Commentary Par XIII 13-15

The daughter of Minos here referred to is Ariadne.  Her 'crown' refers to the garland taken from her head by Bacchus after she died, having been abandoned by Theseus.  Bacchus placed it in the heavens, where it is known as the Corona Borealis (see Ovid, Metam. VIII.174-182).  Dante compares it, a single thing, to a double rainbow.  That the poet refers to Ariadne as herself being translated to the heavens, and not only her garland of flowers, has troubled some commentators.  However, in a sort of reverse metonymy, Dante has given the whole for the part; he clearly wants us to think of Ariadne's garland as representing a circle of saints – twice.  In the last canto ([Par XII 12]), Juno's handmaid (the unnamed Iris) is doubled in the sky, just as here Minos's daughter (the unnamed Ariadne) is.

For a discussion of the several possible Ovidian sources of these verses, see Martinez (Mart.1991.1): Ars. I.525-564; Metam. VIII.174-182; Fast. III.459-516.  That the canto eventually finds its fullest expression of its central theme in Daedalus's trembling hand (see C.Par.XIII.67-78), an object that probably has its source in the next episode in Ovid (Metam. VIII.183-235), tends to strengthen the case for the aptness of the citation from that same locus here.