PART I

The phrase artes liberales and its synonyms make their first appearances in the writings of Marcus Tullius Cicero, Rome’s greatest statesman and orator, and in the works of Vitruvius and Seneca, who follow and build on Cicero’s writings on education. It is surprising to juxtapose the bloody and gruesome violence that destroyed the Roman Republic and Cicero’s descriptions of the beautiful unity and order of nature that he wants his new liberal arts education to emulate. I believe that the liberal arts tradition began in Cicero’s attempt to formulate an educational ideal for young Roman leaders that would use the self-transcendence of Greek philosophical speculation, exemplified in the contemplation of the starry sky, to renew the civic virtue of traditional Roman mos maiorum, the customs of the ancestors, which was based upon another kind of self-transcendence, an ethic of public service and non-violent competition among aristocrats for public office. For Cicero, the affirmation that symmetry, proportion and harmony—beauty, in short—exists in the cosmos establishes the hope that it can exist also in human society, where justice is understood as harmony between social orders, arising from a kind of symmetry between human beings.¹ If beauty is symmetry, and symmetry is the essence of nature, then violence is unnatural.
 
Beauty is thus a forgotten but recoverable ideal of the liberal arts tradition. For Cicero and Seneca, the cosmos of beauty trumps the chaos of violence, whether caused by civil war or cruel emperors. But it is Vitruvius, an architect, not a statesman, who offers the most focused discussion of the nature of beauty and of its relationship to liberal arts education. Let us look at Vitruvius’ conception of beauty, and then use Raphael’s Stanza della Segnatura to help us understand it more fully.
 
After dedicating his treatise De Architectura to Augustus, Vitruvius turns not to architecture, but to the education of the architect:

The architect’s knowledge (scientia) is equipped (ornata) with many disciplines (disciplinae) and various forms of learning (eruditiones), and all the works achieved (perficiuntur) by the other arts (artes) are demonstrated (probantur) according to its judgment. (1.1.1)

What are these “many disciplines”? Vitruvius says that the architect needs to be naturally talented (ingeniosus) and easily taught (docile), so that he can “be liberally educated in letters and writing (litteratus); be an experienced draughtsman (peritus graphidos); be accomplished in geometry (eruditus geometria); know many histories (historiae); have listened carefully to philosophers; understand music; not be ignorant of medicine; know the responses (response) of jurists; and have a grasp of astronomy (astrologia) and the ways (rationes) of the heavens.” (1.1.4)
 
Here is Vitruvius’ explanation of how the architect can learn and hold in his memory all of these disparate subjects:

But perhaps it will seem astonishing to inexperienced persons that [human] nature can learn thoroughly such a great number of subjects (disciplinae) and keep them in its memory.When however they notice that all the disciplines have amongst themselves a union and community of things (coniunctio rerum et communicatio)² they may easily believe that it can happen. For a well-rounded education (encyclios disciplina) is like a single body (corpus unum) composed of its members (membra). Therefore those who are instructed from an early age in various areas of learning (eruditiones) recognize the same characters (notae [Lewis and Short B.1 and OLD 6. a]) in all writings (litterae) and the common ground (communicatio) of all the disciplines, and for this reason learn (cognoscere) all things more easily. (1.1.12)

Vitruvius’ phrase “a union and community of things” (coniunctio rerum et communicatio) could be a gloss on Crassus’ assertion in Cicero’s treatise On the Ideal Orator, the De Oratore, that “all things, above and below us, are one” (omnia haec, quae supra et supter, unum esse [3.20] ). The operative word here is res, “things”: the belief, common to Graeco-Roman antiquity, that there is an objective order in the universe, and that this order is the harmonious unity of all beings, i.e., all “things.” We humans do not create this unity in our minds; we discover it in nature, and become one with it when we contemplate it. What is new, vis-à-vis Cicero’s defense of broad learning, is the simile Vitruvius employs to assert the coherence of the architect’s broad knowledge: a well-rounded education is like a single body composed of its members.
 
