Parterres tend to be based on rectilinear figures. This is the basis of Vitruvian architecture.
These designs tend to be rectilinear (because right angles are the easiest angles to set out on the ground), and small (because this kind of surveying is very prone to accumulating errors, where for example the base unit of measurement is one inch adrift and is replicated 200 times in an avenue). Easy though it is to design like this on paper, as the design increases in size it must be simplified to be practicable, and usually large scale regular garden design of the 17th and 18th centuries was confined to avenues of one kind or another.
On the plus side, most of this setting out requires only two or three lines (usually made of tarred cord, knotted at prescribed intervals). However in my youth we still used the 22 yard chain, carried about in a large wooden box). Sophisticated designs can be generated with these simple tools, however, both the right angle and the tendency to small scale design were picked on by Humphry Repton in around 1800 when he characterised what he called ‘the old false taste of Gardening by Geometric Rule’, emphasising the use of ‘the line and square’ to produce ‘in every direction … ranks of trees, in circles and squares, and triangles, and straight lines, and in every form that the ruler or the compasses could describe.’
On areas up to a couple of acres, the same basic equipment can be used to set out a design by grids, and the drawn design is then reproduced on the ground by scaling up from the paper. This is less accurate, and is still limited in size, but it was used by Joseph Spence, and recommended by the authorities.
It remains the case however, that a regular design becomes increasingly difficult to draw as the scale increases, even for a relatively modest 300 acre park, and increasingly difficult to set out. The theodolite was Capability Brown’s chosen setting out device. It dictated the development of design in his day, which was derived from angles rather than linear measurement.