To unify a façade of two or more storeys, run a single order of pilasters or columns through all of them, from the base to the main cornice.
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.
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
Make the Tuscan column 7 diameters high, the Doric 8 with its base, the Ionic 9, the Corinthian 9½ and the Composite 10; give Tuscan and Doric an entablature of about a quarter of the column, the richer orders a fifth.
7 · 8 · 9 · 9½ · 10 D; entablature ≈ ¼ → ⅕
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
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
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
Make the height of a vaulted room the arithmetic, geometric or harmonic mean of its length and breadth.
arithmetic (a+b)/2 · geometric √(ab) · harmonic 2ab/(a+b)
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
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)
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.
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
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.
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
Let every part of a building be measured by the same unit and relate to the whole by simple whole-number ratios, so that one module generates all its dimensions.
e.g. 2 : 3, 3 : 4, 1 : 2: ratios of small whole numbers of modules
To make a rectangle of 1 : √2, draw a square and swing its diagonal down to extend one side; the result cannot be measured in whole units of the square, but it can be drawn exactly.
√2 ≈ 1.414; halving a 1 : √2 rectangle gives two more of the same shape
Let the rooms of a house share dimensions, so that the length of one is the breadth of the next and each stands to its neighbours in the ratios of the scale; the whole plan then forms one proportional system.
e.g. rooms of 12 × 12, 12 × 18 and 18 × 30 feet, sharing 12 and 18
Where an old structure fixes bays of unequal width, keep the central arch of every Serliana the same and let the flat-headed side openings take up the differences.
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.
Place the stair where it does not spoil the rooms and yet is easily found; light it well; and make the steps no higher than half a foot and the treads at least a foot deep.
riser ≤ ½ ft (≈ 17 cm); going ≥ 1 ft (≈ 35 cm) in Vicentine feet
Build the country house by a navigable river if you can, for cheap transport of the harvest and for beauty, or else by a main road; on raised ground open to the air, away from standing water and deep valleys, and in the middle of its own land.
Put the owner’s house at the centre and join the farm buildings to it with covered porticoes (barchesse), so that one can go everywhere under cover; give granaries, cellars, stables and threshing floor their proper places, in proportion to the estate.
Make the streets of a city straight and wide enough for their traffic; pave the middle for carts and animals and raise the sides a little for people on foot, and where the climate is hot or wet, line them with porticoes so that citizens go about their business under cover.
Make the roads outside a city straight, broad and raised above the fields, and plant trees along both sides, to shade the traveller and delight the eye.
Leave piazzas in several parts of the city for markets and assembly, the principal one in the middle; ring it with porticoes, and set round it the palace of the prince or the signoria, the treasury, the prisons and the basilica where justice is done, with the principal church close by.
breadth : length = 2 : 3 (the Latin forum)