As is clear from other passages in De Architectura, Vitruvius means the human body. The remarkable theory presented in De Architectura is its famous assertion that “. . . without symmetry and proportion no temple can have a rational principle of composition, unless, that is, it have the exact principle (ratio) of proportion of the members of a finely shaped human being (homo bene figuratus).” (3.1.1) Vitruvius makes this claim in Book Three of De Architectura, dedicated to the design of temples. Chapter One of Book Three begins with these words:

The composition of temples (compositio aedium) depends upon symmetry (symmetria), the principles of which architects must diligently master. It is produced by proportion (proportio), which in Greek is called analogia. Proportion is the common adaptation (commodalutio) to a standard unit of measurement (rata pars, literally “fixed part” [OLD]) to the elements (membra) of each work and to the whole, by which the principle (ratio) of symmetries is achieved. (3.1.1) This is the proportion that is to be found in the “proportion of the members of a finely shaped human being” (homo bene figuratus). (3.1.1)

He continues with a description of the proportions between parts of the body: “For nature composed the human body in such a way that the face from the chin to the top of the forehead and the lowest roots of the hair is a tenth part; also the palm of the hand from the wrist to the end of the middle finger is as much . . . .” He goes on, listing other parts of the body. Then he concludes with these words: “The other limbs too have their commensurate proportions, which ancient painters and sculptors used in order to attain great and unending praise.” (3.1.2)
 
But it is not just numerical proportions that Vitruvius finds in a finely shaped human body. He also finds perfect geometry. After describing modular symmetries, he goes on to give the most famous description in his treatise, a description that has come to be known as “Vitruvian man”:

Similarly, in fact, the elements of sacred temples must have a most fitting symmetrical correspondence to the work as a total whole made up of its single parts. Likewise the center and midpoint of the body is naturally the navel. For if a man is placed on his back with his hands and feet spread out and the center of a compass placed at his navel and tracing a circumference, his fingers and toes will be touched by the line. In the same way as the figure of a circumference is formed in the body, so too will a design of a square be found in it. For if we measure from the soles of the feet to the top of the head, and if this measurement is referred to the outstretched hands, this width will be found to be the same as the height, just like areas that have been squared by a square. Therefore if nature so composed the human body that its members in their proportions correspond to its total form, then the ancients seemed right in deciding that in the execution of their works these works have a perfection of symmetry of individual members in relation to the appearance of the work as whole. (3.1.3)

This description would achieve its apogee in the Renaissance, and especially in Leonardo da Vinci’s famous drawing of this man, now seen daily by millions of people on the Italian one-euro coin. In her recent study of Vitruvius’ use of the metaphor of the human body, Indra McEwen points out that Leonardo’s and similar drawings of Vitruvian man are not the man Vitruvius describes in words. Leonardo’s man is free-standing and fully rounded; on the Italian one-euro coin, it is even embossed. But Vitruvius’ man is not standing at all; he is lying on his back. He is only a two-dimensional geometrical template—which seems to be Vitruvius’ point. The man is passive. We measure him, and in so doing we discover that on him can be inscribed a circle and a square.³ The unity of this man’s body and its members is thus not an organic, but rather a mathematical and geometrical one. As such, it links the body to something outside of itself: the cosmos. As McEwen explains in some detail, the circle and the square, along with the “perfect” number ten (a man’s fingers and toes) and the number four (the square, the four elements of the spherical body of the Stoic universe, as well as the tetractys, ten pebbles arranged in rows of one, two, three and four to form a triangle), are specific geometrical figures and numbers Vitruvius borrows from Pythagoras, Plato, the Stoics and even the Etruscan augurs.⁴ These ancient philosophers and priests envisioned mathematics and geometry as keys to unlocking the mysteries of the universe, and as the means whereby human beings could become united to it, and establish a proper relationship with the gods. As McEwen shows, in calculating the proportions of a well-formed man, and in describing how a circle and a square can be traced on his supine body, Vitruvius is thus writing a metaphysical argument for the “truth” of symmetry. These perfect numbers and geometric forms are not opinions in our minds; we discover them in the human body itself—and if in the human body, then in nature. As Vitruvius puts it, “nature so composed the human body that its members in their proportions correspond to its total form . . . .” Nature’s truth is the beauty of symmetry.
 
It is fascinating to speculate that, while Vitruvius may have derived his belief in broad, all-encompassing learning both from his own broad education, and from Cicero’s writings on the ideal orator, to which he explicitly refers,⁵ it was in the guise of an architect designing a temple that he grasped the ultimate unity and coherence of broad learning. Vitruvius calls architecture a temple. Speaking of the art of architecture as a whole, he says:

Since therefore, this great discipline (disciplina) is adorned and fully supplied with many and different kinds of instruction (eruditio), I do not think persons can suddenly declare themselves architects unless they are those who, ascending the steps of these disciplines from boyhood (ab aetate puerili), have arrived nourished by the knowledge of very many writings (litterae) and arts (artes) at the lofty temple (summum templum) of architecture.

