On Measurement: A Survey of Florence

– Mojan Kavosh

The following text is an extract from a longer essay entitled ‘De re mensura: Surveying Practice in Quattrocento Painting’—which the author completed at the Warburg Institute in the autumn of 2025—looking at Renaissance perspective painting to consider how practices of surveying informed the development of perspective as an artistic and intellectual pursuit.

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It is helpful—and perhaps even requisite—to begin with the Latin De re Mensura, or On the Matter of Measurement in English, which refers to a genealogy of writings on painting that emerged in Italy between the fourteenth and fifteenth centuries. De Pictura (On Painting) by Leon Battista Alberti, published in 1435, marks a decisive point of departure of this genealogy, as painting in De Pictura is no longer conceived as a mere depiction of figures, but as the measured construction of the space in which those figures coexist. This concept endured well into the following century, finding renewed expression in works such as Piero della Francesca’s De Prospectiva Pingendi (On the Perspective of Painting) in the 1480s and Leonardo da Vinci’s Trattato della Pittura (A Treatise on Painting) in the 1540s. Alberti’s work in De Pictura seems to gather a fragmented practice of painting into a kind of coherence. We could argue that Quattrocento painting, which captures natural perspective on a flat surface, reached its height in the alliance between practice and theory, particularly evident with the emergence of De Prospettiva Pingendi. For the first time, with della Francesca’s work, the skilled craftsman and the mathematician were seen together as one.

It is well known that perspective first appeared in Florence with Filippo Brunelleschi, the mathematically gifted goldsmith, who, by some flash of divine inspiration, contrived to make art measurable. The story, of course, is far more terrestrial. As Marvin Trachtenberg argues, the culture of measurement never quite vanished after Antiquity, but lingered, quietly persistent even amidst the Florentine Trecento. What appears to us today as a picturesque confusion of medieval streets is in fact a geometric and cunning urban proposition. The piazza della Signoria, for instance, was orchestrated to frame precise alignments toward the Palazzo Vecchio, most notably from the oblique forty-five-degree approach of Via dei Calzaiuoli. Likewise, the eastward vista to the Baptistry of San Giovanni was not the happy accident of an unplanned city, but a deliberated composition—a measured choreography of movement and sight. Trachtenberg’s observations render the underlying order and scenographic intelligence that preceded the vision of Brunelleschi.[1] 

It was from within this culture of alignment and calibration that Brunelleschi emerged, a figure whose reticence in writing seems only to have magnified his legacy. His contemporaries revered him less for what he said—for he said nothing—than for what he built and for what he drew. Two perspective panels, now lost, are attributed to him: one showing the Baptistry as seen from the doors of Santa Maria del Fiore, and the other, the Palazzo as viewed from the edge of the Piazza della Signora. As Trachtenberg describes it, Brunelleschi’s subjects could not have been incidental. Both views staged the very act of looking at what the city itself appears to have been designed to solicit. In various accounts, we are told that Brunelleschi measured his subjects from his position, translating his observations into a network of ruled lines converging toward a fixed eye-point.[2] These panels, if they ever existed, were not imitative pictures, but heuristic experiments through which the act of seeing was made measurable. In them, geometry did not describe vision but rather produced it.

De Pictura came a generation later, transposing those empirical experiments into the decorous order of a treatise where Alberti instructed the painter to imagine a transparent grid stretched like a window between the eye and the world, and upon which rays of vision are inscribed in squares and orderly diminution. John Spencer, who translated Alberti’s De Pictura, remarked in 1966 that Alberti’s method was ‘the measuring of plane geometry based on the practice of surveying’.[3] We could say that perspective in Florence was not discovered but deduced, born not from an artistic epiphany, but from the habit of tracing things back to their scale. If De re Mensura was an inquiry into how the practice of surveying came to serve as the common language of painters in the early Renaissance, this text turns to my own drawing process as a means of re-enacting the language of when drawing first consented to be measured.

