Many people assume that Vitruvius’s theory of architecture is rigidly prescriptive, and that architecture during the Renaissance followed a trajectory defined by an increasingly liberal attitude to strictly codified ancient canons. The following passage from the Ten Books on Architecture indicates that Vitruvius endorsed improvisation: “In fact, Hermogenes, once he had already acquired a supply of marble to complete a Doric temple, changed his mind and made this temple an Ionic shrine to Father Liber. He did not do this because the species and the type of Doric are unattractive, or because it lacks dignity of form, but because it is restrictive and inconvenient in working out the distribution of triglyphs and the spaces between them.”1

Examining Vitruvius’s ideas about optical correction further complicates the assumption. Vitruvius had recommended adjustments to correct the distortion of dimensions that occurred when buildings were viewed from different vantage points. Renaissance theorists had invoked optical correction to justify discrepancies between proportions stipulated by Vitruvius and archaeological evidence. Renaissance architects such as Leonardo da Vinci and Sebastiano Serlio, among others, attempted to quantify aspects of optical correction that had been ad hoc, ambiguous, or lost in Vitruvius’s own writings, leading to a controversy that culminated in Claude Perrault’s rejection of optical correction, the instrumentalization of proportion in the seventeenth century, and the diminishing importance of Vitruvian theory.


The fact that a marginal aspect of Vitruvius’ theory incited Perrault’s critique warrants examination, and can be explained in part by the intersection of architecture and science in Renaissance treatises, and the vulnerability of optics to scientific inquiry. Vitruvius’s description of optical refinements is contained in Books Three and Four of his Ten Books on Architecture as part of a general discussion of proportion, particularly as it relates to the design of sacred buildings. Vitruvian proportion had two components; one was a scientific or quasi-scientific theory of the physics of light and optics derived in part from Euclidian geometry, and the other was symbolic and derived from the human body. Renaissance translations of Vitruvius and independent architectural treatises tended to segregate these components and to valorize one over the other. Vitruvius’s origin narratives make explicit the connection between columns and the human body, although the relationship between the Doric and Ionian columns retained only their (geometric) proportional relationship. Thus, entasis, which means tension, straining, exertion and can refer to the human body, defines the shape of columns. Vitruvius uses it to describe the slight outward curvature in the silhouette of the Doric shaft.2 Leon Battista Alberti’s own narrative in On the Art of Building in Ten Books reduces origin narratives to a “shadowy but unmistakable presence,”3 whereas Cesare Cesariano restores them to prominence in his Italian translation of Ten Books on Architecture.4 The connection between figuration and columns recurs in Renaissance translations. Sebastiano Serlio combines rustic motifs with bound figures in his Extraordinary Book, but this section is appended to his Tutte l’opere d’architettura et prospectiva is appende, far from his treatment of geometry and optics.


Ingrid Rowland suggests that Vitruvius was aware of a tradition of scientific optics, which was both physical (the viscosity of air as optical disturbance) and geometric (vision as pyramidal or conic rays or vectors). He was aware of a debate as to whether vision is the result of the impact of images emitted by the object, or of visual rays shed from the eyes.5 This controversy informed the optical theories of such diverse figures as Leonardo da Vinci, Alberti, and Serlio in the Renaissance. Vitruvius’s aesthetic theory comprises three central elements: proportio, symmetria, and eurhythmia. In the broadest terms, proportion refers to the relationship of part to part and parts to whole. Optical refinements fall into the category of eurythmia, the application of proportional alterations to “correct” subjective distortions. Optical correction requires symmetry, or a system of symmetries, on the basis of which changes can be incorporated in response to contingencies. Contingent factors including the site, and blocking by crowding also warranted structural adjustments to symmetry. Symmetry is fractional and numeric, with ten (telion) the perfect number (the number of digits on both hands) on which all ratios are based.


Panofsky posits a disjunction between technical and objective measurements in the Greek theory of proportions.6 Classical theory also distinguishes between beauty and truth, perception and reason, and beauty and tectonics. Proportion is “organic” and anthropometric, based on the human body and its constituent parts. Proportions are serial and fractional: When, according to Galen, Polyclitus described the proper proportion of finger to finger, finger to hand, hand to forearm, foreman to arm and, finally, each single limb to the entire body, this means that the classical Greek theory of proportions had abandoned the idea of constructing the body on the basis of an absolute module, as though from small, equal building blocks: it sought to establish relations between the members, anatomically differentiated and distinct from each other, and the entire body. Proportion also refers to the visual, rather than tectonic, relationship between solids and voids in the disposition of architectural elements. Vitruvius establishes a series of norms that dictate the ratios between solids and voids in columns: “The larger the space between the columns, the greater the diameters of the shafts must be. For if an araeostyle temple had columns whose diameter were equal to one-ninth or one-tenth the height of the column, the building would seem flimsy and inconsequential, because all along the intercolumnal spaces the air itself seems to diminish the apparent thickness of the shafts.”7 Alberti paraphrases this passage, but includes a brief discussion of the structural consequences of column spacing.8 In other words, Vitruvius regards columns as both structure and ornament.


