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= Trismegistos 59496 = LDAB 596



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Canonical URI: http://papyri.info/dclp/59496

DCLP/LDAB Data [xml]

Title Demetrius Laco, De geometria
Work Demetrius Laco, De geometria
Principal Edition 83608. Johan Ludvig Heiberg, Quelques papyrus traitant de mathématiques , (1900). https://archive.org/details/oversigtoverdetk1900kong/page/146
Reference Edition 83386. Anna Angeli and Tiziano Dorandi, "Il pensiero matematico di Demetrio Lacone," CronErcol, 17 (1987), pp. 89-103. Subscriptio col. 8 col. 9 col. 10 col. 11 col. 12 col. 13
Partial Edition 83678. Enzo Puglia, "Schede demetriache," Papyrologica Lupiensia, 12 (2003), pp. 131-142.
Previous Edition 83801. Vittorio De Falco, L'epicureo Demetrio Lacone, (Napoli 1923). Subscriptio col. 8 col. 9 col. 10 col. 11 col. 12 col. 13
Fragments P.Herc. 1061 col. 14; P.Herc. 1061 col. 15; P.Herc. 1061 col. 16; P.Herc. 1061 col. 10; P.Herc. 1061 col. 11; P.Herc. 1061 col. 12; P.Herc. 1061 col. 13; P.Herc. 1061 col. 8; P.Herc. 1061 col. 9
Support Material papyrus
Date 2. Hälfte II - 1. Hälfte I v.Chr.
More from the period between 150 BCE and 51 BCE
Origin Fundort: Herculaneum (Campania, Italy); Schreibort: Italy ?; Pisones (Italy)
More from Fundort: Herculaneum (Campania, Italy); Schreibort: Italy ?; Pisones (Italy)
Form and Layout papyrus roll (columns: 7+)
Genre prose; philosophy; mathematics
Culture literature
Religion classical
General Notes There are two geometric designs with Greek capitals for each angle on the drafts of the papyrus. On the one hand, a three-sided pyramid with an inscribed equilateral triangle can be found on the rigth-hand side of column 11 ll. 14-18, while on the other hand, there is another equilateral triangle separated by a straight line on the right-hand side of column 13, ll. 4-6. Both pieces can be viewed on the following page: http://clp.classics.ox.ac.uk/gsdl/collect/PHerc/index/assoc/HASH0114/2e49ad6d.dir/herc.v0004.n0912.a.01.hires.jpg
Images cispe.org/.../de_geometria; chartes.it/.../1087
Print Illustrations G. Cavallo, Libri scritture scribi a Ercolano, Naples 1983, pl. 8; D.H.Fowler, The Mathematics of Plato's Academy, Oxford 1987, p.203 fig.1
Availability © Digital Corpus of Literary Papyri. This work is licensed under a Creative Commons Attribution 3.0 License .

Trismegistos: 59496 [source]

Publications De Falco, L'epicureo Demetrio Lacone p. 96-98 (1923) = Bulletin de l'Académie royale des sciences et des lettres de Danemark (1900), p. 154-171 (1900) = Del Mastro, Titoli e annotazioni bibliologiche nei papiri greci di Ercolano p. 220-221 no. 65 (2014)
Inv. no. Naples, Biblioteca Nazionale 108494/1049
Date BC 150 - 50
Language Greek
Provenance Italy, Campania - Herculaneum (Ercolano)[found]; Italy[written]

Introduction

This papyrus has been digitally edited by Marcel Moser and revised by Vincenzo Damiani and Holger Essler as part of the Project Anagnosis and the Würzburger Zentrum für Epikureismusforschung.

DCLP transcription: 59496 [xml]

column 8P.Herc. 1061 col. 8
Sketched 1787-1806 by Giuseppe Casanova

  ̣α̣σησ[⁦ -ca.?- ⁩]
[ε]στιν ο̣ὕτ[ως⁦ -ca.?- ⁩]
[  ̣  ̣  ̣]σ[  ̣  ̣]  ̣ τ[ὴν δοθεῖσαν]
[εὐ]θήα̣ν̣ κα̣ὶ τ[ὸ ἥμισυ]
5ταύτη[ς] τεμοῦ[μεν] κα[ὶ]
πάλιν τὸ τῆς [ἡμ]ισή-
ας ἥμ[ισ]υ καὶ το[ῦτο] μέ-
[χ]ρι τ̣[οῦ ἀπείρ]ο[υ], λύσιν
[ἂν ἔσ]χ̣ε· τῆ[ς γὰρ] ἐλ̣[α-]
10ττώσεως ἐπ' ἄπειρ[ο]ν
[γι]νομένης, ἐπ' ἄπει-
[ρο]ν ἡ τομ̣ὴ ἔσται. τα column 9P.Herc. 1061 col. 9
Sketched 1787-1806 by Giuseppe Casanova

