Easter Greetings to Greek fans who are also math fans!
Despite consulting Smythe and Goodwin on Greek numbers, I am at a loss to make sense of the system behind the variety Nicomachus uses when substantively referring to numbers.
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Most (75%) numbers are preceded by the masculine singular article, as appositives to the expressed or (more often) implied “arithmos”, This makes sense to me.
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But I often see them preceded by a feminine or neuter article in the singular. When I find a suitable referent such as feminine “ekthesis” or neuter “skhēma”, I am relieved but still not 100% sure why he does this. Just as often I can find no suitable antecedent and am truly confused.
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Quite often the numbers are preceded by neuter plural article, perhaps as abstract quantities when no antecedent exists in the clause. This makes sense to me, but less sense than 1). Why does he sometimes do one and not the other? Elegant variation?
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Finally Nicomachus at least once just assigns a gender to some numbers, as in chapter nine below. Note the series with unusually determined numbers: all of them masculine except for 22, which is mysteriously feminine!
θ. Ἀρτιοπέριττος δέ ἐστιν ἀριθμὸς ὁ τῷ γένει καὶ αὐτὸς ἄρτιος ὤν, ἀντιδιαστελλόμενος δὲ ἰδικῶς τῷ προφρασθέντι ἀρτιάκις ἀρτίῳ, ὁ τὴν μὲν εἰς δύο ἶσα διαίρεσιν ἐπιδεχόμενος κατὰ τὸ κοινὸν γένος, τῶν μέντοι μερῶν ἑκάτερον εὐθὺς εἰς δύο ἶσα ἄτμητον ἔχων, οἷον
ὁ ϛ, ὁ ι, ὁ ιδ, ὁ ιη, ἡ κβ, ὁ κϛ,
οἱ ὅμοιοι· μετὰ γὰρ τὸ διχασθῆναι ἕκαστον τούτων ἀδίχαστα εὐθὺς τὰ μέρη εὑρίσκεται.
I have run into none of this trouble in Euclid. Has anyone here had experience with numerical treatises in Greek and can clear me up a bit? I have kept this post as brief as I could, but can easily supply examples for points 1) - 3) if anyone would like.
Eukharistō
Mark
