This article focuses on architectural drawings, some only recently discovered, that contain indications of authentic proportional systems from the ‘inner circle’ of Dutch seventeenth-century classical architecture. These drawings demonstrate how these architects used arithmetical grid systems as well as geometrical constructions in the hope of achieving their classical ideal of beauty and harmony. In light of these proportional systems we may propose a method for analysing other drawings from this period that do not have any proportional systems inscribed.

The study of proportional design in architecture offers a minefield of misunderstandings
and over-interpretations. As historiography of this kind of research illustrates, the
quest for a golden key that may unveil universal harmony in architecture of all ages
resulted mostly in geometrical shapes in which especially the air around or the soil
below the buildings seem to be well proportioned. Both Gothic and classical buildings
always show a manifold of horizontal and vertical lines. By attempting to reconstruct an
architect’s intended geometrical frame on a modern drawing of an existing
building, one always runs a risk of coincidence: there may always be something that, at
first glance, seems to fit in any system imposed on it. The main question, nevertheless,
should be the other end of the design process:

In order to prevent anachronisms in the reconstruction of proportional systems it is essential to go back to evidence of contemporary design practises. Unfortunately, in early modern times written sources on contemporary design systems are rare and drawings showing a proportional system applied are even rarer. The well-known treatises of Andrea Palladio, Vincenzo Scamozzi and others offer some basic theoretical principles as well as the final results, the ground plans and façades of villas and palaces. On the other hand, the actual practise of how to construct a design step by step is never explained — not because this was something ‘secret’, one may presume, but since it was a common practise well known to the reader.

Fortunately, some seventeenth-century witnesses are available who illustrate what had
happened at the architect’s drawing table in Holland (see

This paper will focus on those architectural drawings that contain indications of authentic proportional systems. Some of these are already well known, while others have been discovered only recently. In contrast to the many hypothetical reconstructions of proportional systems presented by later historians, these drawings provide various examples of how these architects actually used arithmetical grid systems as well as geometrical constructions to achieve unity and coherence within their designs.

In addition this paper will look at some other buildings of the period that are well
documented by contemporary prints of the designs, without the proportional systems but
with all essential measurements inscribed by the architect (what interests us now are
the design principles as practised on the architect’s desk, not the measurements
of the final constructions, which are always less perfect than what was envisioned on
the drawing table). The knowledge of the design systems of the period, as demonstrated
by the aforementioned contemporary drawings, and these exact measurements indicated on
the prints enable us to reconstruct design systems applied by the architects.

Mathematical principles were always prominent in Dutch seventeenth-century
architectural treatises and handbooks. Even before the rise of classicist
architecture in Holland in the 1630s, and certainly after, architectural design had
been regarded there as a kind of applied mathematics. Model books, such as
posthumous editions of Hans Vredeman de Vries’s

Marolois,

In his introduction to the

Such a focus on mathematics is not surprising since seventeenth-century Dutch society
was permeated with mathematics. Mathematics was essential to the Dutch mercantile
and maritime society, and as such, was necessary for everybody who was educated for
the pursuit of trade and navigation as well as building and fortification, even
before the rise of classical architecture at the beginning of the century. The first
six books of Euclid may be regarded as a starting point for any applied science
during this period, architecture included. The mathematical principles explained,
for example, in Serlio’s Book I and Scamozzi’s Book I, are based on
these same first six books of Euclid, such as geometry and proportions as well as
square-root proportions and

The focus on proportions in architecture as explained in the works of Palladio and
Scamozzi fitted easily into Dutch society, not only among the scholarly elite but
also among the intellectual middle class. As elsewhere, mathematical principles were
used in architectural design at all times but, with the introduction of the
Vitruvian theory, in its contemporary transformation by Palladio and Scamozzi, into
seventeenth-century Dutch society, proportions became a major issue in architectural
theory (

We have a few authentic witnesses for the use of mathematical systems in
architectural design practice. The first is a series of hundreds of drawings made by
Nicolaus Goldmann, a teacher of architecture in Leiden from 1640 until his death in
1665 (

Nicolaus Goldmann, sketch for a cubic villa (Berlin, Staatsbibliothek).

Reconstruction to scale based on Nicolaus Goldmann’s sketch for a cubic villa. Drawing by the author.

