§1.11.
1.
Proclus Comm. in Eucl. p. 68,23sqq. (ed.
Proclus Comm. in Eucl. p. 68,23sqq. (ed.
Friedlein): Πολλὰ μὲν οὖν καὶ ἄλλα τοῦ ἀνδρὸς τούτου μαθηματικὰ συγγράμματα θαυμαστῆς ἀκριβείας καὶ ἐπιστημονικῆς θεωρίας μεστά· τοιαῦτα γὰρ καὶ τὰ Ὀπτικὰ καὶ τὰ Κατοπτρικά, τοιαῦται δὲ καὶ αἰ κατὰ μουσικὴν στοιχειώσεις, ἔτι δὲ τὸ Περὶ διαιρέσεων βιβλίον.
Friedlein): Indeed, many other mathematical writings of this man are full of wonderful accuracy and scientific theory; for such are both the Optics and the Catoptrics, and such are also the Elements of Music, and further the book On Divisions.
ldem ibid. p. 144,18sqq. δεύτερον δὲ ἀπὸ τῆς ὁλότητος τελειοῦται τῆς εἰς τὰ ἀνόμοια μέρη διακρινομένης, ὅθεν δὴ καὶ αὐτὸς ἑκάστῳ τῶν εἰδῶν ἐπιφέρει τὸ ὅλον, καὶ τῶν σχημάτων ἕκαστον εἰς διάφορα αὐτῶν εἴδη τέμνεται.
Idem ibid. p. 144,18sqq.: Secondly, it is perfected from the totality which is divided into unlike parts, whence indeed he himself applies "the whole" to each of the species, and each of the figures is cut into their different species.
καὶ γὰρ ὁ κύκλος εἰς ἀνόμοια τῷ λόγῳ καὶ ἕκαστον τῶν εὐθυγράμμων διαιρετόν ἐστιν, ὃ καὶ αὐτὸς ὁ Στοιχειωτὴς ἐν ταῖς Διαιρέσεσι πραγματεύεται τὸ μὲν εἰς ὅμοια τὰ δοθέντα σχήματα διαιρῶν, τὸ δὲ εἰς ἀνόμοια.
For indeed the circle is divisible into parts unlike in ratio, and so is each of the rectilinear figures, which is precisely what the Writer of the Elements himself treats in the Divisions, on the one hand dividing the given figures into like parts, and on the other hand into unlike parts.
Cfr.
Cf.
Studien über Euklid p. 36 sqq.
Studien über Euklid p. 36 sqq.
sine dubio cum hoc opere Euclidis adfinitate quadam coniunctus est liber III Metricorum Heronis, sed non ita, ut inde Euclidea peti possint.
Without doubt, book III of Heron's Metrica is connected by a certain affinity with this work of Euclid, but not in such a way that the Euclidean passages can be retrieved from it.