§5.1.1μετὰ δὲ τὴν ὑπώρειαν τῶν Ἄλπεων ἀρχὴ τῆς νῦν Ἰταλίας.
After the foothills of the Alps is the beginning of what is now Italy.
οἱ γὰρ παλαιοὶ τὴν Οἰνωτρίαν ἐκάλουν Ἰταλίαν ἀπὸ τοῦ Σικελικοῦ πορθμοῦ μέχρι τοῦ Ταραντίνου κόλπου καὶ τοῦ Ποσειδωνιάτου διήκουσαν, ἐπικρατῆσαν δὲ τοὔνομα καὶ μέχρι τῆς ὑπωρείας τῶν Ἄλπεων προὔβη.
For the ancients called Oenotria 'Italy', which extended from the Sicilian Strait to the Gulf of Tarentum and that of Poseidonia, but the name, having prevailed, advanced even as far as the foothills of the Alps.
προσέλαβε δὲ καὶ τῆς Λιγυστικῆς τὰ μέχρι Ὀυάρου ποταμοῦ καὶ τῆς ταύτῃ θαλάττης ἀπὸ τῶν ὁρίων τῶν Τυρρηνικῶν καὶ τῆς Ἰστρίας μέχρι Πόλας.
It also took in those parts of Liguria as far as the river Varus and the sea in that region from the Tyrrhenian boundaries, and of Istria as far as Pola.
εἰκάσαι δʼ ἄν τις εὐτυχήσαντας τοὺς πρώτους ὀνομασθέντας Ἰταλοὺς μεταδοῦναι καὶ τοῖς πλησιοχώροις, εἶθʼ οὕτως ἐπίδοσιν λαβεῖν μέχρι τῆς Ῥωμαίων ἐπικρατείας.
One might conjecture that the first to be called Italians, having prospered, shared the name with their neighbors, and that it thus received expansion until the Roman supremacy.
ὀψὲ δέ ποτε, ἀφʼ οὗ μετέδοσαν Ῥωμαῖοι τοῖς Ἰταλιώταις τὴν ἰσοπολιτείαν, ἔδοξε καὶ τοῖς ἐντὸς Ἄλπεων Γαλάταις καὶ Ἑνετοῖς τὴν αὐτὴν ἀπονεῖμαι τιμήν, προσαγορεῦσαι δὲ καὶ Ἰταλιώτας πάντας καὶ Ῥωμαίους, ἀποικίας τε πολλὰς στεῖλαι, τὰς μὲν πρότερον τὰς δʼ ὕστερον, ὧν οὐ ῥᾴδιον εἰπεῖν ἀμείνους ἑτέρας.
At length, after the Romans had shared equal citizenship with the Italiotes, they resolved to grant the same honor to the Galatae and Heneti within the Alps, and to call them all both Italiotes and Romans, and to send out many colonies, some earlier and others later, than which it is not easy to name any better.
§5.1.2̔ενὶ μὲν οὖν σχήματι σύμπασαν τὴν νῦν Ἰταλίαν οὐ ῥᾴδιον περιλαβεῖν γεωμετρικῶς, καίτοι φασὶν ἄκραν εἶναι τρίγωνον ἐκκειμένην πρὸς νότον καὶ χειμερινὰς ἀνατολάς, κορυφουμένην δὲ πρὸς τῷ Σικελικῷ πορθμῷ, βάσιν δʼ ἔχουσαν τὰς Ἄλπεις· συγχωρῆσαι δὲ καὶ τῶν πλευρῶν μίαν τὴν ἐπὶ τὸν πορθμὸν τελευτῶσαν, κλυζομένην δὲ ὑπὸ τοῦ Τυρρηνικοῦ πελάγους.
Now, it is not easy to encompass the whole of present-day Italy in a single geometrical figure, although they say that it is a triangular peninsula projecting towards the south and the winter sunrise, peaking at the Sicilian Strait, and having the Alps as its base; and one might also concede one of the sides, the one ending at the Strait, washed by the Tyrrhenian Sea.