The ground plan is divided into nine squares of 10 x 10 modules, with outer walls 2 modules and inner walls 1 module wide, thus creating nine inner spaces of 8 x 8 modules. The exterior height is divided into 5 modules for the cellars and 25 for the main and upper floors together. Engaged columns are 2 modules wide and 20 high (1:10), with a water table profile of 1 module and a crowning entablature 4 modules in height, which is thus 1/5 of the height of the engaged columns below. The central bay is 10 modules wide on centre (with an intercolumniation of 8), the two outer bays 8 each (with an intercolumniation of 6 modules), and 1 module is added at each end to support the projecting parts of the bases and capitals of the outer pilasters.

Another important contemporary source for our understanding of seventeenth-century
Dutch design practises is a drawing made by Jacob Lois of his design for the
Schielandshuis in Rotterdam, built in 1662 (

Jacob Lois, Schielandshuis, Rotterdam, 1662. Photograph by the author.

Ten years later, in 1672, the architect prepared a manuscript for a book on the
history of this institution, which controlled the dikes and polders in the area. In
this manuscript he included a drawing of the geometrical system of his facade design
(Fig.

Jacob Lois, proportion system of his Schielandshuis, from his manuscript

At first glance this seems to be utter fantasy, but in fact Lois is just showing
various steps of a very lucid design system presented all together in one drawing,
as convincingly demonstrated by Terwen (

Explanation of the four steps in Lois’s drawing. Reproduced from Terwen
(

The starting point is two squares, creating a rectangle of 80 x 40 feet (a).

The floor plan of the Schielandshuis is a square of 80 x 80 feet. The division of the interior spaces behind the façade do not correspond to the bay system of the exterior. While the façade is divided into a sequence of 20 – 40 – 20 feet, as shown above, the ground plan behind it is divided into three bays with widths of 25 – 30 – 25 feet. Lois’s drawing also shows various proportional systems for individual rooms, including two overlapping circles in the main assembly hall in the centre, indicating that this space has a proportion of 2:3, and the small room at the left side on the front with an indication of the proportion of 4:5. As far as we know these are the only examples of such geometrical systems based on intersecting circles drawn in interior spaces. Since interior measurements of individual rooms were mostly the result of the main grid minus the thicknesses of the walls and not the starting points of a proportional division, there is scarcely a whole number to be found with an evident proportional relation to the grid of the plan. But in this building design it seems that Lois wants to show his acquaintance with comparable ideas in Palladio’s and Scamozzi’s treatises and therefore presents things even more perfectly than they were. For instance, the great room at the left side is marked with two interwoven circles, suggesting this space has a proportion of 2:3; however, as the drawing shows, this system does not fit well in the room since it aligns not with the back wall but with a point just in front the chimney.

The preceding examples reveal some general principles. First, in the seventeenth-century Dutch method of mathematical design, the general outline of the volume or façade has to be found, preferably based on a rectangle that has been constructed by adding together squares. That base rectangle may be enlarged by volumes derived from rational or square-root proportions. Once these principal measures are defined, the classical orders are added, these being design elements of a second rank; and after these the other ornaments, if any. A grid system is used to organise the ground plan. Sometimes this is related to the geometry of the façade, sometimes it is not. The walls are drawn alongside the theoretical lines of the grid and as a result — because of the wall thicknesses — the actual interior spaces are never as perfect as those indicated in theory by the grid. These principles may be used as a starting point to investigate other design projects of the same period. Apparently, here we have a set of design tools that we may use to investigate seventeenth-century Dutch architecture without the risk of over-interpretation.

The proportional systems practised by Goldmann and Lois must have been rather common among those Dutch seventeenth-century architects who had a thoroughly artistic and scholarly education, like Jacob van Campen and his former assistants, Pieter Post and Philips Vingboons. There are no drawings of proportional systems from their hands, but there are carefully engraved prints made after their drawings that carry a lot of information. These prints always show many inscribed measurements which are the final results of a design system that is not illustrated. Considering the numbers inserted in these designs, which sometimes seem to be quite awkward or illogical, it may be possible to find the systems behind them.

The design drawings of the Amsterdam town hall by Jacob van Campen from around 1648,
but only published posthumously in 1661 by his former drawing assistant Jacob
Vennekool, constitute a well-known example of such engravings (

Reconstruction of the grid system of the ground plan of the Amsterdam Town
Hall and its division into bays (

At the sides of the building the walls between the corner pavilions are each 120 feet
long. The central part of this wall in between is divided into 6 bays of 12 feet 5
95/102 inches each.