For the commentator of the most recent French edition of De Architectura, this image evokes the sacred and solemn movement of ascending the steps of a temple.⁶ In the context of Vitruvius’ discussion of the design of temples, however, to say that the architect’s “well-rounded education (encyclios disciplina) is like a single body (corpus unum) composed of its members (membra)” (1.1.12), and that this single body of knowledge is a “lofty temple” (1.1.11), is to invite us to transfer to the architect’s education exactly what Vitruvius says about the human body as a template for the design of temples: “its members in their proportions correspond to its total form” (3.1.3), which is Vitruvius’ definition of symmetry. Belief in this symmetry is the ground for Vitruvius’ belief in the objective unity of all areas of learning.
 
But what exactly, for Vitruvius, is the beauty of symmetry? Where is it to be found? Is symmetry located in the mind’s grasp of mathematical harmonies, or in the eye’s perception of pleasing forms? We can answer this question best by following two intersecting lines of thought in Vitruvius’ effort to explain the exact nature of modular symmetry.
 
Vitruvius says that symmetry is commodulatio or commensurability (3.1.1), which makes symmetry a quantity that can be measured mathematically by a common unit. But there’s more to symmetry than numerical quantities. Insofar as the symmetry the architect creates must be seen, symmetry is also a quality, which Vitruvius names eurhythmia. He defines eurhythmia as the “graceful appearance (venusta species) and agreeable aspect (commudus aspectus) in the composition of the members.” He goes on to say that eurhythmia occurs when there is agreement or harmony (convenientia) between the height, breadth and length of a work’s members “and when all things respond (respondent) to the total symmetry (symmetria) of the work.” (1.2.3) In the definition of symmetria that immediately follows his definition of eurhythmy, Vitruvius says that “[j]ust as in the human body the symmetrical quality (qualitas) of eurhythmy comes from the elbow, the foot, the palm, the finger, and other small parts, the same happens in bringing to completion (perfectio) works [of architecture].” (1.2.4) The perception of beauty is thus both intellectual and sensory; it comes from the combination of actual quantitative “modular” symmetry and the appearance of such symmetry to the human eye. In fact, to achieve the appearance of symmetry, the architect will sometimes have to depart from the quantities required for perfect mathematical symmetries. Vitruvius says that the corner columns of a temple must be one-fiftieth thicker in their diameters than the other columns because corner columns “are cut all around by the air and seem more slender to viewers.” (3.3.11) He accounts for this and other adjustments to the diameters of columns by evoking a sensory need for beauty. “Our vision,” he says, “always pursues beauty (venustas), and if we do not flatter its pleasure (voluptas) with proportion and the addition of modules (modulorum adiectiones), in order to compensate for the eye’s error, a clumsy and unattractive (invenustus) appearance will be produced for its viewers.” (3.3.13)
 
The particular word Vitruvius uses for beauty is venustas. It is a word well adapted to convey the concept of the appearance of symmetry. “Charm and grace of appearance” would be one way to translate it.⁷ The signal importance of venustas appears in Vitruvius’ famous assertion that architecture’s constructions must have three characteristics: solidity (firmitas), utility (utilitas) and beauty (venustas). (1.3.2) In his study of the words the Greeks and the Romans used in speaking about art, J. J. Pollitt observes that ancient art criticism tended to use the word pulchritudo to suggest a transcendental or ideal Platonic beauty, whereas venustas refers more to the beauty one experiences through sense perception. Vitruvius does not use the word pulchritudo at all.⁸
 
Vitruvius’ understanding that through number architecture is linked to the universe amounts to the metaphysical affirmation that being is order, not disorder. The human intellect seeks such order—but, so too, does the human eye. Vitruvius’ understanding of beauty as venustas, which as an “appearance” must arise out of the interplay of “perfect” mathematical proportions and slight variations of these proportions, as in the case of the columns of a temple cited above, amounts to a Roman’s synthesis of Greek philosophy and Greek art. In anchoring his understanding of beauty in the concept of modular symmetries, symmetries based upon precise units of measurement, Vitruvius links the art of architecture to the powerful tradition of ancient thought, beginning with Pythagoras and exemplified in the writings of Plato, that being is number, and that the truth is most closely approached through mathematics and geometry. Plato argues in the Republic that the true motions of the heavens are to be found in true numbers and in true geometric forms, which are grasped by reason and thought, not by sight. The motions astronomers observe are connected to bodies and are visible; it is thus impossible to believe they are always the same and never deviate.⁹ In the Sophist, Plato points out that, in very large statues and paintings, we do not see true proportions; otherwise the upper parts would seem smaller. He then asks if, in order to produce the illusion of beauty, “craftsmen say goodbye to truth and produce in their images the proportions that seem to be beautiful instead of the real ones?” ¹⁰
 
