## [In Greek:] Deodomena kai Marinou Philosophou eis dedomena Eukleidou Hypomnema. Euclidis Data Opus ad veterum Geometriae Autorum Archimedis, Apollonii, Pappi, Eutocii... Marini Philosophi Commentarius Graece & Latine, quo Dati natura, Datorumque Euclideorum utili¬tates explicantur.

Paris: Melchior Mondiere, 1625.

Very rare *editio princeps* of this important text by Euclid, his only work in pure geometry, other than the *Elements*, to have survived in Greek. It is here accompanied by a commentary, or rather an introduction, by Marinus of Naples (5th century AD), the pupil and biographer of Proclus. Although the importance of the first printing of any Euclidean text goes without saying, the work is of particular interest given contemporary developments in French geometry — Descartes, Mersenne, Fermat, etc., to whose circle the translator Claude Hardy belonged.

“The *Data* … is closely connected with books I-VI of the *Elements*. It is concerned with the different senses in which things are said to be given. Thus areas, straight lines, angles, and ratios are said to be “given in magnitude” when we can make others equal to them. Rectilineal figures are “given in species” or “given in form” when their angles and the ratio of their sides are given. Points, lines, and angles are “given in position” when they always occupy the same place, and so on. After the definitions there follow ninety-four propositions, in which the object is to prove that if certain elements of a figure are given, other elements are also given in one of the defined senses” (*DSB* IV.524).

The most interesting propositions are a group of four which are exercises in geometrical algebra corresponding to *Elements* 11.28, 29. Proposition 58 reads: “If a given area be applied to a given straight line so as to be deficient by a figure given in form, the breadths of the deficiency are given;” Proposition 84, which depends upon it, reads: “If two straight lines contain a given area in a given angle, and if one of them is greater than the other by a given quantity, then each of them is given.” These propositions are together equivalent to asserting the existence of the solution of a certain quadratic equation. Propositions 59 and 85 give the corresponding theorems for the excess, and are again equivalent to a quadratic equation.

“A clue to the purpose of the *Data* is given by its inclusion in what Pappus calls the *Treasury of Analysis*. The concept behind the *Data* is that if certain things are given, other things are necessarily implied, until we are brought to something that is agreed. The *Data* is a collection of hints on analysis. Pappus describes the contents of the book as known to him; the number and order of the propositions differ in some respects from the text which has come down to us” (*ibid*.).

Claude Hardy (1598?-1678) was a lawyer by profession, but took part in the weekly meetings of Roberval, Mersenne, and the other French geometricians in the Académie Mersenne, and was a friend of Claude Mydorge, who introduced him to Descartes. In his *Examen* of 1630, and again in his *Refutation* of 1638, Hardy exposed the fallacy of Paul Yvon’s solution to the problem of the duplication of the cube, a problem which attracted the attention of several seventeenth century writers, including Viéte, Descartes, Fermat, and Newton. Hardy also engaged in the dispute between Fermat and Descartes over the former’s method of maxima and minima; Hardy, together with Desargues and Mydorge, supported Descartes, while Fermat found two zealous defenders in Roberval and Pascal. “Hardy owed his greatest fame, however, to his knowledge of Arabic and other exotic languages, and in particular, to his edition of Euclid’s *Data* (1625), the *editio princeps* of the Greek text, together with a Latin translation” (DSB, under Hardy).

OCLC lists copies at New York Public, Harvard, Stanford, Wisconsin and Hong Kong only. *DSB* IV.524; Brunet 11.1081; Graesse II, p. 511; Hoffmann II, p. 167; Riccardi, *Bib. Euclidea* 1625; Steck VIII.10.

4to (223 x 178 mm), pp 8, 181, [3:errata], text in Latin and Greek in parallel columns, printer’s device on title, woodcut initials and headpieces, woodcut diagrams in text, printed marginal notes. Contemporary limp vellum. A very fine and completely unrestored copy.

Item #3427

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Price:
$12,500.00
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