Philips Vingboons concludes his 1648 publication,

Philips Vingboons’ ‘ideal’ villa, published in his

He is well aware that these projects are beyond the usual scale of construction
demanded by his Dutch mercantile patrons. Apparently, these projects represent true

Reconstruction of Vingboons’ design system for the villa of 1648. Drawing by the author.

The height of the façade, from the pavement of the ground floor up to the
cornice, is also 48 feet, plus another 5 feet from the raised basement to the
pavement. The result is that the front of the central projection, measured from the
pavement of the ground floor, fits inside a square of 48 x 48 feet. This square is
flanked on each side by walls of 24 x 48 feet, and beyond them, further back in the
distance, additional side walls of 12 x 48 feet (Fig.

In the ground plan of 120 x 120 feet we find two interwoven ratios: a system in which
these 120 feet have been divided into 10 units of 12 feet (like the exterior), and a
second system that divides them into 8 units of 15 feet. These two divisions create
the possibility for manifold proportions of the internal spaces, such as 12 x 12, 15
x 15 and 15 x 30, but also combinations of both systems, such as 12 x 15 (4:5), 15 x
24 (5:8) and 24 x 30 (4:5). For instance, the entrance hall is drawn on this grid as
48 x 30 (8:5), both spacious side rooms as 30 x 50 (3:5), and the main salon at the
rear, 48 x 45 feet (16:15). These interior measurements are all theoretical
proportions, created by

This grid-based system of design, as shown in the preceding theoretical design by
Vingboons, may be productively compared with the design of an actual building, the
Town Hall of Maastricht, designed in 1656 by Pieter Post and built from 1659 to 1664
(Fig.

Pieter Post, Town Hall, Maastricht, 1656. Photograph by the author.

This investigation is based on the original design as published by Post himself in
1666 (

Reconstruction of Pieter Post’s design system for the Maastricht town hall. Drawing by the author based on Post’s publication of his town hall design of 1664.

The front façade of 100 feet is divided by two interwoven central projections of
50 and 33 1/3 feet into ratios of 25:50:25 feet and 33 1/3:33 1/3:33 1/3 feet. The
first and second storeys together are also 33 1/3 feet high, situated on a ground
floor of 13 1/3 feet, which can be derived, in approximation, from the ratio
1:√2 (as shown in Fig.

With examples of Goldmann, Lois, Vingboons and Post at hand, it seems the design
toolbox of the qualified Dutch seventeenth-century architect was primarily focussed
on the exterior measurements of the building volume. To take the external silhouette
as the starting point of the design makes sense if we presume it was important above
all to create a convincing impression of balance and order for spectators and
visitors of the building. But in the meantime there were other possibilities as
well, as illustrated by a set of drawings by Adriaan Dortsman, overlaid with
proportional grids that show another attitude. These are the designs for the floor
plan of Finspång Castle in Sweden, the country house and centre of an
industrial development built by Louis de Geer the Younger in 1670 and subsequent
years (Fig.

Adriaan Dortsman, Finspång Castle, Sweden, 1669–1670. Photograph by the author.

Dortsman created the drawings in Amsterdam between 1669 and 1670, who did not visit
the building site but sent his drawings to Sweden by mail (

The starting point of the design is a square grid of 75 x 75

Adriaan Dortsman, Finspång Castle, ground plan on a grid of 5 x 5

In small notes on the drawing Dortsman explains that 1

The internal walls are 1

Adriaan Dortsman, Finspång Castle, detail, ground plan on a grid of 5 x
5

Therefore neither the actual measurements of the internal spaces nor the exterior
dimensions of the building correspond with the proportional system of the grid. For
example, the facade is not 75

This grid of squares of 5 x 5

To most builders in seventeenth-century Holland the introduction of the classical
architectural style according to Palladio and Scamozzi simply amounted to a change
of ornament. Only among a small group of architects, including Jacob van Campen,
Pieter Post and Philips Vingboons, and some of their patrons, were the theoretical
principles of this new kind of architecture seriously studied. The examples
discussed here were selected from this limited group. To these architects, the true
principles according to ‘the proportions and rules of the Antique’
(‘de liefde tot de Bouwkunst, op maet en regelen der Ouden’), to quote
Vingboons from his 1648 publication (

The general outline of the building volume or the façade was the first concern of the design systems, preferably based on whole, perhaps even decimal, numbers, as demonstrated by the various examples. The classical orders were added afterwards. A grid system, not only of squares but sometimes of rectangles, was used to organise the floor plan. In general the outer lines of the grid are coincident with the exterior of the outer walls, while the interior walls are situated alongside the grid. The example of Finspång, however, shows that the grid could also be used to mark the centre lines of the walls. Proportional systems may differ in time and place and we are well aware there is no universal system that can be imposed on the history of architectural design in general. Even within one period and within one peer group of architects, we must be careful not to look for general solutions as these case studies demonstrate.

