Quite beyond the solemn reality brought to bear on the central mystery of the Christian faith, Masaccio’s Holy Trinity fresco has played a pivotal role in the history of art as both a definitive example of earty Renaissance linear perspective and as a kind of prophetic forerunner of the perspective method discussed neartye decade later by Leon 8attista Alberti1 While Alberti’s Della Pitture of 1435 may be the first written docu ment to articulate a new humanist ideal of pamting in which visual appearances are controlled by geometric principles em bedded in nature, Masaccio’s fresco of the Trinity is the first extant painting fully informed by that ideal.2 The magnificent vault arching over the austere figures in Masaccio’s fresco of the mid-1420s is an utterly convincing illusion of archi tectural form oxtendmg into space, and for centuries it has boon justly celebrated on that account.
Yet it is not an historical ex emplar devoid of uncertainties. It has been difficult, for Instance, to determine exactly where the figures of the Virgin and St. John stand with respect to the projected ground plane, and ascertaining the position of God the Father’s feet has proved a particularly mystifying problem. So far as the perspective con struction itself is concerned, there is little agreement among scholars about either the vertical position of the projected cen tnc point on the wall or the distance of the viewer from the painting1 These are important issues for ad historians to resolve, and much time has been spent in considering them within the con text of the Renaissance awakening. Yet having succumbed to the fascinating pursuit of Albertian consistencies, are we really any closer to understanding the method and conceptual frame work of Masaccio’s perspective scheme except in the limiting terms proposed by AJberti? Was Masaccio simply unable to master the difficultdisotto m su projection that would have suc cessfully foreshortened the awe inspiring figures in the fore ground of his fresco? Is it because the fresco has been moved several times that we are unable to decode Masaccio’s perspec tive projection?
Or the stringently rational context of Alberti’s Delia Pttura really appropriate for understanding a painting cre ated in Ftorenco during the 1420s, when one might still expect to find a fluid dialogue between reason and faith in an image of the Corpus Dommi executed for the conservative Dominican church of Santa Maria Novella? Certainly Joseph fblzer’s detailed photographs of the points and lines embedded in the fresh plaster provide strong evidence that the illusionistic impact of the vault depended on many drf ferent artiste techniques.’ It needs now to be said that this di versity of techniques Includes orthographic, conical, and stereo graphic methods made familiar to late Medieval painters through instructive working drawings of architects and instrument mak ers as much as through practical geometry texts that had gov erned the artist’s early education.* If the very complexity of the Trinity fresco vault projection has long encouraged art histori ans to conjecture Filippo Brunelleschi’s involvement in its plan ning, the diversity of the projection techniques discovered there would seem all the more to confirm the architects participation in the complex project.
Perhaps more importantly, as Poker has shown, that diversity of means is competingly unified both pictorially and theoretically at the level of mathematics and mea surement. The imaginatrve sweep of Masaccio’s accomplish ment is not to be found solely in the precise ordering of lines and planes, however, for ho (or more likefy Brunelleschi) dis carded earlier and more tentative experiments in favor of a ra tionally consistent method of structuring his own arching sepul chral vault which drew on and mirrored the mathematically defined coordinates of the vault of the heavens. It is the aim of the following essay to show that the one pre existing graphic tradition of great authority for projecting these mathematically regulated and symbolically charged spatial co ordinates was the tradition of medieval astronomical diagrams. This tradition was not only useful in practical detail, but it was also intrinsically suggestive to early perspectives, and prob ably determinative with respect to the special viewing circum stances presented by the Trinity. Not only did this graphic tradi tion take into account the position of tho viewer looking intcntty upward; its most familiar projections were ordered according to the exemplary symmetries of a divinely created cosmos. The orthographic and stereographic protections of medieval astrono mers and the common ground they shared with mathematical diagrams provided a readily availaNe source to Masaccio and Brunelleschi of a full range of necessary diagramming techniques at the same time that they affirmed the mathematical order be lieved to control all of nature.
To draw on such a tradition was not only an act of great practical consequence for painters; it was an affirmation of great conceptual force. Masaccio planned the entire structure of the Trinity fresco in a most deliberate and mathematical way. As Joseph Poker has shown, he controlled the composition through the rational forces of measurement and geometry by initially dividing the principal pictorial held into three squares averaging approximatety 211 cm wide and 207 cm high, the skewing from perfect squares being accounted for by the moving of the fresco or by the diffi culty of maintaining constant pressure on ropes when snapping lines or deserting arcs over a considerable distance .* The bottom two squares are made to come out right within the rectangular field of the composition by overlapping them from the base of the ledge on which the donors kneel to the edge of the painted chapel floor. Finaly, the top square is inscribed with the illusionishcaliy recoding semi circular nbs of the bonel vault. Whet distinguished Masaccio’s squares and circles from those commonfy used by medieval predecessors and set paint ing on a new path was his insistence that the surface divisions be Inked to the projection establishing the apparent recession of a barrel vault .