[2 lines missing]
3[  ̣  ̣  ̣  ̣  ̣  ̣  ̣]  ̣τει[  ̣  ̣κύ-]
κλ̣ο̣ς̣ [ἐ]στ[ὶ σ]χῆ̣[μα] ἐ[πί-]
5πεδο[ν ὑ]πὸ [μι]ᾶς γρα[μ-]
μῆς [περι]εχόμε[ν]ον,
π̣ρὸς [ἣν] ἀφ' ἑ[νὸς] ση[με-]
ίο[υ τῶν ἐ]ντὸ[ς το]ῦ κύ-
κλου κ̣ε̣ιμέν[ω]ν [π]ᾶ-
10σαι αἱ πρ[οσ]πείπτου-
σαι εὐ̣[θῆ]αι ἴσαι [εἰσίν·]
[ο]ὕτω [γὰρ αὐτὸν ὁρί-]
[ζου]σιν ο[ἱ γεωμέτραι] column 10P.Herc. 1061 col. 10
Sketched 1787-1806 by Giuseppe Casanova

σε[  ̣  ̣  ̣  ̣] τ̣ὴ̣ν̣ β̣άσιν. ἀ-
νίσου δε̣[⁦ -ca.?- ⁩]
δ̣ο̣θ[εισ  ̣  ̣  ̣  ̣  ̣  ̣]ρα  ̣ο
[  ̣  ̣]ν̣[- ca.9 -]αν̣[⁦ -ca.?- ⁩]
5[⁦ -ca.?- ⁩]ινο̣[⁦ -ca.?- ⁩]
  ̣[⁦ -ca.?- ⁩]
[  ̣  ̣  ̣  ̣  ̣  ̣  ̣]  ̣α[⁦ -ca.?- ⁩]
του[  ̣  ̣]βωσιν  ̣τ[  ̣  ̣]  ̣  ̣  ̣
δοθ[εῖ]σ̣αν [γωνίαν] ἔστ̣ι̣ν̣
10δ[ί]χ̣α̣ τεμ[εῖν. τὸ] τ̣ὴ̣ν̣
——
δοθεῖσαν γωνίαν [δ]ίχ[α]
τ[εμεῖ]ν π[ρο]λαμβάνου-
σ[ιν, ὅ]τ̣ι δ[ύο] δοθε[ισῶν]
εὐθ[ηῶ]ν ἀν̣[ίσω]ν̣ ἀ̣[πὸ]
15τῆ̣ς̣ [μεί]ζον[ος τῆι ἐλάτ-]
τον[ι ἴση]ν [ἀφε]λεῖν ἔσ-
[τι]ν κ[α]ὶ̣ τ̣ὰ̣ ἄλλα τ[ο]ιου-
[τό]τροπα. χά̣ριν δὲ τού-
[του] λ̣εγομέν[ου  ̣  ̣  ̣  ̣  ̣  ̣] column 11P.Herc. 1061 col. 11
Sketched 1787-1806 by Giuseppe Casanova
Sketched 1787-1806 by Giuseppe Casanova

α[  ̣  ̣]θα[  ̣]αι[  ̣  ̣  ̣]  ̣ιος τῆς
[  ̣  ̣  ̣]ου̣[  ̣  ̣ἐλάτ]τονι α. Δ
[  ̣  ̣  ̣  ̣  ̣  ̣]τε ἄ̣\λ̣/λον [  ̣  ̣  ̣]ν
[  ̣  ̣  ̣  ̣  ̣  ̣]τῆς δοθείσ̣η[ς]
[5 lines missing]
10[⁦ -ca.?- ⁩ἔστω,]
φα̣σ̣ίν, ἡ δεδομέν[η γω-]
νία ἡ̣ περιεχομ[ένη]
Α̣[ὑπὸ] τῆς ΑΒ
[π]λ̣ευ̣[ρᾶς]
15κ[αὶ τῆς Α]Γ
καὶ ση[μεῖον]
τῆς ΑΒ
πλευρᾶς
[Δ, δεῖ] ἀ[φ-]
20[ε]λ[εῖ]ν̣ μῆκος τὸ ΑΔ ἱκα[νὸν] column 12P.Herc. 1061 col. 12
Sketched 1787-1806 by Giuseppe Casanova

[- ca.10 -] καὶ τῶν
[- ca.9 -]ν τὸ̣ τρ̣ί-
γω̣[νον ἐπὶ τ]ῆ̣ς̣ Δ[Ε] καὶ
αἱ β[  ̣  ̣  ̣  ̣  ̣  ̣  ̣  ̣]αι ΖΕ καὶ
5[Δ]Ζ[⁦ -ca.?- ⁩]
[2 lines missing]
8[  ̣  ̣]ι̣  ̣  ̣[  ̣  ̣  ̣  ̣  ̣  ̣  ̣  ̣]η[⁦ -ca.?- ⁩]
τὸν η̣[  ̣  ̣  ̣  ̣  ̣  ̣]τὴν τ[έτ-]
10μη̣[ται ὑπὸ τῆς⁦ -ca.?- ⁩]
ἀν[ίσου⁦ -ca.?- ⁩]ΑΔ[⁦ -ca.?- ⁩]
[ἐπ]εὶ οὖν [ἴση ἐστὶν ἡ] Α[Δ]
τῆι Α[Ε] καὶ κο̣[ινὴ ἡ ΑΖ,]
δύ[ο ἄρα δυσὶν ἴσαι αἵ]
15τ̣ε Α̣Δ [καὶ] ΑΖ [καὶ αἱ ΑΖ]
καὶ ΑΕ καὶ β̣άσ̣ι̣ς ἡ ΔΖ
τῆι ΕΖ· ἰ[σ]όπλευ̣ρον γὰρ
συνεστάθ̣η τ[ρίγ]ων̣ο̣ν·
——
οὗ [αἱ] Ζ̣Δ καὶ Ζ[Ε]
20[  ̣  ̣  ̣  ̣  ̣  ̣]ν[⁦ -ca.?- ⁩] column 13P.Herc. 1061 col. 13
Sketched 1787-1806 by Giuseppe Casanova