Vitruvian optical refinements include hypotrachelium contraction, entasis, stylobate curvature, column inclination, fluting adjustment, and surface inclination. Hyptrachelium contraction refers to the ratio between the diameters of the tops and bottoms of columns. Optical correction dictates adjustments according to the height of the columns: The neck contraction of the uppermost surface of the columns, it seems, must be made so that if the column measures up to fifteen feet, the diameter at the bottom should be divided into six parts and the diameter at the top should measure five of these parts. Again, if a column ranges from fifteen to twenty feet, the bottom of the shaft should be divided into six-and–one-half parts and the uppermost diameter of the column should measure five-and-one-half of these units, etc.9 Entasis refers to the swelling curvature within a column shaft, and was probably implemented by stretching a circle to form an ellipse. (A diagram that was originally appended to the scroll for Book Three has never been found.) Entasis, in Greek, means tension or bowing. Stylobate curvature refers to the “dressing down” of the stylobate relative to a level datum (Fig. 1). “The stylobate should be leveled so that in the middle it has an increment provided by the scamilli impares. For if it is constructed exactly on the level, it will appear somewhat hollowed to the eye.”10 A catenary curve reflects the curvature of the stylobate (the capitals are not set on levelbut according to a uniform unit, such that whatever addition was made to the stylobate repeats on the upper level). Vitruvius prescribes inclining all surfaces above the capitals by one-twelfth the height of the surface, and increasing the number of flutes in interior columns. “The corner columns, moreover, must be made thicker than the others by one-fiftieth of their diameter, because they are cut into by air on all sides and therefore seem more slender to the viewer. Thus where the eye deceives us, reasoning must compensate.”11 


These corrections were, according to Panofsky, applied only by “rule of thumb.”  "These adjustments to the diameter are added because of the extent of the distance for the ascending glance of our eyes. For our vision always pursues beauty, and if we do not humor its pleasure by the proportioning of such additions to the modules in order to compensate for what the eye has missed, then a building presents the viewer with an ungainly, graceless appearance."12


Although references to optical correction abound, the extent to which it was actually deployed in architectural practice is difficult to assess. Columns almost universally incorporated entasis. The contract that was drawn up between Michelangelo and the executors of the estate of Julius II stipulates the configuration and dimensions of forty carved figures: “Around said casket comes six pedestals, on which come six figures of the same size, all six seated; then, on the same level where these six figures are, above that face of the tomb which attaches to the wall, emerges a shrine which goes up about thirty-five palmi, in which go five figures larger than all the others, because they are farther from the eye.” The design for the Tomb for Julius II underwent a series of iterations that changed the number and dimensions of the sculptures, but optical correction was retained as an organizing principle.


On the other hand, evidence suggests that optical correction was largely a theoretical concern that was implemented only haphazardly. Alberti’s speculative project for a triumphal arch includes prescriptions for the size of statues: “The height of the statues set at the very highest level should be no less than one sixth and no more than that of the first set, positioned above the columns,”13 although it is not clear how the size of the statues relates to the overall scale of the building. The principles of optical refinements were reiterated in many Renaissance treatises. Although the geometric portion of the scientific aspect of optical correction was subjected to the rationalizing impulses that characterize the Italian Renaissance through quantification, the physical portion was accepted uncritically, for reasons that invite speculation.


Alberti’s On the Art of Building in Ten Books contains references to Vitruvius “system,” although he doesn’t address the topic in great detail. Alberti amplifies some of Vitruvius principles but omits others. He proposes increasing the number of flutes as an alternative corrective to increasing the thickness of corner columns. He also proposes spiral fluting as a strategy for increasing the apparent thickness of a column. “Of spiral fluting there are different kinds, but the less the line deviates from the vertical, the thicker the column appears.”14 Sebastiano Serlio discusses optical correction in Tutte l’opere d’architettura et prospectiva di Sebastiano Serlio. Serlio, paraphrasing Vitruvius, invokes the erosion caused by the density of air as objects recede from a viewer in two instances. He describes a method for assigning numeric values to the distortion of vertical dimensions (Fig.2): Then, at eye level–the eye should be the centre–he should draw the quarter part of a circle. Following that, at the place where he intends to put the elements to be made at eye level, he should draw a line on the wall at the said level, and from that line upwards draw the intended element the size that he wants all the others to appear. Then, from the top of that element he should draw a line to the centre of the eye and, where that line intersects the curved line, divide the circle into equivalent parts. He should then draw lines from the centre so that they pass through the circle and strike the said wall. These divisions on the wall will get larger and larger, such that at a distance they will appear the same size. 15


