From DT Online
The image Vitruvian Man drawn by Leonardo da Vinci around 1490 is perhaps his most famous illustration. The image reflects Leonardo's keen interest in proportion and his attempts to relate man to nature. The illustration is a pen ink drawing of a male figure whose outstretched limbs touch the circumference of a circle and the edges of a square. His navel falls in the exact center of the circle.
Since the the time of Pythagoras, the circle was seen in the dome of the sky with its spherical stars and planets and the square was represented by four directions, four seasons, and four elements (i.e. Fire, Air, Earth, and Water). Showing that man was related to both square and circle was important to philosophers. Leonardo achieved this by starting with a perfectly proportioned man and then finding the circle and square in the figure rather than forcing the figure to fit. The result is that circle and square are only tangent at the base and have different centres.
The ideas on proportion were not Leonardo's alone, but were developed from the writings of the Roman architect Vitruvius. Both men believed that the same principles should be used when designing buildings but Leonardo took the idea further and spent much of his life searching for connections between the structure of the human body and other patterns in nature. In his notes, he proclaimed that Man is the model of the world.