Leon Battista Alberti, On the Art of Building (1452 (printed 1485))

The first architectural treatise of the Renaissance: ten books modelled on Vitruvius but rethought from first principles, defining beauty as a harmony of all the parts so complete that nothing could be added or taken away without making it worse.

Alberti was a humanist scholar, papal secretary, painter-theorist and, later, the designer of San Francesco at Rimini, the façade of Santa Maria Novella and Sant’Andrea at Mantua. His treatise deliberately had no pictures (he feared copyists would corrupt them), and it addresses the educated patron as much as the builder.

He divides a building into six elements (region, site, compartition, wall, roof and opening), defines beauty as concinnitas (the agreement of number, outline and position) and distinguishes beauty, which is inherent, from ornament, which is added. He derives architectural ratios from the harmonic intervals of music, and treats the column as the chief ornament of architecture: a piece of wall left standing, pierced through.

The book, part by part

I Books I–III: Lineaments, materials, construction

The six elements of building; design (lineamenta) as something that exists in the mind apart from matter; materials and the craft of walls, vaults and roofs.

Rules: Beauty is concinnitas

II Books IV–V: Works of public and private use

Cities, roads, bridges, harbours; the houses of the prince, the magistrate and the private citizen, each appropriate to its occupant.

III Books VI–IX: Ornament

Beauty and ornament defined; the orders, sacred buildings (temples, basilicas), public secular buildings, private buildings. The harmonic ratios of music applied to rooms and elevations.

Rules: Ratios from the musical consonances · The column is the chief ornament

IV Book X: Restoration

The repair of buildings and the management of water.

Rules drawn from On the Art of Building

The flatter the arch, the harder it pushes

An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.

H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)

The villa garden: porticoes, grottoes, evergreens in rows

Give the villa garden porticoes for sun and for shade, grottoes made in imitation of nature with tufa and shells, evergreens planted in straight rows at equal distances, and hedges of box; set vines on columns over the walks.

Beauty is concinnitas

Beauty is the reasoned harmony of all the parts within a body, so that nothing may be added, taken away or altered but for the worse.

Ratios from the musical consonances

Proportion rooms and façades by the same ratios that make musical consonances: 1:2 (octave), 2:3 (fifth), 3:4 (fourth), and their compounds.

short plans 1:1, 2:3, 3:4 · medium 1:2, 4:9, 9:16 · long 1:3, 3:8, 1:4

The column is the chief ornament

In all architecture the principal ornament is the column: a part of the wall left standing and pierced through.

The three means

Between two numbers a and b, find the arithmetic mean (a + b)/2, the geometric mean √(ab) and the harmonic mean 2ab/(a + b); use them to find a third dimension that belongs to the other two.

for 6 and 12: arithmetic 9 · geometric 8.49 · harmonic 8; always A ≥ G ≥ H, and G² = A × H

The centrally planned church

Where the purpose allows, plan the church about a single centre (a circle, a square or a Greek cross) so that every part stands in the same relation to the middle, under a dome.

The piazza as a double square, framed by porticoes

Make a public square twice as long as it is wide, surround it with porticoes, and keep the buildings round it in proportion to the open space: about a third of its breadth high, and never less than a sixth.

length = 2 × breadth; height of the buildings = ⅓ to ⅙ of the breadth

The temple raised above the city

Set the principal temple where it can be seen, standing free in its own open space, and raise it on a podium reached by steps, so that it stands above the ordinary business of the town.

Straight streets of equal houses

In a great and powerful city make the main streets broad and straight, lined with porticoes and with houses of the same height and design, so that the street itself becomes an ornament; in a small town let the streets wind instead.