ordered the elements of those works so that
I really think again that Vitruvius is interested in this concept of order and the power of architecture to mirror the human body. No matter how many imperfections our bodies can show, I still think Vitruvius is fascinated by the miracle of the human body and the way that it is mathematical, in the same way that a building is.
For if a person is imagined lying back with outstretch arms and feet within a circle whose center is at the navel, the fingers and toes will trace the circumference of this circle as they move about. But to whatever extent a circular scheme may be present in the body, a square design may also be discerned there. For if we measure from the soles of the feet to the crown of the head, and this measurement is compared with that of the outstretched hands, one discovers that this breadth equals the height, just as in areas which have been squared off by use of the set square.
This particular section is interesting because shape is something we often see as being separate to the human body, but Vitruvius is encouraging his audience to see shape as something which in fact the human body operates within. Our limbs can fit within squares and circles and I think Vitruvius must have been fascinated by the way the body had a composition in the same that architecture did. I know others above have commented on the fact that Vitruvius does not seem to take account of the fact that the human body can have many imperfections, and this is a really important point to take further.
correspondence to the likeness of a well-formed human being
This is a really important parallel that Vitruvius now tries to make and I was thinking that his argument/idea is that architecture is a reflection of the human and what it means to be human. Just as buildings have order and proportion so does the human body.
compositional system
But why? Why can there not be beauty in imperfection? I know that's probably a very modern question, but it repeats what I'm saying in the previous comment about why this should be such a stressed point for Vitruvius... I wonder if it is to do with the fact that order is a very important concept in ancient architecture, and the kind of power it can show
Symmetry derives from proportion, which is called analogia in Greek.
This is an important idea in Vitruvius's view of the world and it is no doubt something that we are going to come back to, and I realise also that many of the comments above have focused on these concepts of symmetry and proportion. For me, one of the interesting ideas that is emerging in Vitruvius is the idea of order - we see this especially in the way he is keen to give "orders" of column (Ionic, Doric, Corinthian), but this is true in a mathematical sense too. In this chapter he refers to the Greeks and the ancients quite frequently, and I think this shows the debt that the Romans had towards the Greeks in a cultural sense. It would be interesting to discuss whether Vitruvius sees symmetry and proportion as ways of bringing order to civilisation. I know the Greeks were interested in the idea of creating order out of chaos, and perhaps they expressed this in the way they saw symmetry in both buildings and in the human body, as Vitruvius is suggesting here. I guess I'm asking what are the different ways, both symbolic and practical, in which symmetry is so important to Vitruvius?