It is not often that a history-of-science book makes the front page of the New York Times. Well, it was the Arts section, but still: the Yale University installation of this exhibition made waves in Manhattan (see E. Rothstein, ‘It took tools to build a revolution’, New York Times, 27 February 2010, p. C1). Originally mounted at the Oxford Museum for the History of Science, Gerbino and Johnston's exhibition brought together dozens of mathematical drawing instruments used in architecture, maps and plans that were drawn with them, and a few choice objects that tie the world of the mathematical practitioner and architect to the world of practice. This book showcases those objects, but is far more than an exhibition catalogue, seeking to demonstrate that there was a ‘global vision of mathematics’ (p. 84) within premodern architecture that included not only proportion and scale, but also mechanics, physics and engineering (machinery).

The book has eight gloriously illustrated chapters as well as a separate fifteen-page essay by Gordon Higgott on the geometry and structure of St Paul's Cathedral dome, and has only a relatively brief twenty-four-page exhibition checklist tucked in at the end. Mainly the book's chapters develop the story of architecture not from the point of view of great designers or great builders, but from the tools from which they were made and the manuscripts where the designers worked out their design. In ways, though, this is an exhibition pivoted about Sir Christopher Wren and St Paul's Cathedral that explores how architecture moved from a craft practice, through a gentlemanly and instrumental trade, to a more institutionalized form in the century after the Great Fire of 1666.

Gerbino and Johnston bring together a vast array of earlier secondary literature to tell the story of architecture from the Middle Ages to the eighteenth century, and often intersperse small new archival findings. In the end, though, the volume should be considered more synthesis than revelation. Their juxtaposition of fields that usually have little to do with one another – the history of architecture and the history of mathematical practice and science – deserves considerable praise. And to do so in the context of a object-focused museum installation turned into what could be mistaken for a coffee-table book makes their success all the more appealing. Other hybrid investigations could indeed be catalysed by such an approach (computing history and the history of management, or genetics and popular culture of crime dramas come to mind) and it remains to be seen how their work may generate new ways of seeing in other mathematical/practical contexts.

Beginning with some medieval and Tudor examples of architecture, the book segues through Inigo Jones (himself something of an Italianophile anomaly for the time) to Sir Christopher Wren and less well-known mid-seventeenth-century designers like John Thorpe. Curiously, objects offer compelling evidence for the first half of the book, though when the topic moves to Wren and St Paul's drawings become the almost sole focus – having the known name of Wren no doubt helped at the exhibition even if he is not billed on the marquee. Objects included in the last third of the book more often dazzle than elucidate, as for example George III's glorious silver microscope with dancing nymphs that looks more like a candelabra than a scientific instrument – whose central Corinthian column supporting the objective stage is claimed to show an inherent architectonic over artistic aesthetic. At the end, instruments (especially the architectonic sector that drives Chapter 7) and the education of the gentleman in the eighteenth century provide closure to the narrative arc. That ending, though, is surprisingly a story of failure in that such things as the Five Orders and gentlemanly architectural expertise ultimately become a target of satire in the age of Hogarth.

The study is unapologetically Anglocentric, which is itself not a problem, though it often precludes what could be interesting discussions of, for example, Platonic solids and neo-Pythagoreanism in the early modern world or the rise of architectural design academies on the Continent just as their English story is concluding. The ‘Wren question’ that drives the study – why and how did a professor of astronomy become England's leading architect? – is answered somewhat convincingly in the idea that his search for material explanations of natural-philosophical quandaries (the catenary and tension/compression, for example) became an overarching theme for ideas of proportion in architecture and especially the form of the dome of St Paul's. Reminding us of the context of the early Royal Society's experiments, they argue (p. 96) that architecture was Wren's ‘visual, concrete, geometrical, and practical’ conception of ‘science’ (explicitly not natural philosophy, and always in quotes). The idea is partially undermined in terms of Wren himself and yet bolstered for the field of mathematically driven architecture in general by the inclusion of a great deal of information on the secondary and often unknown designers in the St Paul's building office, and the development of technical drawing, that clearly helped converge on the final design.

There is a double pun in the title of the book as well: we are mostly prone to recognize the two words ‘compass’ and ‘rule’ as nouns but one can also see them as verbs – to (en)compass and to rule – and one might be tempted to take their work further than this book does, to talk about the ability to bound and divide as well as to govern that these instruments provide. Since the focus of the work, and especially its second half, is so explicitly on architectural design, these avenues remained unexplored in the book, but I look forward to both authors taking up these ideas in the future. For now, this is a handsome book, at a reasonable price, and those interested in instruments and architecture will certainly want a copy.