In his notebooks, Leonardo da Vinci describes a theory of perspectival proportion that involves the dissection of the projection of an object by a transparent plane (Fig.3): Perspective is nothing else than seeing a place (or objects) behind a plane of glass, quite transparent, on the surface of which the objects behind that glass are to drawn. The vertical plane is a perpendicular line, imagined as in front of the central point where the apex of the pyramids converge. And this plane bears the same relation to this point as a plane of glass would, through which you might see the various objects and draw them on it. And the objects thus drawn would be smaller than the originals, in proportion as the distance between the glass and the eye was smaller than that between the glass and the objects. 16 On the other hand, Leonardo includes a discussion of the effect of air on perception. Leonardo assigned numeric values to the dimensional distortions apparent in an object as its distance from a spectator increased.


Serlio derived much of his information about the related topic of perspective from Leonardo. Vitruvius attributes the diminution of objects the greater their distance from a viewer to the viscosity of the air that surrounds them. Air cuts into or erodes objects. This theme persists in Renaissance treatises. Alberti alludes to this phenomenon: “It is obvious, for example, that columns seem narrower in the open air than in an enclosed space.”17 George Hersey points out that everything we know about classical architecture comes from Vitruvius. Ancient authority played a vital role in Renaissance architecture and architectural theory. Choay ascribes Vitruvius’s central role in Renaissance architectural theory in part to the obscurity and ambiguity of his writing. Architectural treatises that combined text and illustrations were an innovation that had far-reaching consequences. A representative image is a woodcut that comes from Cesariano’s Italian translation of Vitruvius, for which no English translation exists, as far as I can tell (Fig.4). It shows Ionic architecture and a compendium of optical effects, and combines elements of linear perspective and orthographic projection. The spectator stands on the bottom edge of the picture plane. What appears at first glance as simple orthographic projection is complicated by the perspective treatment of the cornice, whose vanishing point terminates at the spectator’s eye. Surface inclination appears as the canted sculpted figure on the building’s roof. Entasis is indicated by the curved lines on the column shaft. Vaughn Hart has noted the similarity between illustrated Renaissance architectural and scientific treatises (Fig.5).


Their publication and translation from Latin into other languages and vernaculars, a consequence of developments in printing, stimulated the dissemination of humanist Renaissance ideals, but also exposed these ideals, which had been the cloistered province of the “literate” (those who knew Latin), to the light of day.18 They were the sites where the competing claims of ancient authority and historic precedent on the one hand and progressive scientific inquiry, which eventually took the form of Cartesian philosophy and the science of Galileo, on the other were played out. Perrault, who was after all a physician, published Ordonnance des Cinque Especes de Colonnes in this context.


1. Ingrid D. Rowland and Thomas Nobile Howe, Vitruvius, Ten books on Architecture, (Dover, Cambridge, New3 York, Melbourne,

Madrid, Cape Town; 1999) p. 57

2. George Hersey, The Lost Meaning of Classical Architecture, (The MIT Press Cambridge, Mass., London, 1988) p.58.

3. Alina Payne, The Architectural Treatise in the Italian Renaissance (Cambridge University Press, Cambridge, New York, Melbourne, 1999) p. 100.

4. Hersey, The Lost Meaning of Classical Architecture, (The MIT Press Cambridge, Mass., London 1988).

5. Rowland, p.229.

6. Erwin Panofsky, Meaning in the Visual Arts, (Doubleday, Garden City, N.Y.; 1955) p. 65.

7. Rowland, p. 50.

8. Leon Battista Alberti On the Art of Building in Ten Books, translated by Joseph Rykwert, Neil Leach, and Robert Tavernor, (MIT Press, Cambridge, Mass., London, 1988) p. 199.

9. Rowland, p. 50.

10. Ibid. p. 50

11. Leon Battista Alberti On the Art of Building in Ten Books, translated by Joseph Rykwert, Neil Leach, and Robert Tavernor, (MIT Press, Cambridge, Mass.,London, 1998) p. 217.

12. Vaughn Hart and Peter Hicks, Sebastiano Serlio on Architecture (Yale University Press, New Haven and London, 1996) p. 18.

13. Jean Paul Richter, The Notebooks of Leonardo da Vinci (Dover Publications, New York, 1970) p. 54.

14. Leon Battista Alberti On the Art of Building in Ten Books, translated by Joseph Rykwert, Neil Leach, and Robert Tavernor, (MIT Press, Cambridge, Mass.,

London, 1988) p. 215.

15.Hart and Hicks, p. 18.

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