
Vitruvius described as the principal source of proportion among the orders of proportion of the human figure. . According to Leonardo's notes in the accompanying text written in mirror writing it was made as a study of the proportions of the male human body as described in a treatise by the Ancient Roman architect Vitruvius who wrote that in the human body: a palm is the width of four fingers or three inches a foot is the width of four palms and is 36 fingers or 12 inches a cubit is the width of six palms a man's height is four cubits and 24 palms a pace is four cubits or five feet the length of a man's outspread arms is equal to his height the distance from the hairline to the bottom of the chin is onetenth of a man's height the distance from the top of the head to the bottom of the chin is oneeighth of a man's height the maximum width of the shoulders is a quarter of a man's height the distance from the elbow to the tip of the hand is onefifth of a man's height the distance from the elbow to the armpit is oneeighth of a man's height the length of the hand is onetenth of a man's height the distance from the bottom of the chin to the nose is onethird of the length of the head the distance from the hairline to the eyebrows is onethird of the length of the face the length of the ear is onethird of the length of the face Leonardo is clearly illustrating Vitruvius' De architectura 3.1.3 which reads: The navel is naturally placed in the centre of the human body and if in a man lying with his face upward and his hands and feet extended from his navel as the centre a circle be described it will touch his fingers and toes. It is not alone by a circle that the human body is thus circumscribed as may be seen by placing it within a square. For measuring from the feet to the crown of the head and then across the arms fully extended we find the latter measure equal to the former; so that lines at right angles to each other enclosing the figure will form a square. Though he was certainly aware of the work of Pythagoras it does not appear that he took the harmonic divisions of the octave as being relevant to the disposition of form preferring simpler wholenumber ratios to describe proportions. However beyond the writings of Vitruvius it seems likely that the ancient Greeks and Romans would occasionally use proportions derived from the golden ratio most famously in the Parthenon of Athens and the Pythagorean divisions of the octave. These are found in the Rhynd papyrus 16. Care should be taken in reading too much into this however while simple geometric transformations can quite readily produce these proportions the Egyptian were quite good at expressing arithmetic and geometric series as unit fractions. While it is possible that the originators of the design may not have been aware of the particular proportions they were generating as they worked it's more likely that the methods of construction using diagonals and curves would have taught them something. The Biblical proportions of Solomons temple caught the attention of both architects and scientists who from a very early time began incorporating them into the architecture of cathedrals and other sacred geometry. Regarding the Pythagorean divisions of the octave mentioned above these are a set of whole number ratios based on core ratios of 1:2 octave 2:3 fifth and 3:4 fourth which form the Pythagorean tuning. These proportions were thought to have a recognisable harmonic significance regardless of whether they were perceived visually or auditorially reflecting the Pythagorean idea that all things were numbers. 