It was with this measured city in mind—Florence built much upon sight-lines—that I began to draw my own series. My concern turns from text to drawing, not as a way of reconstructing Brunelleschi’s experiments nor replicating Alberti’s methods or demonstrating Piero’s proofs, but as a way of locating the ground from which to navigate between all three; to perform, for myself, the connection between their works and their relation to surveying. The drawings that follow were developed as part of this inquiry. They are not reconstructions, but studies—a sequence through which surveying is revisited as a form of thought. Between the Baptistery of San Giovanni and the Palazzo Vecchio, there runs an invisible alignment, an urban theorem of sorts, that seems to have invited much experiment. The first drawing sets out this relation with dutiful restraint. Both buildings are placed in plan, measured and drawn true to their scale, their positions held in dialogue across the grid as the governing scheme of scale. The grid, in its impartiality, demonstrates that measurement controls more than narrative can persuade.

I begin by taking Piazza della Repubblica as the centre of Florence, not for its geographic centrality but for its notional one.[4] The area dates back to the forum of the Roman city of Florentia, which over time gave way to the main market of the city, Mercato Vecchio. Florence of the Duecento to Quattrocento was governed by a negotiated exchange between the sacred, the mercantile and the domestic; Piazza del Mercato Vecchio was characterised by a dense warren of streets converging around the Colonna  dell’Abbondanza (Column of Abundance), surrounded by stalls and buildings.[5] Interestingly, the site also marks the point at which the city’s historical continuity perceptibly changed. In the Ottocento, the medieval spatial order of the market was replaced by an orthogonal piazza. This transformation invites a critical interpretation of the grid and its subsequent imposition upon the pre-existing urban fabric. Did the Risorgimento miss the point, or did it, too, regard the medieval era as an age of darkness?[6]

The second drawing, emboldened by the first, permits a small act of intervention: one that comes from my earlier work on surveying Rome and its monuments.[7] The foreground is enlarged, not to deceive the eye, but to test its obedience. This simple inflation has the effect of bringing the buildings perceptibly closer, as though coaxed into conversation, while accurately maintaining their centre points in relation to the centre point of the city. Measure can be quite accommodating when persuaded by mathematics. The two buildings appear to pivot beside one another in orthogonal plan view, allowing a complete survey of plan, elevation and even section, when required, to be recorded through a planimetric view from below. The effect is of one looking upward through the plan, with only the y-axis activated while x-axis remains fixed at zero.

By the third drawing, the grid operates less as an interlocutor and more as a background. The drawing recalls that Brunelleschi’s method depended on establishing an exact position for the viewer in relation to the subject. In both cases, the Trecento vision is recorded as a fixed alignment between observer, subject and plane.

The fourth drawing extends this inquiry into the logic of perspective itself. In linear perspective, the ground projects into depth as a field of invisible tiles—the vanishing point fixes the horizon and, together with the viewer’s distance, compresses the grid so that equal modules appear progressively smaller. This perspectival ground becomes a new measurable grid, a terrain upon which calculated space can be narrated through the rhythm of its intervals.

To set this drawing series against today’s widespread computer-generated images may seem almost perverse in its insistence on the analogue. Yet it is precisely this distance from automation that lends drawing its critical urgency. The computer, for all its precision, has rendered measurement a process too easily executed to be truly understood. To draw by hand today is therefore not an act of resistance, but of recovery. The drawings gathered here are less demonstrations of skill than exercises in attention: an attempt to restore the intervals between eye, mind and scale that define the making of space. If Brunelleschi, Alberti, della Francesca and da Vinci sought to reconcile vision with geometry, then the task that follows today is to reconcile geometry with perception once again, to re-establish drawing as a mode of thought rather than a means of production. In this sense, the grid of the surveyor and their practice remains our most radical instrument: a skill at once ancient, still questioning how one sees through measure.

Notes

Mojan Kavosh is a London-based architect whose work explores the intersection of architecture and art through the practice of surveying and the form of measured drawing. Her research uses both drawing and writing to examine the loss of historical and geometrical knowledge in architectural representation with the advent of computer modelling.