[GALILEI, Galileo] – VIVIANI, Vincenzo (1622-1703). Quinto libro degli elementi d’ Euclide, ovvero scienza universale delle proporzioni spiegata colla dottrina del Galileo. Florence: Condotta, 1674 [1676]. [Bound with:] –. Enodatio problematum universis geometri propositorum. Florence: Joannis Gugliantini, 1677.

Signed presentation copy of two first editions of important works by Galileo's famous pupil and assistant, including previously unpublished texts from Galileo himself, in contemporary calf. There are two recorded issues of the first work; the present copy is intermediate between these two. The first issue appeared in 1674, with text paginated to 149, followed by three unnumbered pages of addenda and privilege; the work was reissued in 1676, with a further section written in answer to questions posed by a Leiden student in 1675, the two plates, and the dedication dated 16 May 1676. However, unlike most copies of the second issue, in this copy the title-page date remained 1674. See Gamba 1048 (résumé in Riccardi). The work comprises a group of previously unpublished writings by Galileo, together with pieces by Torricelli and Viviani, including the text of a manuscript fragment containing Galileo's demonstration of the fifth and seventh propositions of Euclid given to Viviani by Cardinal de' Medici. The second work contains Viviani's treatise on the problem of trisecting an angle, using a method based on the equilaterial hyperbola or the conchoid. I Carli and Favaro 339; Cinti 151 (first issue only) and 152; Riccardi I.2 625.2; II Riccardi I.2 627.4

Two works in one, quarto (242 x 170mm). I: half title, 2 folding engraved plates, diagrams in text, woodcut initials and ornaments (neatly repaired wormholes to lower margin of title, some light foxing, a few sheets toned); II: half title, 4 folding engraved plates (light foxing). Contemporary calf, spine gilt in compartments, speckled edges (joints splitting but secure, repairs to spine, a few wormholes). Provenance: partially lined-through autograph dedication to an "illustrissimo et eccellentissimo Signore" from Viviani (half-title verso of first work) – sparse ink corrections to first work possibly by Viviani – "V.V." (Viviani? signet stamp at close of text of first part, p. 149) – Piero Ginori Conti, Prince of Trevignano, 1865-1939 (engraved bookplate of the Florence skyline by Michelassi after Lessi).