The 2006 book by Branko Mitrović and Stephen R. Wassell, Andrea Palladio: Villa Cornaro in Piombino Dese, which was based on a 2003 survey as well as supplementary measurements made in 2004, contains analyses that suggest several potential aspects of Palladio’s design methodology for the villa. This present paper offers additional analyses, based not only on the previous data but also on subsequent measurements that the author took of column diminution as well as the ceiling heights of the main hall and the upper-story hall of the villa.
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Palladio uses both grossezza (thickness) and diametro (diameter) in his treatise (see, for example, Palladio 1997: 18ff.), but in what follows I will use only “diameter” for simplicity.
Regarding all of this analysis, please see (Mitrović and Wassell 2006: 41ff) for further details.
It should be observed that it is the column diameter at the bottom that is used as the module.
For a nice discussion of Palladio’s repetition of ratios in the horizontal and vertical directions, see Mitrović (2004): 70ff.
As noted in the 1997 translation, the “[sic]” here refers to the fact that Palladio means chapter 3, at least according to our modern division of chapters. Palladio’s chapter reference is in keeping with that of Fra Giocondo (1511). Our modern division of chapters did not come into being until the edition of Vitruvius published by Johann Gottlob Schneider in 1807. I am indebted to Kim Williams for this observation.
Palladio’s error has been previously described in (Vila Domini 2003).
Both Vitruvius and Daniele Barbaro after him would explain that this is in keeping with what nature teaches us, since growing things such as trees are wider at the base and thinner at the top (Barbaro 1567: 133 and 214; Williams 2019: 231 and 345).
I was assisted by María Celeste Delgado-Librero in the 2007 supplementary survey.
Even using the smaller upper-hall ceiling height measured in 2007, the ratio 8975:7310 is only about 0.2% off of 16:13.
See (Robison 1998–1999: 177ff) for a detailed discussion, especially pp. 179–180 regarding the Villa Poiana.
Just to reiterate, we would expect our measured heights to be slightly less than what they were when first constructed, both because of sagging and because of the stucco applied to the ceiling; as for Palladio’s specifications in his treatise, we saw above that they seem to be approximations.
This sequence was described in 1202 by Leonardo of Pisa, posthumously known as Fibonacci, in a problem on the breeding pattern of rabbits (Fibonacci 2002: 404). The rule of the sequence, which was the result of Fibonacci’s model for how pairs of rabbits breed, is that each new term is the sum of the previous two terms. Modern authors often start the sequence with 1 and 1 (or even 0 and 1), rather than 1 and 2 as Fibonacci did.
In fact, March suggests that the first of these, 1, 10, 11, 21, 32, 53, …, may have been an inspiration for Palladio at the Villa Cornaro, since 53:32 equals 26½:16 (and it should be noted that both 10 and 21 appear). This conjecture certainly has merit, but while Palladio uses 26 ½ as a dimension in his treatise, we have seen that 26 is much more prominent in the villa as constructed.
While Kepler may have been the first to write about this relationship, he may not have been the first to have known about it. For example, Roger Herz-Fischler describes an annotated copy of Pacioli’s 1509 edition of Euclid’s Elements showing the use of the numbers 89, 144, and 233 to develop a close approximation of the extreme and mean ratio, and he states that “it appears from the handwriting that the annotator was an Italian writing in the early part of the 16th century” (Herz-Fischler 1998: 157).
For my previous extended note regarding Wittkower’s interpretation of the memorandum, see (Belli 2002: 26). The case for Alberti was much easier for Wittkower to make, of course, since Alberti’s De re aedificatoria had much more philosophical content than Palladio’s Quattro libri.
This is based on private correspondence with Kim Williams, who has just completed a translation of Barbaro’s Vitruvius (Williams 2019).
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I would like to thank the perspicacious reviewer of this article, who I eventually learned is Elwin C. Robison, for his extremely insightful comments and suggestions. Many thanks as well to Kim Williams, who provided invaluable feedback on multiple occasions throughout the writing process.
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Wassell, S.R. A Revised Analysis of the Villa Cornaro. Nexus Netw J 21, 383–403 (2019). https://doi.org/10.1007/s00004-019-00447-2
- Geometric analysis
- Fibonacci sequence