Finally, the question remains whether or not these kinds of design systems had
anything to do with aesthetic thoughts of Dutch seventeenth-century patrons or
architects. Sources to answer this question are scarce. Once again it is in the
writings of Constantijn Huygens that we find hints to the tradition begun by Alberti
two centuries before, where the essentials of classical architecture are not the
five orders or other ornament, but the harmony of proportion of the design. In the
minds of Huygens, Van Campen and their circle, the antique idea of macrocosmic
harmony as the divine principle of universal beauty was still rather vivid (

There is a central axis, dividing Hofwijk into two parts, the left side is exactly the same as the right side.

[…]

He who negates this division, despises himself above all as well as the most beautiful creature of God. Before I started digging

I took a wise lesson as guideline for my work:

I just regarded my own body, that was enough.

(

From his point of view, symmetry, balance and order were basic necessities for decent architecture. On the other hand, he abhorred oblique angles and irregularities:

Wherever I looked, I couldn’t find any rule better than this one. Away, I
shouted, away with oblique angles and irregularity, and cross-eyed disorder.
(

Several years before he described the discussions about the creation of a new urban
quarter in The Hague, where Huygens and the Prince of Orange opposed an earlier plan
by the local authorities with an irregular layout of streets instead of an open
square, as a battle of compass and ruler against outrageous errors and injustice
forces (

Being a gifted musician, Huygens also studied theoretical connections between
principles of musical harmony and architecture, like those presented by Daniele
Barbaro in 1556 in his commentary on Vitruvius (

Presumably Huygens’ and Van Campens’ engagement with classicist theory was exceptional. Elsewhere in the Dutch Republic as well, order and regularity were regarded as desirable qualities. To the civic elite of the Republic and their architects, classicist architecture may well have been regarded as an expression of social order, class and style, but to what degree they shared Huygens’s scholarly ideas on universal beauty is uncertain. The use of proportional grid systems in their architectural drawings may have been merely a design tool.

This article is partly based on an earlier conference paper focussed on the
designs by Philips Vingboons (

For other detailed examples of the use of proportional systems by Post and
Vingboons, see Ottenheym (

See also the contribution by Jeroen Goudeau to this volume.

The Rijnland foot was the most common scale in the Dutch Republic during the
seventeenth and eighteenth centuries. It measures 31.4 cm and is divided into 12

Wegener Sleeswijk was one of the assisting architects of the 1935–1939
restoration of the former Town Hall; see Vlaardingerbroek (

Unlike the columns from which they originate, the shafts of these pilasters do not have an entasis; they have the same width on top and below. According to Scamozzi, in the Composite order the width on top is 6/7 of the width at the bottom of the shaft. At the Amsterdam town hall, as in most other cases in Dutch seventeenth-century classicism, the size on top became the standard for the whole shaft. Nevertheless, for finding the right proportion between the width of the pilaster and its height, the modulus of the original column was used (7/6 of the width of the pilaster).

To find the width of one bay one should theoretically add one pilaster of 3 feet
to the length of 200. Thus 203 feet divided into 17 gives a width of 11 feet 10
6/17 inches for each bay. This is what Wegener Sleeswijk did in his drawing (our
Figure

This part of the wall measures 75 feet 2 10/17 inches; divided into 6 this makes
12 feet and 5 95/102 inches per bay. See Wegener Sleeswijk (

The architect did not supervise the construction, since the city of Maastricht was 200 km away from his home town of The Hague, and the final result thus differs in many details and in essential proportions from the design. In 1664, when the building was finished, Post published his own original designs in a series of engravings.

Stockholm, National Museum, Tessin-Hårleman collection, inv. nrs. 2951, 2959, 2988, 2989.

Barbaro’s notes on the relations between architecture and music were also
incorporated into the Vitruvius edition compiled by Johannes De Laet in 1649
(

In 1628 Samuel Marolois presented in the introduction of his treatise

This book project came never to an end and Huygens’ concept for this publication was finally taken over by De Laet in his Vitruvius edition in Latin, 1649. See above, note 11.