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2. The Data.
The Data (δεδομένα) are included by Pappus in the Treasury of Analysis (τόπος ἀναλυόμενος), and he describes their contents1 They are still concerned with elementary geometry, though forming part of the introduction to higher analysis. Their form is that of propositions proving that, if certain things in a figure are given (in magnitude, in species, etc.), something else is given. The subjectmatter is much the same as that of the planimetrical books of the Elements, to which the Data are often supplementary. We shall see this later when we come to compare the propositions in the Elements which give us the means of solving the general quadratic equation with the corresponding propositions of the Data which give the solution. The Data may in fact be regarded as elementary exercises in analysis.
It is not necessary to go more closely into the contents, as we have the full Greek text and the commentary by Marinus newly edited by Menge and therefore easily accessible2.
3. The book On divisions (of figures).
This work (περὶ διαιρέσεων βιβλίον) is mentioned by Proclus3. In one place he is speaking of the conception or definition (λόγος) of figure, and of the divisibility of a figure into others differing from it in kind; and he adds: “For the circle is divisible into parts unlike in definition or notion (ἀνόμοια τῷ λόγῳ), and so is each of the rectilineal figures; this is in fact the business of the writer of the Elements in his Divisions, where he divides given figures, in one case into like figures, and in another into unlike4.”
“Like”
and “unlike”
here mean, not “similar”
and “dissimilar”
in the technical sense, but “like”
or “unlike in definition or notion”
(λόγῳ): thus to divide a triangle into triangles would be to divide it into “like”
figures, to divide a triangle into a triangle and a quadrilateral would be to divide it into “unlike”
figures.
The treatise is lost in Greek but has been discovered in the Arabic. First John Dee discovered a treatise De divisionibus by one Muhammad Bagdadinus5 and handed over a copy of it (in Latin) in 1563 to Commandinus, who published it, in Dee did not himself translate the tract from the Arabic; he in 15706. Dee did not himself translate the tract from the Arabic; he
1 Pappus, VII. p. 638.
2 Vol. VI. in the Teubner edition of Euclidis opera omnia by Heiberg and Menge. A translation of the Data is also included in Simson's Euclid (though naturally his text left much to be desired).
3 Proclus, p. 69, 4.
4 ibid. 144, 22-26.
5 Steinschneider places him in the 10th c. H. Suter (Bibliotheca Mathematica, IV_{3}, 1903, pp. 24, 27) identifies him with Abū (Bekr) Muh. b. 'Abdalbāqī al-Baġdādī, Qād|ī (Judge) of Māristān (circa 1070-1141), to whom he also attributes the Liber judei (? judicis) super decimum Euclidis translated by Gherard of Cremona.
6 De superficierum divisionibus liber Machometo Bagdadino adscriptus, nunc primum Ioannis Dee Londinensis et Federici Commandini Urbinatis opera in lucem editus, Pisauri, 1570, afterwards included in Gregory's Euclid (Oxford, 1703).
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
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