[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor and professor of theology at Oxford, and afterwards Chancellor of St. Paul's and confessor to Edward III. The English ascribed their success at Crecy to his prayers. [506] He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year. [507] "One paltry little year." [508] The title is carelessly copied, as is so frequently the case in catalogues, even of the Libri class. It should read: _Arithmetica thome brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads: _Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare," although of course no works of that period are common. See the editor's _Rara Arithmetica_, page 61. [509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505; Vienna, 1515, with other editions. [510] The colophon of the 1495 edition reads: _Et sic explicit Geometria Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._ This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He studied mathematics and philosophy at Paris, and took the doctor's degree there. He taught at the University of Alcala and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them the _Liber arithmeticae practicae qui dicitur algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium liberalium_ (Alcala, 1516). [511] Star polygons, a subject of considerable study in the later Middle Ages. See note 35 on page 44. [512] "A new theory that adds lustre to the fourteenth century." [513] There is nothing in the edition of 1495 that leads to this conclusion. [514] The full title is: _Nouvelle theorie des paralleles, avec un appendice contenant la maniere de perfectionner la theorie des paralleles de A. M. Legendre_. The author had no standing as a scientist.