Compass and Rule: Architecture as Mathematical Practice in England 1500–1750 (review)

Anthony Gerbino and Stephen Johnston’s Compass and Rule is a handsome, intellectually ambitious catalog of a 2009–10 exhibition of English technical drawings and geometric instruments at the Museum of the History of Science, Oxford, and the Yale Center for British Art. Gordon Higgott contributes an essay on “Geometry and Structure in the Dome of St. Paul’s Cathedral.” The catalog’s objective was to embed Christopher Wren’s architectural practice at Saint Paul’s, London, in a broad historical context. It offers a richly interwoven illustrated material history of multiple geometrically grounded disciplines.

Equating architecture and geometry, and seeing Euclid as the master mason, were Gothic commonplaces. Gothic masonic geometry, however, was a practical, not theoretical, enterprise. In the fifteenth century a rigorous Euclidean discipline began to penetrate builders’ lodges, first in Italy and Spain, then in France. At the same time, Renaissance architects aspiring to humanist status elevated design based on archaeological and theoretical investigations above practice. England embraced these transformations relatively late, beginning in the mid-sixteenth century. This volume offers the first accessible overview of English rather than continental European developments in geometrical design technologies, assimilating British literature on extant drawings and catalogs of drafting and surveying equipment.

Gerbino and Johnston begin with a survey of scarce extant English medieval architectural, surveyor, and cartographer drawings. Juxtaposing architectural, legal, and topographic drawings reinforces their common scaling and geometrical imprecision, presuming viewers who understood context and details. In the 1540s, under Henry VIII, urgent military works ushered in greater precision in English technical drawings, especially those of Richard Lee and John Rogers, master masons and military engineers. Although geometric sophistication spread earlier throughout Europe, our authors dismiss any direct influence of Italian or French engineers on these Englishmen. A 1545 plan of Portsmouth, here tentatively attributed to Lee, is the earliest accurately surveyed plan of an English town. Books advanced this program: an Elizabethan practical mathematics text aimed at tradesmen, Leonard Digges’s Tectonicon (1556), lambasted inexact calculation methods, recommending precise standardized rules and instruments made by specialists such as Thomas Gemini or, later, Humfrey Cole.

Inigo Jones inaugurated seventeenth-century English Renaissance practice based on learned texts—Vitruvius, Serlio, Palladio, Vignola—requiring command of the proportional ratios of the five Roman orders. Such study suited aristocratic amateurs better than Elizabethan master tradesmen, whose new literacy already had raised their status as high as post-medieval society would allow. Our authors, following a study by Alexander Marr of an alabaster model donated to the Bodleian Library in 1620 by Clement Edmonds depicting together the five Platonic solids and the five orders, postulate a deepening contemporary linkage of architecture and geometric theory. Their argument, unfortunately confusing icosahedra, tetrahedra, and octahedra, remains tentative.

Two chapters on Christopher Wren suggest connections between his scientific and architectural careers and report recent discoveries at his Trinity Library, Cambridge, including inverted foundation arches distributing concentrated loads on alluvial soil and tensile rods transferring bookshelf loads to walls. In addition, Gerbino, Johnston, and Higgott all examine a Wren drawing that employed Robert Hooke’s cubic power parabola to determine an interim profile (ultimately rejected) for the structural inner dome of Saint Paul’s. An intensely layered plan by Nicholas Hawksmoor and an unidentified draftsman that explores the crossing and drum of Saint Paul’s exemplifies Wren’s delegation of responsibilities. These drawings could have been profitably compared with Late Gothic tower plans of the Stephansdom in Vienna.

Chapters 7 and 8 recount the invention of highly specialized geometric architectural tools. Gunter sectors, also known as joint rules, first served as surveying calculators and then evolved into nightmarish instruments for drawing the five orders, using Palladio’s, Vignola’s, Scamozzi’s, or William Halfpenny’s competing proportions. Splendid eighteenth-century sectors and other scientific and drafting instruments by Thomas Heath and George Adams were luxury goods, appealing to royal and aristocratic clienteles in George III’s reign. Professional...