Vitruvius’ De Architectura embodies a creative tension between unchanging number and changeable matter. As a practicing architect, Vitruvius knows that art cannot be “Platonic” because all art, even music, is perceived by the body as well as the mind. Vitruvius can thus speak of numbers as ontological entities and, at the same time, argue that that “our vision always pursues beauty (venustas)” and that we must “flatter its pleasure (voluptas) with proportion and the addition of modules.” (3.3.13)
 
What is truly fascinating about Vitruvius’ discussion of beauty, however, is not just his recognition of the role the human eye plays in the perception of symmetry, but in his discovery of beauty’s underlying symmetries in matter, and specifically in the human body itself. The centrality Vitruvius gives to the human body in his treatise on architecture is remarkable. He has reappropriated and applied to architecture the pre-Platonic tradition of classical Greek sculpture, which visualized Homer’s image of a world made radiant by the presence of the gods.¹¹ In fact, he likely derived his ideas about the symmetry of a well-formed man from the famous Canon of the Greek sculptor Polyclitus, probably written during the third quarter of the fifth century B.C. Vitruvius thus blends actual Greek artistic practice with Pythagorean and Platonic philosophical speculation to present an understanding of beauty as an objective order in nature in two complementary ways: as capable of being described and created mathematically; and as capable of being discovered by the human eye in the proportions of a well-formed human body.
 
These two perspectives on beauty have been and continue to be the perennial ways in which Western culture does its thinking about beauty: beauty as transcendent, supersensory truth, and beauty as pleasurable form perceived by the senses. These two perspectives are often associated with the schools of Plato and Aristotle.¹²
 
Philosophy is concerned with the nature of being. Early Greek philosophers struggled with the problem of change, or, as they put, with the difference between becoming and being. If what exists is constantly changing, then we can never know anything, because there are no identifiable things to know, just continual flux and metamorphosis. But if what exists is pure being, how can we account for the changes we experience in ourselves and the world around us? Plato’s response to this dilemma was to posit that true being exists in a supersensible harmonious realm of unchanging Ideas or Forms, which are only imperfectly reflected in the constantly changing world of matter. Human beings can get some inkling of these Ideas by pondering the unchanging symmetries of numerical ratios and geometric forms: they are always the same whenever and wherever they occur. In his love of numbers, Vitruvius is very much a Platonist. The central idea of De Architectura is modular symmetry. The ratios of symmetria guarantee the beauty and truth of architectural forms, and link these forms to the cosmos.
 
Aristotle, Plato’s student, brought his teacher’s transcendental ideas down to earth and located them in the forms of material bodies. Aristotle solved the problem of becoming versus being not by juxtaposing a sensible to a supersensible realm, as Plato had done, but by positing an intellectually apprehensible “form” as that which turned inchoate matter into a knowable thing. Aristotle’s “form” was also the “act” whereby passive matter realized its potential identity, such as an acorn’s becoming an oak tree. According to Aristotle, we first know a thing through sense perception. Our eyes come in contact with a particular thing, and then our intellect generalizes from the eye’s particular perception of a single thing to the universal form which makes this thing a particular kind of being, say a horse rather than a tree or a table. In his recognition of the importance of sense perception, Vitruvius is very much an Aristotelian. The human eye, along with the human hand, plays a major role in De Architectura. Vitruvius is also Aristotelian when he argues that the particular “glory” that accrues to the architect, rather than the commissioner or the builder of a structure, is the fact that the architect has the “form” of the building in his mind before it is constructed. (6.8.9) And while Vitruvius understands symmetry as number, it is highly significant that he finds the perfect ratios of symmetry not in abstract reasoning, but in measuring the finely formed—albeit two-dimensional and idealized—body of a man. If Vitruvius’ mathematical symmetria can be understood as transcendental Platonic beauty, his visual eurhythmia and his choice of the word venustas for “beauty” are fully consonant with Aristotelian thought. Eurhythmy, according to Vitruvius, is the “appearance” of symmetry. Beauty, for Aristotle, is a form that can be perceived as a completed and unified whole by the eye, in the case of a physical body, or by the memory, in the case of a work of literature.
 
