work can be completed purely with the simple tools of dividers, compass and rule.

The following section contains various fret patterns and designs; they are as interesting to draw as they are to produce in stone or timber. Many of the circular designs overlap, so care needs to be taken when carving these sections to prevent inadvertently removing material that will be needed as part of the design. This section also describes the correct detail to create an ellipse, parabola or hyperbola, with the necessary calculations to work out areas and volumes also. The final part of this section details the entasis of a column and an ionic volute; both are a test for the draughtsman, but are extremely satisfying to draw. The volute is a complex design that requires extreme precision to complete, as the construction lines are very close to one another at its centre. Geometrical solids and projections of solids, provided at this point, are useful examples, since being able to develop shapes and moulds is an integral part of the setting out process in stonemasonry.

The final section in Geometry of Construction continues to develop the skills of the student as the drawings become ever more detailed. Examples of this complexity can be seen in the cutting of a sphere, continued developments and interpenetrations of moulds. An excellent example of a pediment moulding shows clearly how setting out should be done. Intricate tracery is also shown in detail; this work is popular with masons as it is a challenge to produce. Another great technical challenge is that of the hemispherical dome and the setting out of barrel vaulting. Careful attention to detail must be paid when drawing, as all sections have to be correct - mistakes can be costly if drawings with errors go through to the production process. The last pages detail shadow projection within a drawing, difficult to produce and a test of highly skilled draughtsmanship.

Geometry of Construction was reprinted in 1948 and this second enlarged edition was produced in 1954. It was written in response to the demand and encouragement from lecturers and students to add further pages of drawings and accompanying text concerning raking sections, the projection of points, of lines, and of planes, the true lengths of lines, the oblique plane and on roof surfaces. These additions were incorporated into each relevant section within the original book. One technical magazine of the time (Illustrated Carpenter & Builder) is quoted as saying

Authors and publishers deserve to be congratulated on the production of an attractive book to suit the needs of students taking National Certificate, L.I.O.B., City & Guilds and similar courses. Arrangement of the text on the left hand pages and the corresponding diagrams on the right hand pages is commendable in a book for students, as it makes each page and facing page a self-contained lesson. Draughtsmanship is of a high standard, while the text is clear, concise and adequate.

Unfortunately after several reprints, this valuable book gradually became unavailable to purchase or even to borrow from a library, and students were denied the benefit of this excellent guide. Now republished by Donhead Publishing, the second edition of Geometry of Construction provides again one of the most detailed and valuable resources to develop the knowledge and skills of a draughtsman. It also offers an unparalleled insight into the world of drawing itself.  

R.J. Hoyle – Stonemasonry Lecturer/Advanced Practitioner

Richard Hoyle was born in Yorkshire to a family whose history in the stone industry now spans three centuries. Richard developed a great passion as a young boy to follow in his ancestors’ footsteps and become a skilled stonemason, continuing the family tradition.After leaving school, Richard served his apprenticeship with a local stonemasonry firm and trained at York College under the expert guidance of lecturer Kevin Calpin. With a firm background and knowledge of the industry behind him, he started his own business, which ran successfully for five years, before making the decision to move into lecturing stonemasonry at Moulton College, Northampton, where he is now one of the College’s advanced practitioners.

Daren Tailby – Stonemasonry Lecturer

With over 25 years experience in the stone industry, Daren Tailby is a highly skilled, experienced and accomplished mason. Starting work at the age of fifteen for a local company in Kettering, Northamptonshire, he quickly developed an extensive range of skills which include letter cutting, carving and banker masonry, these skills being further enhanced by the quality of his draughtsmanship. Daren has worked for several monumental and banker masonry companies, on many prestigious buildings across the country, from churches and cathedrals to stately homes and private dwellings. Keen to share his extensive range of skills and experience, Daren now lectures in stonemasonry at Moulton College.