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23 Jan 2024
updated 23 Jan 2024

The Philosophical Pearl

The central figure in this tableau is the Margarita Philosophica (Philosophical Pearl), frontispiece to the encyclopaedia compiled by Gregor Reisch (ca 1470-1526) and first published in 1503.

The first seven sections in the Margarita cover the seven liberal arts, beginning with the elementary trivium (logic, rhetoric and grammar) – whence the adjective 'trivial' – and followed by the more advanced quadrivium (arithmetic, music, geometry and astronomy). The last five books discuss natural and moral philosophy.

The upper area is embellished with images of the popes Augustine, Gregory and Ambrose, and the lower area with images of Aristotle and Seneca, as far as I can tell.

This particular manifestation of the Margarita, Typus arithmeticae, represents arithmetic, of course, the first subject of the quadrivium, and the seated figures evidently represent Boethius and Pythagoras.

On the left, Boethius, the snappily dressed confident one is using the arithmetical skills introduced to Europe centuries earlier by Fibonacci. On the right however, Pythagoras, the shabbily clad scruffy one, is having a hard time with his abacus, the traditional aid to computation.

But the historical Pythagoras (570 BC – 490 BC) would have scorned the abacus, redolent of logistikos, the marketplace and the workshop. And Boethius (ca 480 – 524) was more of a philosopher, author of the Consolation of Philosophy, than a devotee of mathematikos. The so-called Rota Fortunae (Wheel of Fortune) is closely associated with him (and his own misfortune).

Be all that as it may, this image is a thought-provoking illustration of the art and practice of arithmetic.

αριθμός είναι όλος
number is all

This next manifestation of the Margarita, Typus geometricae, represents geometry, of course, the third of the quadrivium needs a certain amount of interpretation, reflecting Kepler's interest in calculating the capacities of wine-barrels

(24 Sep 1501 - 21 Sep 1576)

Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.

There’s a quirky connection between the notorious modern criminal organisation which refers to itself as Cosa Nostra (‘Our Thing’) and the mediӕval algebraists who were described as ‘cossists’ as the solution they sought was known not as ‘x’ but as cosa (‘the thing’)!