Euclidis Elementa Prima, Definitiones 1-12

I had a conversation on Twitter last night with a teacher who has been incorporating STEM elements into her Latin classes. A very interesting approach and one that got me thinking about all of the Latin/Greek sources that could be used in a class like this. Aristotle, Theophrastus, Celsus, Vitruvius, Pliny, Galen, the list could on—and I’ve only reached the 2nd c. CE.

I wanted to post something today in keeping with this site’s Google-Books-crate-digging approach to the comparative method. Euclid popped into my mind and sure enough I was able to find a few 16th c. Latin translations without much difficulty. Here are the first 12 definitions from the first book of the Elements, the Greek with the Latin translation as well as some illustrations, from the 1573 edition by Marnef and Cavellat.

Εὐκλείδου Στοιχεῖον Πρῶτον / Euclidis Elementum Primum

Ὅροι / Definitiones
α. Σημεῖον ἐστιν, οὗ μέρος οὐθέν. / 1. Punctum est, cuius pare nulla est.

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β. Γραμμὴ δὲ, μῆκος ἀπλατές. / 2. Linea vero, longitudo latitudinis expers.

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γ. Γραμμῆς δὲ πέρατα, σημεῖα. / 3. Lineae autem termini, sunt puncta.

δ. Εὐθεῖα γραμμή ἐστιν, ἥ τις ἐξ ἴσου τοῖς ἐφ’ ἑαυτῆς σημείοις κεῖται. / 4. Recta linea est, quae ex aequo sua interiacet puncta.

ε. Ἐπιφάνεια δὲ ἐστιν, ὃ μῆκος καὶ πλάτος μόνον ἔχει. / 5. Superficies est, quae longitudinem latitudinumque tantum habet.

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ϛ. Ἐπιφανείας δὲ πέρατα, γραμμαί. / 6. Superficiei extrema, sunt lineae.

ζ. Ἐπίπεδος ἐπιφάνεια ἐστιν, ἥ τις ἐξ ἴσου ταῖς ἐφ’ ἑαυτῆς εὐθείαις κεῖται. / 7. Plana superficies est, quae ex aequo suas interiacet lineas.

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η. Ἐπίπεδος δὲ γωνία ἐστιν, ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπλομένων ἀλλήλων, καὶ μὴ ἐπ’ εὐθείας κειμένων, πρὸς ἀλλήλας τῶν γραμμῶν κλίσις. / 8. Planus angulus est, duarum linearum in plan se mutuo tangentium, & non in directum iacentium, alterius ad alteram inclinatio.

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θ. Ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ, εὐθεῖαι ὦσιν, εὐθύγραμμος καλεῖται ἡ γωνία. / 9. Cum autem quem angulum continent lineae, rectae fuerint, rectilineus ille angulus appellatur.

ι. Ὅταν δὲ εὐθεῖα ἐπ’ εὐεῖαν σταθεῖσα, τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιεῖ, ὀρθή ἐστιν ἑκατέρα τῶν ἴσων γωνιῶν· καὶ ἡ ἑφεστηκυῖα κάθετος καλεῖται ἐφ’ ἣν ἐφέστηκεν. / 10. Cum vero retta linea super rectam consistens lineam, eos qui sunt deinceps angulos aequales inter se fecerit: rectus est uterque aequalium angulorum: & quae insistit recta linea, perpendicularis vocatur eius cui insistit.

ια. Ἀμβλεῖα γωνία ἐστιν, ἡ μείζων ὀρθῆς. / 11. Obtusus angulus est, qui recto maior est.

ιβ. Ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς. / 12. Acutus vero, qui minor est recto.

Screen Shot 2013-08-07 at 10.20.12 AM

from Marnef & Cavellat’s 1573 Euclidis Elementorum Libri XV, Graece et Latine, p. 33ff. (


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