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De quadratura circuli libri duo, ubi multorum quadraturae confutantur, & ab omnium impugnatione defenditur Archimedes. Eiusdem, annotationum opuscula in errores Campani, Zamberti, Orontii, Peletarii, Io. Penae interpretum Euclidis.

Lyon: apud Gulielmum Rouillium, sub scuto Veneto, 1559.

Collation: 8vo: a–s⁸, 144 leaves, pp. 283 [5] (last 2 leaves blank, s8 pasted down as an endleaf). Italic letter with Roman headings; woodcut printer’s device on title, woodcut headpieces and initials, woodcut diagrams in the text, several full page.
Condition: 162 x 105mm. Faint paper discolouration, waterstains in upper outer corners; wormholes in first and last few leaves but not affecting the text.
Binding: Contemporary Italian limp vellum, yapp fore-edges, gilt and gauffered page edges, MS spine lettering. Spine torn and defective. In a cloth folding case.
Provenance: Inscription on title Dom. Prof.  Neap[?]. Soc. Je. Cat. inscrip pro bo[?]’ on title and ‘Venetia’ on front pastedown.
References: Baudrier IX, p. 259; Adams B3358; Thomas-Stanford XX.
Price: £2,200

First (only) edition.

¶ An attack on circle squarers and a commentary on the errors of several interpreters of Euclid. Apart from his 6 years in Paris (1522–1528), where he studied with Oronce Finé, Buteo lived a monastic life at the Abbaye de St Antoine in France. He had no pupils but wrote several books, though the first was not published until he was sixty years old. These are Opera geometrica (1554); the present work;  Apologia (1562); and Logistica (1559) which Verdonk considers his most important work.

Except for this work, which Thomas-Stanford catalogues under fragmentary editions of Euclid, the only sixteenth-century Euclid printed in Lyon was Peletier’s folio edition printed by de Tournes in 1557. Buteo’s text is not however, as one might imagine given his hostility to Peletier, a response to Peletier’s edition, because Buteo’s privilège to print the work was granted to him in January 1553. This was in the year before his first published work, the Opera geometrica appeared.

Nicholas Pickwoad has kindly looked at images of the binding and identified it as Italian. He tells me that while gilt edges on a plain parchment binding are not unknown, they are not common and represent ‘the top end of the laced-case heirarchy’. It seems that Italian owners appreciated the plain exterior of the covers of their books, in more elegant work leaving the decoration to the edges and endbands.

<<[In this work] Buteo refutes the pretensions of those who claimed to have found the solution of the quadrature, most notably those of his master, Oronce Finé. By contrast, he discusses appreciatively the approximations found by Bryson, Archimedes, and Ptolemy. He also mentions two approximate values for [pi]: 3-17/120 (from Ptolemy) and [square root]10 (Indian, although he believed it to be Arab). 

In the second part of this work, Buteo criticizes errors of many of his contemporaries, particularly in terminological questions. An interesting point is his proof that the author of the proofs of Euclid’s Elements was not Theon, as was the current opinion, but Euclid himself. Here, too, are the beginnings of the famous dispute involving Peletier, Clavius, and many others of the angle of contact. In the Apologia (1562) Buteo pursued his refutation of Peletier’s theories.

>>J.J. Verdonk, DSB 2, 618.