1. The first line is given by the "lower" edge of the pointing stick in Pacioli's right hand. This line intersects the top edge of the picture at a significant vertical axis through his the V-shaped gap in the fringe of his hair, and the middle of the knot of his belt.

2. A circle is drawn on this vertical with the diameter given by the height of the picture. This circle intersects the pointing stick exactly where it meets the upper edge of the chalkboard.

3. Two regular pentagrams are inscribed in the circle, one "upright" and one "upside down". The point where they intersect on the horizontal diameter of the circle is the same point at which the pointing stick cuts it. Thus the stick is exactly positioned to define the two pentagrams. The sides of the pentagrams pass through Pacioli's right eye, the two outer knots on his belt, the gap between his 2nd and 3rd fingers on his left hand, the end of the "ink-cylinder" and the clothing of P and his mysterious friend. Notice in particular how his right thumb exactly touches the horizontal of the upside down pentagram.

4. The end of the stick is at an angle of 36 degrees below the horizontal, and therefore a line from this end-point through the circle centre also intersects with the pentagrams. The top of the stick is defined by a horizontal through other intersection points.

5. The book to which Pacioli refers with his left hand would appear to be Euclid. The right hand page is headed with the Roman numerals XI. I suggest the page is open to Elements Vol 4 Proposition XI: To inscribe an equilateral and equiangular pentagon in a given circle.

Related Pages:

Grid Construction of the regular heptagon

Hidden Geometry in Art:
Pierro Della Francesca:
Fra Angelico 
Fra Luca Pacioli
Denderah Zodiac

Geometrical Analysis of the East Meon Crop Circle