Divide the inside of a dome into coffers that shrink in step with the meridians as they rise, so that their perspective deepens the dome and draws the eye to the light of the lantern.
Proportion every step so that twice its height plus its depth equals the length of a natural pace on the level: two feet, or 24 pouces.
2 r + g = 24 pouces ≈ 65 cm (modern practice: 60–66 cm)
Hold that the beauty of the orders comes from fixed proportions that please by nature, as consonances do in music; where the ancients differ, the differences answer to circumstances such as distance and height.
Give the flight of steps before a temple an odd number, so that one who starts with the right foot will also set the right foot first on the top.
Take the plan, the orders and the details from the builders’ pattern books, simplified for timber and for the carpenter: a symmetrical front, a central hall and stair with rooms either side, a doorway under a pediment or fanlight, and mouldings drawn to be made with the plane.
Judge every building against the first shelter: four trees for columns, branches laid across them for the entablature, and a pitched roof whose end makes the pediment. These three are the essential parts; all else is added.
Let columns stand free, round and upright, carrying a straight entablature directly; do not engage them in walls, replace them with pilasters, or set them on pedestals.
Avoid the ornaments that have no model in the hut: broken or curved pediments, pediments on the long side of a roof, orders piled storey upon storey on a church front, arches carried on columns, and twisted or cabled shafts.
Seek in every building only fitness (solidity, healthiness, convenience) and economy (symmetry, regularity, simplicity); a building that has these will please, and ornament added for its own sake is waste.
Compose any building on squared paper: first draw its principal axes, then a grid of equal squares; place the walls on the axes and the columns at their intersections; only then open the walls and combine the parts.
grid module = the interaxis of the columns; walls on grid lines; supports on grid points
Build every type (temple, museum, college, hospital, barracks) from the same small set of elements, combined about axes parallel, perpendicular or concentric to one another.
Draw the solid masonry of a plan in black, filling every pier and thickened wall, so that the rooms read as shaped voids carved from a mass.
Understand every building as a combination of four elements (the hearth, the roof on its supports, the enclosure and the mound), each descended from a craft: ceramics, carpentry, weaving and masonry.
Every building must satisfy three demands at once: it must stand up (firmitas), serve its purpose (utilitas), and give pleasure to the eye (venustas).
architecture = firmitas + utilitas + venustas
Keep the lowest third of the shaft cylindrical; above it, reduce the radius along a curve found by dividing a quarter-circle and the upper two-thirds of the shaft into the same number of equal parts.
r(k) = R · cos(α·k), cos α = r_top ⁄ R, k = 0…1 over the upper ⅔
Divide the whole front of the cornice into nine parts; give one of them to the height of the tympanum, measured at its centre.
tympanum height = cornice width ⁄ 9 (≈ 12½°)
An order consists of a column (base, shaft and capital) carrying an entablature (architrave, frieze and cornice), optionally raised on a pedestal (plinth, die and cap). Each part is proportioned to the lower diameter of the column.
order = [pedestal] + column(base, shaft, capital) + entablature(architrave, frieze, cornice)
Divide the whole height into nineteen parts: four for the pedestal, twelve for the column, three for the entablature. Without a pedestal, divide it into fifteen, giving twelve to the column and three to the entablature.
pedestal = ⅓ column; entablature = ¼ column
Make the Tuscan column 14 modules high, the Doric 16, the Ionic 18, and the Corinthian and Composite 20, the module being half the lower diameter.
Tuscan 7 D · Doric 8 D · Ionic 9 D · Corinthian 10 D · Composite 10 D
When orders are placed one above another, put the stronger below and the more delicate above (Doric under Ionic under Corinthian), and make each upper column a quarter shorter than the one beneath.
upper column = ¾ lower column; order sequence: Tuscan → Doric → Ionic → Corinthian → Composite
Set arches on piers and frame each bay with an engaged column or pilaster carrying a continuous entablature, so that the arch does the work and the order gives the measure.
arch height ≈ 2 × arch width (Vignola); impost at ⅔ of the column
Build every profile from a small set of elements (fillet, torus, astragal, scotia, ovolo, cavetto, cyma recta and cyma reversa), alternating curved with flat and light with shadow.
Use the orders according to their character: the Doric for strength and gravity, the Ionic for a middle dignity, the Corinthian for delicacy and splendour.
Make rooms round, square, or with a length equal to the diagonal of the square, to a square and a third, a square and a half, a square and two-thirds, or two squares.
circle · 1:1 · 1:√2 · 3:4 · 2:3 · 3:5 · 1:2
Place rooms on the right of the entrance equal and corresponding to those on the left, so that the house is alike on both sides and the walls bear the roof equally.
Give the front of a country house a portico with a pediment, as the ancients did, for it shows the entrance, gives grandeur, and makes a place to display the owner’s arms.
Combine a central arched opening with two narrower flat-headed openings on either side, the arch springing from the entablature of the side openings.
side lights ≈ ½ central span; arch springs from the lintel of the sides
Distinguish positive beauty, which pleases everyone for evident reasons (fine materials, size, precise workmanship, symmetry), from arbitrary beauty, which pleases through custom, including the exact proportions of the orders.
