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.
