Pythagoras of Crotona

Knapp painted the philosopher as a lecturer among his instruments, and Hall's caption complains on his behalf: all too lightly the world has passed over the achievements of the first philosopher to whom it is indebted for so many of the basic theorems of mathematics, music, and astronomy. The plate is that complaint set right. Pythagoras stands in a white robe between classical columns, with a temple and a statue behind him, and everything round him is a proof.

Over his head, in a small triangle on the wall, are ten dots in four rows: one, two, three, four. This is the tetractys, and Hall explains it in two places in the book, once as the sign of the number ten, which Pythagoras held to be the most perfect of all numbers, and once through Theon of Smyrna, who said that to the discerning mind the ten dots revealed the mystery of universal nature. The white pyramid in the philosopher's left hand is the same figure lifted off the page, a triangle in every face. He holds it up the way a teacher holds up the thing he is about to explain.

The rest of the picture is the syllabus. A lyre stands at the left, because Pythagoras found that the intervals of music are ratios of small whole numbers; beside it lie a set square, compasses and a scroll with a branching figure drawn on it. On the table a celestial globe rests on its stand next to a glass flask, and a scroll hangs over the edge with the squares on the three sides of a right-angled triangle drawn out in chequers, the theorem that still carries his name; his right hand points a pair of compasses at it. The plate gathers arithmetic, geometry, music and astronomy round one man because that is the quadrivium, the four mathematical arts of the medieval schools, and Hall wanted his reader to see where it began.

The archive keeps only one mark on this plate, because Hall's caption is about the man and his school and does not read the objects one by one; the tetractys and the pyramid are the exception, since the book explains them elsewhere. The lyre, the globe, the flask and the theorem are described here as seen, and they mean what any student of the last two thousand years would take them to mean. That is the plate's argument: that we are all still in this room.