Find every member of an order by dividing the given height into equal parts with the compasses, and those parts again, so that no arithmetic is needed.
height → 5 parts: 1 entablature + 4 column (without pedestal)
Draw the Ionic volute seven eye-diameters high and six wide, with the eye four diameters below the top; lay three turns about centres set out in the eye so that each winding is half as wide as the one outside it and the spiral runs into the top of the eye.
height = 7 e, width = 6 e; eye centre 4 e below the top; radii from the eye centre (e = 16 parts): 60, 52, 44, 36, 30, 26, 22, 18, 15, 13, 11, 9 → 8
Compose from the plan: base it on the elemental figures (circle, square, rectangle and their derivatives), arrange its parts symmetrically about axes, and develop section and elevation from it together.
Do not leave a large circular building as a bare cylinder: steady it with features that break the curve and fix its axes: a portico, stairs, a projecting bay or a recess on the axis.
Make a simple square room as high as it is wide, so that it encloses a cube; for oblong rooms the double cube (twice as long as it is wide and high) is satisfactory in almost any circumstances.
For a hall of assembly use the “D” or tribune plan, a half-circle closed by a straight side: it gives ample room to the audience, a central place to the speaker and scope for display in the architecture.
Use the elliptical plan chiefly for interiors, where the whole curve is seen at once; on the outside of any but a very large building its changing curvature looks like a distorted circle, and the circle is better.
If a room is no longer than twice its breadth, make it as high as it is broad; make a coved room higher than a flat one, with a cove a quarter to a fifth of the whole height; take a vaulted room to the crown at half the sum of its length and breadth.
flat: H = B (L ≤ 2B); coved: H = B + (⅕ to ⅓)(L − B), cove = ¼–⅕ H; vaulted: H = (L + B) ⁄ 2
Keep a corridor’s height to no more than one and a half times its width, and divide its length into bays about as long as it is wide, marked by pilasters and by the divisions of the ceiling or vault.
H ≤ 1½ W; bay ≈ W
Place the staircase by three tests: its relation to the principal rooms it serves; keeping the main axial communications free of obstruction; and light, for itself and, as a well of light, for the corridors and vestibules around it.
Give a portico three jobs: to shelter those who arrive, to mark the main entrance, and to give the building dignity and character with its depth of light and shade; proportion it, as a rule, like a temple front.
To divide a line in extreme and mean ratio, make the whole stand to the larger part as the larger part to the smaller; the ratio is φ = (1 + √5)/2 ≈ 1.618. Construct the golden rectangle by swinging the line from the midpoint of a square’s side to its far corner.
φ = (1 + √5)/2 ≈ 1.618; φ² = φ + 1; 1/φ = φ − 1 ≈ 0.618
Raise the principal rooms of a house on a basement storey that holds the kitchens, cellars and service rooms, and reach them by an external stair; put the lesser rooms above them.
Divide the inner surface of the dome into sunk panels arranged in rings and meridians; let them diminish as they rise with the converging meridians, and stop them short of the crown so that a smooth zone surrounds the eye.
Pantheon: 5 rings × 28 coffers, each stepped in several recessions
Pierce a massive rectangular pier with one arch, or with a tall central arch between two lower ones; frame the openings with columns on pedestals carrying an entablature, and crown the whole with a high attic for the dedicatory inscription.
Arch of Titus: 13.5 × 15.4 m, one opening 5.4 × 8.3 m; Arch of Constantine: 25.9 × 21 m, openings 6.5 × 11.5 m and 3.4 × 7.4 m
Put a pediment only where the roof actually ends in a gable, on the short sides of a building, never along its length or stacked one above another, because the pediment represents the gable of the roof.
Break the slope of the roof on all four sides: a steep lower slope, nearly a wall, which holds a storey of rooms lit by dormers, and a shallow upper slope, often invisible from the street.
lower slope ≈ 60–75° · upper slope ≈ 15–30°
Plan a town as a park is cut through a forest: with many straight streets, squares from which several streets branch, and broad entrances, so that there is regularity in the details and variety, even a certain disorder, in the whole.
Lay out a town as a gardener lays out a forest park: wide, straight streets as its avenues, squares where they meet, well-marked entrances, and within that order enough variety of buildings that the whole never becomes monotonous.
Do not leave the fronts of houses to the whim of each builder: let the authorities fix their line, height and design so that a street or square is composed as a whole, and vary the designs from one street to the next so that uniformity does not become tedium.
On a ridge, run the principal street along the crest and make it the widest; set a square at each end of it; lay two more streets along the flanks, and narrow lanes between them for coach-houses, shops and lesser houses.
Build the outer streets on one side only, so that every house looks across open gardens to the landscape beyond, and keep the far side of the street free of building.
End each long street on a monument: put a church on the axis of the main street at the far side of each square, so that the view along it finishes on a portico and a dome or steeple.