Bibliotheca Polyglotta

Euclid: Elementa

Ἐὰν ὦσι δύο πυραμίδες ὑπὸ τὸ αὐτὸ ὕψος τριγώνους ἔχουσαι βάσεις, διαιρεθῇ δὲ ἑκατέρα αὐτῶν εἴς τε δύο πυραμίδας ἴσας ἀλλήλαις καὶ ὁμοίας τῇ ὅλῃ καὶ εἰς δύο πρίσματα ἴσα, ἔσται ὡς ἡ τῆς μιᾶς πυραμίδος βάσις πρὸς τὴν τῆς ἑτέρας πυραμίδος βάσιν, οὕτως τὰ ἐν τῇ μιᾷ πυραμίδι πρίσματα πάντα πρὸς τὰ ἐν τῇ ἑτέρᾳ πυραμίδι πρίσματα πάντα ἰσοπληθῆ.

eng

If there be two pyramids of the same height which have triangular bases, and each of them be divided into two pyramids equal to one another and similar to the whole, and into two equal prisms, then, as the base of the one pyramid is to the base of the other pyramid, so will all the prisms in the one pyramid be to all the prisms, being equal in multitude, in the other pyramid.

lat Sic

Si sunt due piramides sub eadem altitudine trigonas habentes (bases), dividatur autem utraque earum in duas piramides equales sibi invicem et similes totius, in duo prismata equalia et factarum piramidum utraque eodem modo (divisa) et hoc semper fiat, est sicut unius piramidis basis ad alterius piramidis basim ita et que in una piramide prismata cuncta ad prismata que in alia piramide cuncta equalem habentia multitudinem.

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