τρίγωνον δὲ ἰδίως τὸ εὐθύγραμμον καλεῖται σχῆμα· ἐνταῦθα δὲ καὶ ἡ βάσις καὶ ἡ πλευρὰ περιφερεῖς εἰσιν, ὥστε, εἴ φημι δεῖν συγχωρεῖν, περιφερογράμμου σχήματος θετέον καὶ τὴν βάσιν καὶ τὴν πλευράν, συγχωρητέον δὲ καὶ τὴν λόξωσιν ταύτης τῆς πλευρᾶς τὴν ἐπὶ τὰς ἀνατολάς, τἆλλα δʼ οὐχ ἱκανῶς εἰρήκασιν, ὑποθέμενοι μίαν πλευρὰν ἀπὸ τοῦ μυχοῦ τοῦ Ἀδρίου μέχρι τοῦ πορθμοῦ.
But strictly speaking, a triangle is called a rectilinear figure; whereas here both the base and the side are curved, so that, if I must say we should concede, we must assume both the base and the side to belong to a figure bounded by curves, and we must also concede the slant of this side towards the east; but in other respects they have not spoken adequately, since they assume one side to be from the innermost recess of the Adriatic as far as the Strait.
πλευρὰν γὰρ λέγομεν τὴν ἀγώνιον γραμμήν, ἀγώνιος δʼ ἐστὶν ὅταν ἢ μὴ συννεύῃ πρὸς ἄλληλα τὰ μέρη ἢ μὴ ἐπὶ πολύ.
For we call 'side' a line without an angle, and it is 'without an angle' when its parts either do not incline towards each other or do not do so to any great extent.
ἡ δὲ ἀπὸ Ἀριμίνου ἐπὶ τὴν ἄκραν τὴν Ἰαπυγίαν καὶ ἡ ἀπὸ τοῦ πορθμοῦ ἐπὶ τὴν αὐτὴν ἄκραν πάμπολύ τι συννεύουσιν.
But the line from Ariminum to the Iapygian promontory and the one from the Strait to the same promontory incline towards each other to a very great degree.
ὁμοίως δʼ ἔχειν οἴομαι καὶ τὴν ἀπὸ τοῦ μυχοῦ τοῦ Ἀδρίου καὶ τὴν ἀπὸ τῆς Ἰαπυγίας· συμπίπτουσαι γὰρ ἐπὶ τοὺς περὶ Ἀρίμινον καὶ Ῥάουενναν τόπους γωνίαν ποιοῦσιν, εἰ δὲ μὴ γωνίαν, περιφέρειάν γε ἀξιόλογον·
And I think it is the same with the line from the innermost recess of the Adriatic and the one from Iapygia; for meeting around the places of Ariminum and Ravenna, they form an angle, or if not an angle, at least a remarkable curve.
ὥστʼ, εἰ ἄρα, τοῦτʼ ἂν εἴη μία πλευρὰ ὁ παράπλους ὁ ἀπὸ τοῦ μυχοῦ ἐπὶ τὴν Ἰαπυγίαν, οὐκ εὐθεῖα· τὸ δὲ λοιπὸν τὸ ἐνθένδε ἐπὶ τὸν πορθμὸν ἄλλην ἂν ὑπογράφοι πλευράν, οὐδὲ ταύτην εὐθεῖαν.
So that, if indeed, the coastwise voyage from the innermost recess to Iapygia would be one side, and not a straight line; and the remaining part from there to the Strait would trace another side, nor would this one be straight.
οὕτω δὲ τετράπλευρον μᾶλλον ἢ τρίπλευρον φαίη τις ἂν τὸ σχῆμα, τρίγωνον δʼ οὐδοπωσοῦν, πλὴν εἰ καταχρώμενος.
Thus, one might call the shape quadrilateral rather than trilateral, and by no means triangular, unless by an abuse of terms.
βέλτιον δʼ ὁμολογεῖν, ὅτι τῶν ἀγεωμετρήτων σχημάτων εὐπερίγραφος ἡ ἀπόδοσις.
But it is better to admit that for non-geometrical figures, a description by a rough outline is acceptable.