Neither the transcendental nor the formal explanation of beauty is sufficient, although each teaches us something about an important aspect of beauty. Plato acknowledges the fact of matter, but he doesn’t trust the human senses. In fact, the theory of transcendental beauty can accuse visual art of being a lie, as Plato does when he censures the craftsman’s need to set aside true proportions in order to produce the illusion of beauty. And yet, perhaps precisely because it sees matter as imperfect—as belonging to “becoming” rather than “being”—the Platonic theory of transcendental beauty points to a fundamental truth about art: in every experience of beauty, whether in nature or art, there arises a haunting sense of an even greater beauty somewhere else, and a longing to be joined to it. It was this sense of a greater and perhaps materially unattainable beauty that drove Michelangelo, very much a neoplatonist, to leave unfinished, and even to destroy, some of his works.
 
The Aristotelian perspective respects matter and our actual experience of our bodies and our senses. But Aristotle’s approach to beauty can lead to a purely formal aestheticism divorced from any concern with objective truth and moral goodness. In fact, in his Nichomachean Ethics, Aristotle distinguishes between production and action. The crafts, he says, are concerned with production, not action (1140a). He applies the word kalos, “fine, beautiful,” only once in this treatise to a person’s physical beauty, but very often to virtuous actions, and never to craft production, which is, presumably, to be judged according not according to truth and goodness, but rather to how well it is made.
 
In Part II of this essay, I will apply these principles to Raphael’s art.
 
NOTES

1. As Cicero puts it: “assigning to each his own, and maintaining with generosity and equity this partnership of human union (societas coniunctionis humanae) . . .” (De finibus 5. 65).
2. The Oxford Latin Dictionary (OLD) uses this passage from Vitruvius as its second entry for the word communicatio, which it translates as “community of ground,” which makes sense if one construes the plural genitive rerum, “of things,” as the complement of both coniunctio and communicatio.
3. Indra Kagis McEwen, Vitruvius: Writing the Body of Architecture (Cambridge, Mass.: MIT Press, 2003), pp. 156–160.
4. Ibid., pp. 49–51, 166–73.
5. 9 Praef. 17.
6. See Fleury’s commentary on this passage in Vitruve, De l’architecture (Paris: Les Belles lettres, 2003–04), p. 93.
7. As does the OLD.2.
8. J. J. Pollitt, The Ancient View of Greek Art: Criticism, History, and Terminology (New Haven and London: Yale University Press, 1974), p. 448. For a fuller discussion of qualitas, venustas, eurhythmia, see McEwen, pp. 54–55 and 199–200.
9. Republic 7. 529e–530ab. See Gros’s Introduction to Book III, pp. liii–liv in Vitruve, III.
10. Sophist 236a.
11. Hans Urs von Balthasar observes that it is in the mythological world of Homer’s epics, in his concrete poetic portrayals of the interaction between men and gods, that the image and affirmation of beautiful order as the ultimate truth of existence makes its first and lasting appearance in Western civilization. Balthasar writes that: “[t]he plastic arts of antiquity draw their life from Homer’s image of the world: it is in the Homeric Athens of Phidias, Polycletes, Praxiteles and Zeuxis that the ‘sophistis’ and philosophers wander about and whereas they criticize the old world of the gods, they live without criticism in the radiant world of art which the world of the gods produced.” Consider what Balthasar says about Plato: “Only the West received the grace of birth under the sign of a perfected cosmos, in which religion and art are one—the cosmos of Homer’s epics. This world was so strongly fashioned that, when philosophy and religion grew out beyond their beginning, they both developed a common heritage and strove in various ways, and with varying good fortune, to recover what has been lost along the way. Art remains covered in Homer’s mantle; even Plato, who fights against him, quotes him on every other page, while for Aristotle he is the origin and measure of all poetry . . . .The clear lineaments of the figures of Homer’s gods, in contrast to the formless gods of Asia and the Minoan period, remain binding on the Greeks, despite all contradictions and additions (such as Dionysius); the Romans let their deities be transformed by the Homeric gods.” Hans Urs von Balthasar, The Glory of the Lord: A Theological Aesthetics, IV: The Realm of Metaphysics in Antiquity (San Francisco: Ignatius Press, 1989), pp. 45, 43–44.
12. Arthur Pontynen, in his For the Love of Beauty: Art History and the Moral Foundations of Aesthetic Judgement (New Brunswick, New Jersey and London, U.K.: Transaction Publishers, 2006) uses the distinction between a Platonic–Augustinian tradition and an Aristotelian–Scholastic–Kantian–Nietzschean tradition to narrate the history of the idea of beauty in the West.

American Arts Quarterly, Volume 27, number 1.