Circle, pentagon and human body: the geometry of the second book

After numbers, the second book of the De occulta philosophia moves on to figures. If number is the abstract form of order, the geometric figure is its visible form, and for Agrippa it shares in the same virtues. Circles, triangles, squares and pentagons are not mere tools of the geometer but images of the harmony of the cosmos. The chapter devoted to figures prepares one of the most famous sections of the work, the one on the proportions of the human body, accompanied in the 1533 edition by a series of illustrations.

Figures and their virtues

The circle takes first place. It is the most perfect and most capacious figure, without beginning or end, and for this reason, Agrippa writes, taking up a long tradition, it is the image of eternity and of God. The triangle points to the number three and to the Trinity, the square to four, to the earth and to stability. Each figure thus inherits the meaning of the number of its sides or vertices.

Special prominence is given to the pentagon, with the five-pointed star obtained by extending its sides. Agrippa reports that, according to tradition, this figure possessed great power against evil spirits by virtue of the number five. The pentagram had, moreover, an ancient history: it had been a sign of recognition among the Pythagoreans, as late antique authors recall, and it appeared in medieval Christian and chivalric contexts.

Man in the circle and the square

The most famous part concerns the proportions of man. Agrippa takes up the idea, formulated in the first century BC by Vitruvius in the third book of De architectura, that a man with arms and legs outstretched can be inscribed in a circle centred on the navel and in a square. Vitruvius used it to explain the proportions of temples; Agrippa interprets it as proof that the human body sums up in itself the geometric order of the world.

The 1533 edition contains a series of woodcuts showing human figures inscribed in circles, squares and pentagons, with the planets and signs placed at the extreme points of the body. These are images that the modern reader instinctively associates with Leonardo's famous drawing of Vitruvian man, made around 1490, which however remained unpublished and which Agrippa could not have known: both derive from the same ancient source.

Measures, numbers and microcosm

Alongside the figures, Agrippa gathers a series of bodily measurements attributed to the ancients, such as the ratio between height and arm span or the division of the face into equal parts. These proportions, in his view, are not an anatomical fact but a sign: they reveal that man was built according to the same numbers and harmonies as the universe, and that he is therefore truly a little world.

From this came, in tradition, the conviction that the parts of the body were governed by signs and planets, an idea widespread in medieval calendars and almanacs with the figure of the zodiac man. Agrippa places it within a broader and more philosophical framework, in which the geometry of the body becomes the key to understanding the relationship between microcosm and macrocosm.

These pages show clearly how the Renaissance could unite art, science and speculation. The same proportions that served architects in designing churches and palaces served philosophers in thinking about man's place in the cosmos. In the woodcuts of 1533 the human body thus becomes a diagram of the entire universe. It was a way of seeing that joined the eye of the painter to that of the philosopher.