Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
Bologna, 1612, folio.[94]
Rheticus,[95] Vieta, and Cataldi are the three untiring computers of
Germany, France, and Italy; Napier in Scotland, and Briggs[96] in England,
come just after them. This work claims a place as beginning with the
quadrature of Pellegrino Borello[97] of Reggio, who will have the circle to
be exactly 3 diameters and 69/484 of a diameter. Cataldi, taking Van
Ceulen's approximation, works hard at the finding of integers which nearly
represent the ratio. He had not then the _continued fraction_, a mode of
representation which he gave the next year in his work on the square root.
He has but twenty of Van Ceulen's thirty places, which he takes from
Clavius[98]: and any one might be puzzled to know whence the Italians got
the result; Van Ceulen, in 1612, not having been translated from Dutch. But
Clavius names his comrade Gruenberger, and attributes the approximation to
them {70} jointly; "Lud. a Collen et Chr. Gruenbergerus[99] invenerunt,"
which he had no right to do, unless, to his private knowledge, Gruenberger
had verified Van Ceulen. And Gruenberger only handed over twenty of the
places. But here is one instance, out of many, of the polyglot character of
the Jesuit body, and its advantages in literature.