To make a square of half the area of another, join the mid-points of its sides: the rotated square so drawn has exactly half the area. Repeat to halve again.
side of inscribed square = s ⁄ √2 · area = ½ s²
Rules · Cities · Plans · Modules
Equal plots at a fixed rent
Give every settler a house plot of the same size in the town, at the same yearly ground rent, with a garden plot and a share of fields outside; so the blocks are divided into narrow lots of equal frontage, each house on the street with its yard behind.
The charters of customs were the founders’ advertisement: they promised settlers a plot for a house (place, ayral), usually a garden (casal) just outside the town and a portion of arable land, all for fixed rents and with freedom from many seigneurial dues, and often the right to elect consuls. The equal plot was both fair and easy to administer: rents could be counted by the number of plots.
The resulting fabric is unmistakable: long rows of narrow houses, each the same frontage (at Monpazier about eight metres), with their gardens behind, and the grid of the town readable in every roof line.
Related rules
Proportion every member of a vaulted choir from its clear width: the wall a fixed fraction of the width (a tenth, as the rule is usually read), and buttresses, window jambs, mullions and ribs as simple multiples or fractions of the wall.
wall ≈ W ⁄ 10 · buttress, jambs, ribs = multiples of the wall
End the choir in a semicircle of piers; wrap an aisle (the ambulatory) around it, and open a ring of chapels off the ambulatory, each with its own altar and windows, so that the east end steps down in tiers of roofs and buttresses.
Put the hall at the heart of the house and enter it at one end, by a passage running through the house from front door to back door, screened from the hall. Open the buttery, the pantry and, between them, the way to the kitchen off that passage, at the hall’s lower end; put the family’s parlour, and the great chamber over it, beyond the hall’s upper end, where the high table stands.
Build the monastery, if possible, so that everything it needs (water, a mill, a garden and the various crafts) is inside the enclosure, so that the monks need not wander outside, which does their souls no good; and set a wise old monk at the gate, with a cell beside it.
Let all the monks sleep in one place if their number allows, each in his own bed, clothed and ready to rise, with a light burning until morning; place the dormitory where they can go straight to the church for the night office.
Cite this page Chris Paton, “Equal plots at a fixed rent”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/bastide-plots. Text, drawings and models licensed under CC BY-NC 4.0.