"X. Y.--The Chaldeans began the mathematics, in which the Egyptians
excelled. Then crossing the sea, by means {59} of Thales,[110] the
Milesian, they came into Greece, where they were improved very much by
Pythagoras,[111] Anaxagoras,[112] and Anopides[113] of Chios. These were
followed by Briso,[114] Antipho, [two circle-squarers; where is Euclid?]
and Hippocrates,[115] but the excellence of the algebraic art was begun by
Geber,[116] an Arabian astronomer, and was carried on by Cardanus,[117]
Tartaglia,[118] Clavius,[119], Stevinus,[120] Ghetaldus,[121]
Herig_e_nius,[122] Fran. Van Schooten [meaning Francis Van Schooten[123]],
Florida de Beau_m_e,[124] etc."
Bryso was a mistaken man. Antipho had the disadvantage of being in advance
of his age. He had the notion of which the modern geometry has made so
much, that of {60} a circle being the polygon of an infinitely great number
of sides. He could make no use of it, but the notion itself made him a
sophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab
astronomer, and a reputed conjurer in Europe, seems to have given his name
to unintelligible language in the word _gibberish_. At one time _algebra_
was traced to him; but very absurdly, though I have heard it suggested that
_algebra_ and _gibberish_ must have had one inventor.
Any person who meddles with the circle may find himself the crane who was
netted among the geese: as Antipho for one, and Olivier de Serres[126] for
another. This last gentleman ascertained, by weighing, that the area of the
circle is very nearly that of the square on the side of the inscribed
equilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did
not pretend to more than approximation; but Montucla and others
misunderstood him, and, still worse, misunderstood their own
misunderstanding, and made him say the circle was exactly double of the
equilateral triangle. He was let out of limbo by Lacroix, in a note to his
edition of Montucla's _History of Quadrature_.