The five orders as sets of mathematical proportions: Hans Blum, 1550

The five orders as sets of mathematical proportions: Hans Blum, 1550

Source: Hans Blum, Qvinqve colvmnarvm exacta descriptio atque deliniatio, cum symmetrica earum distributione. Zurich, 1550. Full text available on

In order to be disseminated from Italy to northern Europe and from learned scholars to literate artisans, further simplification was required. One of the most influential vehicles for this simplification is this little book by the German architect Hans Blum (fl. 1549-52). Although the conceptions underlying the book we based closely on Serlio, Blum departed from the Bolognese master in several important respects. First of all, he confined his attention to the five orders, offering ‘an exact description and delineation of the five columns’. Second, he expounded these with reference to what he here calls a ‘symmetrica earum distributione’. By that phrase the author meant that he had reduced the complicated verbal descriptions in previous discussions of the subject to a set of geometrical proportions presented visually in graphic form. Rather than having to rely on a very difficult written text, these diagrams showed how all the absolute dimensions of any of the five orders could be derived geometrically once the overall height of the column (including its pedestal and capital) was known. For our purposes, Blum’s little treatise beautifully illustrates the foundation of the classical language of architecture in mathematics, which helped elevate this mechanical art by grounding it in a liberal one. 

Images 1-8  show Blum’s depiction of the Tuscan (1), Doric (2), Ionic (3-4), Corinthian (5-6), and Composite 'orders' (7) – that is, the entire composition of pedestal, column and capital – as well as well as a more detailed analysis of one of the capitals (8). In each case, the geometrical proportions which structure each order are indicated in the engraving and described in a single column of text alongside it. 

Image 9 contains the English translation of Blum’s commentary on the Tuscan order, the beginning of which is reproduced below for easier legibility. In the version of the text below, (1) the punctuation and capitalisation have been changed to make the text more intelligible; (2) the text has been divided into separate bullet points for additional clarity; (3) the explanations from the glossary on the previous page are inserted in square brackets, along with (4) additional commentary. All the commentary not included in the original text is presented in italics.

Image 1. Tuscan

The first instruction determines the vertical proportions of the Tuscan order as a whole.

The whole height of this Pillar devide in 9 parts. These 9 parts are innumerated in the vertical line to the left of both images.

The second instruction determines the vertical proportions of the three parts of the pedestal (called ‘stilobata’) on which the column rests.

Giue 2 of those parts to Stilobata or Pedestal with Basis (all the moulding or foot of the pedestal) and vpper Cimatium (the more elaborate moulding at the top of the pedestal). As can be seen from the image, 2 of the 9 units are given to the pedestal as a whole, including the broad base of foot of the column and the moulding on top.
Deuide the 2 parts into 6, as you may see on the right side of Stilobata. These can be seen on the vertical line to the right of the pedestal.
1 of ye 6 parts is for Basis Cimatium or base below, 1 other to Stilobata Cimatium or decorative moulding above, … the 4 remaining maketh ye square of the great Basse or pedestal, crossed with 2 Diagonall lynes:

The third instruction determines the diameter of the column which stands on the pedestal. The first paragraph determines the diameter of the base of the column, the second the diameter at the top of the column.

In this great square is made a Circle, and observ: where ye Circle crosseth the Diagonall lynes, there make another Square: in which square yu must make another Circle, whose circumference must touch the side of the said sqvare, being ye thicknesse of Scapi (the body of the Pillar) Cimatium, the space betweene ye 2 squares, is to be for the standing forth of the fore Scapi Cimatium.
The last Square spoken of, deuide into 8 parts.  These are enumerated horizontally in the middle of the circles. 
Giue 6 of those parts to another circle, which is the bignesse of Scapi at Tenia or top of ye Pillar. This diameter can be seen at number 6 on the facing page.

The fourth instruction (not reproduced here) determines the details of the base and the upper moulding. A further set of proportions are given for the height of the column, its entasis or curvature, and the capital and other details at the top.

Commentary. Howard Hotson (October 2021)

Further information on Blum and his treatise: Yves Pauwels, 'Blum, Hans' (2009), Architectura, ed. Frédérique Lemerle et Yves Pauwels.