Quōmodo v. Quā ratiōne

Question

I'm looking at a Latin translation of the Apology of Socrates by Marcellus Ficinus and I'm puzzled by the very first clause.

Quā vōs quidem ratiōne, Ō virī Athēniēnsēs, affēcerint accūsātōrēs meī, nesciō.

I'm having trouble understanding quā ratiōne here. Obviously it's supposed to be "how," but I don't see how you get there. "I don't know for what reason they affected you"? "I don't know by what logic they affected you"? I've seen another translation that started with the same phrase except instead of quā ratiōne it used quōmodo, which is what I'd expect.

I guess the question at the base of this is, how is Quā vōs ratiōne affēc[ērunt] different from Quōmodo vōs affēc[ērunt]?

Answer 1

Quomodo is more idiomatically "how," while qua ratione can suitable though it seems more often to mean "why" and not "how."

Terence Phormio, act II

[Demipho] qua ratione inopem potiu' ducebat domum?
Why did he rather lead a pauper home?

[Geta] non ratio, verum argentum deerat.
No reason, but he lacked money.

Cicero, Pro Quinctio 76

Ego haec duo quaero, primum qua ratione Naevius susceptum negotium non transegerit, hoc est cur bona quae ex edicto possidebat non vendiderit.

I seek two things, first "on what account" Naevius did not finish the undertaken business, that is why he did not sell the goods which he had taken possession of in accordance with the edict.

_{Modified translation of Yonge's 1903.}

It can mean "how," though, and for the Ficinus passage, without too much thought, I'd probably say something along the lines of "in what way" or even perhaps "in what manner." There is significant overlap in the meanings of ratio II.B.c. and modus. Calculating and measuring are not all that different, after all. The Greek too is a simple ὅτι, so perhaps Ficinus' translation is a bit overwrought, and only needed a simple, suitable "how."

Answer 2

The comparison here is between the nouns modus and ratio. Both words are extremely broad as the linked entries in L&S indicate. Both dictionary entries contain the translations "manner", "method", and "mode" (modus II.B, ratio II.B.1.c.α). I assume this is the intended meaning, in which case both quo modo and qua ratione mean "how".

That said, the words are different. Although their meanings overlap, they certainly differ in tone. It seems to me that modus is more "measure" or "limit" and ratio is more "reckoning" by basic meaning. However, in this particular use the two words seem essentially synonymous to me. In particular, it seems that the fixed expression quo modo (spelled together or separately) has a much narrower meaning than the entry for modus would suggest.