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According to Vitruvian principle, measure and number have ‘ideal’ qualities which should be used to enhance a design and move it as close as possible to natural perfection. 

Renaissance artists and architects believed that perfection derived from the imitation of Nature. In architecture this required that form should be controlled by certain geometries, and that modules should regulate the dimensions of the whole design. Vitruvius had taught the importance of achieving a congruity of all the parts so that measurements and form are interrelated. He called this approach dispositio. Buildings should be governed by symmetria, which means not only that one form balances another across an axis (the modern meaning of ‘symmetry’), but also that every element is governed by the same ratios as those of the whole, and that a consistent module is used throughout. The module that established the fundamental beauty of a building – its general form – was usually a standard measure, such as the foot. The surface ornament would be controlled by a module taken from some principal ornament, commonly the diameter of a column. Each module would be multiplied by certain preferred numbers which have their roots in classical theory, especially the Pythagoreo-Platonic number sequences which related number to universal harmony. 

Marcus Vitruvius describes the perfect numbers in relation to ideal measure. He explains that buildings were designed using a standard which reflected human proportions, and that there existed a traditional belief that symmetry in architecture echoed the principles governing symmetry of the human body. A point he held to be particularly relevant to sacred architecture. The ‘perfect’ numbers are to be found in ‘ideal’ human proportions. The ancient measures – the finger (digitus), palm (palmus), foot (pes) and cubit (cubitus; the length of the forearm) – are dominated by two ‘perfect’ numbers, 6 and 10: 10 is ‘perfect’, Vitruvius explains, because of our 10 fingers, 4 of which make a palm, while 4 palms make a foot; 6 is ‘perfect’ because it is the sum of its factors and because the foot is one-sixth of a man’s height. These numbers combine to make the ‘most perfect’ of all numbers, 16. 

Leon Battista Alberti, set out to examine this reasoning in his Tabulae Dimensionum Hominis (Tables of Human Dimensions), appended to his treatise De Statua(On Sculpture). Through a blend of classical and medieval commentaries on human proportions and his own measurements, Alberti repeated Vitruvius’s proportional schema in general (a foot is one-sixth of a man’s height, etcetera.), though he switched from the description by Vitruvius of an ‘ideal’ man whose navel is the centre point of a square and circle (a symbolic centre point) to one whose centre is marked by the base of the pelvis (the true mid-height of a man). Although in this system the navel is not centrally located, Alberti accorded it a significant proportion in relation to a man’s overall height, using the ‘perfect’ numbers: the distance from the foot to the navel and that from the foot to the top of the head are in a ratio of 6:10. Moreover, his ‘tables’ show that this proportion is distributed throughout many parts of the body. 

In his treatise on architecture, Alberti related this experience to the Vitruvian rules which determine the proportions of the classical orders:

When [the ancients] considered a man’s body, they decided to make columns after its image. Having taken the measurements of a man, they discovered that the width, from one side to the other, was a sixth of the height, while the depth, from navel to kidneys, was a tenth. The commentators of our sacred writings also noted this and judged that the Ark built for the Flood was based on the human figure. The ancients may have built their columns to such dimensions, making some six times the base, other ten times.

On the proportions of man and Noah’s Ark, Alberti was following the 4th- century writings of St Augustine, but the parallel between sacred Christian numbers and those of ancient ‘pagan’ columns was his own. Recent studies have shown that this association between man, a God-given archetype, and a primitive formulation of the orders was of fundamental importance to the principal exponents of Quattrocento architecture, the evidence of its application has been found in Alberti’s church of S. Andrea in Mantua, and Bramante’s Tempietto in Rome (a building greatly admired by Andrea Palladio): combinations of 6, 10, 16 permeate and regulate their form and measures. 

The Vitruvian notions of dispositioand symmetria, which determine the elements and numbers within a building like this, were brought together by Alberti under a single heading, concinnitas – a blend of number, measure, proportion and arrangement, which was wholly classical in conception.