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P. Mich. 143 = Trismegistos 59769 = LDAB 873 = michigan.apis.3163



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Canonical URI: http://papyri.info/dclp/59769

DCLP/LDAB Data [xml]

Title An Excerpt of Definitions from Euclid
Works
  • Euclides, Elementa 1.Demonstration.1-10
  • Euclides, Definitiones 1-10
Principal Edition P.Mich. 3 143
study 63880. Tiziano Dorandi, "La tradizione papiracea degli "Elementi" di Euclide." in Proceedings of the 20th International Congress of Papyrologists. Copenhagen, 23-29 August, 1992., 306-311. 310
Reference Edition 57536. Eric G. Turner, David H. Fowler, Ludwig Koenen, and Louise C. Youtie, "Euclid, Elements I, Definitions 1-10." in Papyrology = YCS 28 (1985)., P. Mich. III vol. 143 13-24.
Catalog(s) MP3 00366.000
Fragments Ann Arbor, Michigan University, Library P. 925
Support Material papyrus
Support Dimensions 5.5cm wide x 19.2cm high
Date 200 - 299
More from the period between 200 CE and 299 CE
Origin Fundort: Egypt; Schreibort: Egypt
More from Fundort: Egypt; Schreibort: Egypt
Form and Layout papyrus sheet (columns: 1, pagination: 0)
Genre prose; mathematics
Culture literature; science
Religion classical
Images quod.lib.umich.edu/.../x-3163
Print Illustrations YCS 28, 1985, Pl. IV
Availability © Digital Corpus of Literary Papyri. This work is licensed under a Creative Commons Attribution 3.0 License .

Trismegistos: 59769 [source]

Publications P. Mich. 3 143 (1936) = Yale Classical Studies 28 (1985), p. 13-24 (1985)
Inv. no. Ann Arbor, Michigan University, Library P. 925
Date AD 200 - 299
Language Greek
Provenance Egypt[found & written]

Catalog Record: michigan.apis.3163 [xml]

Title Elements I, Definitions 1-10
Author Euclid
Summary Excerpt, on a sheet cut from a letter, of the ten first Definitions of the Elements of Euclid. Private copy, perhaps a memorandum written by a teacher preparing his class
Citations Robbins FE, PMich III, 143, 1936 Turner EG - Fowler DH - Koenen L - Youtie LC, YCS 28, 13-24, 1985, Pl. IV
P.Mich.:2:143
Inv. Id P.Mich.inv. 925
Support/Dimensions 1 papyrus ; 5.5 x 19.2 cm
Condition Complete (Verso only; Recto cut at the top and left)
Lines 29
Recto/Verso Source of description: Verso
Hands Small and awkward hand (Robbins); small, rather personal hand of the third cent. A.D. (Turner et al.)
Origin Unknown
More from Unknown
Language Greek
Date IIIrd century A.D.
More from the period between 200 CE and 299 CE
Note (general) Location: Ann Arbor
Note (general) Pub. status: Verso; Recto: fragment from a letter
Subjects Schools, Greek--Egypt.; Euclid���s Elements.; Literary: Mathematical; Papyrus
Images Recto thumbnail
Images Recto medium
Images Recto large
Images Verso thumbnail
Images Verso medium
Images Verso large
License Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 License.

DCLP transcription: 59769 [xml]

Σημεῖόν ἐστιν, οὗ μόρον(*)
οὐθέν. Γραμμὴ δὲ μῆκος̣
ἀπλατές. Γραμμῆς δὲ πέρα-
τα σημεῖα. Εὐθεῖα γραμμή
5ἐστι{ς}(*), ἥτις ἐξ ἴσου τοῖς ἐ-
φ’ ἑαυτῆς σημείοις κε͂ται(*).
Ἐπιφάνια(*) ἐστὶ̣(*), ὃ̣ μ̣ῆ̣κ̣[ο]ς̣ κα[ὶ]
πλάτος μόνον ἔχει. Ἐπι-
φανείας δὲ πέρατα γραμαί(*).
10Ἐπίπεδος ἐπιφάνιά(*) ἐστιν,
ἥτις ἐξ ἴσου τα̣ῖ̣ς ἐφ’ ἑαυ
εὐθεαις(*) κεται(*)-
τῆς. Ἐπίπεδος δὲ γωνί-
α ἐστὶν ἐν ἐπιπέδῳ δύ-
15ο γραμμῶν ἁπτομένων
ἀλλήλων καὶ μὴ ἐπ’ εὐ-
θείας κιμένων ἡ πρὸς
ἀλλήλας(*) τῶν γραμῶν(*)
κλίσις. Ὅταν δὲ αἱ ἔκου-
20σαι γραμμαὶ εὐθεῖαι
ὦσι, εὐθ̣ύγρ̣αμος̣ ἡ γωνί-
α καλεῖσθαι̣.(*) Ὅταν δὲ εὐ-
θεῖα ἐπ’ εὐθεῖαν στ̣αθεῖ-
σα{ν} τὰς ἐφεξος(*) γω-
25νίας ἴσας ἀλλήλας̣(*) ποι-
ῇ, ὀρθὴ ἑκατέρα τῶν ἴ-
σων γωνιῶν ἐστι,
28καὶ ἡ ἐφεστηκυῖα γραμή κάθετος καλεῖται(*)
——

Apparatus


^ 1. l. μόριον, papyrus : μέρος mss.
^ 5. papyrus : ἐστιν mss.
^ 6. l. κεῖται
^ 7. l. Ἐπιφάνεια, papyrus : Ἐπιφάνεια δὲ mss.
^ 7. l. ἐστιν
^ 9. l. γραμμαί
^ 10. l. ἐπιφάνειά
^ 12. l. εὐθείαις
^ 12. l. κεῖται
^ 14-18. l. κειμένων, papyrus : ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ’ εὐθείας κειμένων πρὸς ἀλλήλας mss.
^ 18. l. γραμμῶν
^ 19-22. l. καλεῖται, i.e. εὐθύγραμμος, i.e. ἔχουσαι, papyrus : Ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν, εὐθύγραμμος καλεῖται ἡ γωνία. mss.
^ 24. l. ἐφεξῆς
^ 25. l. ἀλλήλαις
^ 28-29. l. γραμ |μή, papyrus : εὐθεῖα κάθετος καλεῖται, ἐφ’ ἣν ἐφέστηκεν. mss.

Editorial History; All History; (detailed)

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