As Poler has pointed out. the bond between surface geometry and the ilusion of recession was ac complished by having the base line of the top square delimit the springing of the barrel vault in the distance and by further subdi vision of the top square at its midline marking the spnnging of the barrel vault in the extreme foreground.’4 From a further study of the vault it becomes clear that Masaccio, despite the per ceived regularity of the apparent recession, deliberately adjusted the standard (that «s, Aberttan) components of a Renaissance perspective construction to achieve maximum visual appeal as well as to assert the power of the surface grid.” The eye level and the horizon line, for instance, coincide with the base of the middle square, and the ‘viewer’s eye” lor centric point of the projection) is located at the base of the central axis of the com position. Moreover, Masaccio insisted on the formal control of the basic square module by calculating a ‘viewing distance’ equal to the length of the side of e square.
Thus the “viewer” in Masaccio’s perspective scheme was fully integrated into the overall surface geometry of the composition, and the hypotheti cal person stationed in front of tho painting with ono oyo closed was. in fact, reduced to a potent mathematical entity While Professor Poler has shown that the precise confluence of circle, square, and projection of the vault in depth restricts the perspective projection to the basic square module, I hope to show that the artist’s surface geometry was joined in both a practical and symbolically provocative way to a rigorous, mathematical interpretation of how points, lines, and planes behave in the ideal worlds of Euclidean geometry and medieval mathematical astronomy. The development of Renais sance perspective will be seen to be dependent as much on knowledge of a long mathematical past and on placing under heavy subscription the ancient and medieval tradition of math ematical graphics as on any recently enhanced acuity. Masaccio’s combination of squares, double squares, circles, and semi circles frankly invokes the traditional values ascribed to these presumably perfect forms in medieval as well as Re naissance aesthetics and theology. As Rona Goffen has argued, ‘It seems likely that Masaccio’s architecture is intended as a mathematical expression of God’s perfection and harmony, wor thy of the ’real tabernacle’ of the Lord…’ Perhaps more appro pnate tor the growing secular testes of the Renaissance, this overlapping combination of squares and circles also alludes to the almost irresistible Vitrwian symbol of a man contained in the circle and ihe square and thus to the assumed affinity be tween m«rocosm and macrocosm.
The rhetorical intent of Masaccio’s geometry is further suggested by the location of the incised centric point denoting the height of the “viewer.” at al most 3 breccia above the church floor, a measure which carries with it the same connotations of the ideal as the circles and squares ol the surface geometry.M While Alberti would main tain that this was the height of the average viewer, giving it a seemingly practical sanction, it fits neatly into the Vitruvian scheme of ideal human proportions In addition, it is a com- monly known symbolic height in late medieval guide books to Jerusalem, where 3 breccia is proclaimed to be the height of the perfect man. Christ.Despite the fact that the location of the centric point coincides with e reasonable viewing height, its place ment confirms Masaccio’s attention to non-physical and non visual considerations associated with the time honored symbolic power of numbers as well as the purity of mathematical relation ships and analogues.
That one should find such doubly potent symbols of perfection in an image of the Tnnity in Santa Maria Novella is keeping with the central role played by the Corpus Domim in the sacerdotal life of this conservative Dominican Church.’ M Masaccio’s fresco was adventurous, even radical, in its aggressive imitation of a powerful, physically present nature, the inteiectuel context of his grid and projection systems, as well as the newly rationalized aesthetic on which they depended, remained firmly linked to a traditional and highly suggestive re ligious interpretation of natural order in which mathematics func tions as a bridge between concrete, sensible reality and univer sal or divine truth.17 Quite beyond shape end measure conveying meaning in an obvious and frankly didactic way. the points, lines, and pianos which make sense to many as surface geometry, medieval math ematicians would have understood within the broader context of a mathematical graphics tradition intent on explaining another kind of absolute perfection, the continually changing relation ships among the coordinate systems of a vast and earth-cen tered universe as those systems were projected onto a plane surface. These projections were a part of an unbroken tradition of mathematical diagramming techniques dating back at least to the 4th century B.C.
The many different diagrams bound by this tradition were found in widely circulated copies of ancient texts by Euclid. Archimedes, and Ptolemy, medieval commentaries by Messahala. Jordanus de Nemore. and Campanus of Novara, as well es in the practical geometry tracts that formed the foun dation of an artist’s education in the Florentineabbaco schools.The precision with which some of the still visible construction lines wore scratched into the wet surface of the Trinity offers some proof that Masaccio (or more likely Brunelleschi) was not only familiar with this graphic tradition but even painstakingly followed its rules Not merely the result of convenience, the compositional grid of the Trinity is ihe product of a highly conflated application of different lines of mathematical reasoning to a spatial problem whose main features derive directly from the astronomical con ventions of the day. First of ail. Masaccio’s apparent use of a centric point to designate the projection of a ray (in this case, the principal line of sightl onto the plane of projection, together with the right angle relationship of ray to plane were not only defined by Alberti in 1435 but were typical aspects of medieval astro nomical projections.50 Also, certain lines, generally regarded as mero surface marks by art historians, would have been inter preted by mathematicians and anyone familiar with the astrolabe . the most popular astronomical siting device of the late Middle Ages, as projections of planes perpendicular to the plane of representation.