[⁦ -ca.?- ⁩] ἐπὶ τῆς δο-
θείσης̣, φασίν, εὐθή̣[ας]
τῆς ΜΝ
τρίγω-
5νον̣ [ἰσό-]
π̣λ[ευρον]
[συνεστάτω]
[1 line missing]
9[⁦ -ca.?- ⁩] δει
10[⁦ -ca.?- ⁩]  ̣[⁦ -ca.?- ⁩]
[⁦ -ca.?- ⁩]ε̣  ̣  ̣[  ̣]  ̣  ̣τ  ̣ τὴν
δοθ[εῖσ]αν εὐ[θήα]ν δί-
χα τεμεῖν[⁦ -ca.?- ⁩]
[2 lines missing]
16[  ̣  ̣  ̣  ̣  ̣  ̣]ν  ̣[⁦ -ca.?- ⁩]
[  ̣  ̣εἰ] γὰρ τ[ὴ]ν δοθ̣ε̣ῖσαν
εὐθήαν ἔστι δ̣[ί]χ̣α τε-
μεῖν   ̣  ̣[  ̣  ̣]  ̣[  ̣  ̣  ̣  ̣  ̣]α
20[⁦ -ca.?- ⁩]  ̣  ̣[⁦ -ca.?- ⁩] column 14P.Herc. 1061 col. 14

πλευρᾶς ε̣ὐθή̣αν   ̣  ̣  ̣
εἴπερ ἡ ΜΡ καὶ [Ρ]Ν [ἴσαι]
κα[ὶ] ἡ δοθ̣[εῖσα εὐ]θήα
[ἡ] ΜΝ δίχα τ̣[έτ]μητα[ι,]
5τ̣ὸ̣ δ' αὐ[τὸ] ἔ̣στ̣α̣ι κ̣αὶ̣ [  ̣]ι̣
τω̣ν μ[  ̣]ι[  ̣  ̣  ̣]  ̣ν̣[⁦ -ca.?- ⁩]
[1 line missing]
8[.]ντο[⁦ -ca.?- ⁩]
ναμα[  ̣]ει[  ̣  ̣  ̣ἐπεὶ γὰρ]
——
10ἴση ἐστὶν ἡ ΞΜ̣ τ̣ῆ̣[ι ΞΝ]
⁦ vac. 3 lines⁩
γωνία ἡ Ο τῆι Π ἴση{ι}
15δ[ί]χα γὰρ ἡ̣ Μ[Ν τέτ]μη-
[τ]αι̣, οὕτως[⁦ -ca.?- ⁩] column 15P.Herc. 1061 col. 15

[ἐ]φαρ[μ⁦ -ca.?- ⁩]
ναι δύ̣ο̣[⁦ -ca.?- ⁩]
το[  ̣  ̣  ̣]ν[⁦ -ca.?- ⁩]
  ̣  ̣επιτ̣  ̣ν̣[⁦ -ca.?- ⁩]
5θεο̣[  ̣  ̣  ̣  ̣  ̣  ̣  ̣]  ̣ατ  ̣[⁦ -ca.?- ⁩]
[9 lines missing]
15ξ  ̣  ̣εισαν[  ̣  ̣  ̣]α[⁦ -ca.?- ⁩]
δ̣  ̣  ̣[⁦ -ca.?- ⁩] column 16P.Herc. 1061 col. 16

  ̣η̣ι̣[  ̣περὶ] τ[οῦ] προβ̣λή
ματός ἐστιν τ[ο]ιαῦτα·
——
πάντα μὲν ἡ̣μῶν οὐ
προενην̣[εγ]μένων
5ἵνα μὴ εἰς [ἄ]ληκτον ἐκ
[⁦ -ca.?- ⁩]ντων
[⁦ -ca.?- ⁩]λε̣[⁦ -ca.?- ⁩]
⁦ vac. 1 line⁩
[⁦ -ca.?- ⁩]  ̣ετρι[⁦ -ca.?- ⁩]
10[⁦ -ca.?- ⁩]εἰς ο  ̣
[⁦ -ca.?- ⁩]λ̣ε̣ν̣
[⁦ -ca.?- ⁩]καὶ
[⁦ -ca.?- ⁩]ι̣σ̣[⁦ -ca.?- ⁩] column 17P.Herc. 1061 subscriptio
Sketched 1787-1806 by Giuseppe Casanova

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