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How, in classical Latin, did one say "all the more so" or otherwise indicate that a proposition harder than you're trying to prove has just been proven, so your proposition must be at least as certain?

In English, we sometimes say a fortiori to indicate this: "Unicorns don't exist, so, a fortiori, one couldn't have bitten you." I'm researching the origins of the term a fortiori, and so far, I have not found the idiom a fortiore ratione in any Ancient Roman writing. It seems likely, though, that people would have some sort of common way of expressing the concept.

I do know of a phrase with this meaning which occurs throughout Latin translations of the Bible: quanto magis. Here are a couple examples:

Si ergo uos cum sitis mali nostis bona data dare filiis uestris, Quanto magis pater uester de cælo dabit bona petentibus se? (Matthew 7:11, Old Latin)

If ye then, being evil, know how to give good gifts unto your children, how much more shall your Father which is in heaven give good things to them that ask him? (KJV)

Respicite uolatili a cæli, quoniam non serunt neque metunt neque congregant in horreo. Et pater vester cælestis alit illas. Nonne magis uos pluris estis illis? (Matthew 6:26, Old Latin)

Behold the fowls of the air: for they sow not, neither do they reap, nor gather into barns; yet your heavenly Father feedeth them. Are ye not much better than they? (KJV)

I've read, though, that "how much more?" is a direct translation of the Hebrew word אַף (af) or וְאַף, "and how much more", commonly used in Jewish rhetoric at that time to indicate an a fortiori argument. I can't tell if it's a Hebrew expression mostly limited to Bible translations, just as in English, or if it took root in Latin also. (Not to be confused with קַל וָחֹמֶר, qal vachomer, "light and heavy", another Hebrew expression for the same kind of argument.)

To put this another way, how would Vitruvius say, "Plant-stalks with animal-heads don't exist, so ⎯⎯⎯⎯ one couldn't have bitten you"?

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I would translate the phrase "all the more" using eo magis. Note that this phrase is much more common when "balanced" with an introductory phrase that introduces the comparison, usually with a comparative adverb.

Here are a few examples of usage: (hasty translations mine)

ita, quo minus petebat gloriam, eo magis illum sequebatur. (Sallust, The Catilinarian Conspiracy, 54)

Thus, the less he sought glory, the more it pursued him.

and

quod quo studiosius absconditur, eo magis eminet

The more carefully it is hidden, the more it juts out.

and with atque:

reliquum erat certamen positum in virtute, qua nostri milites facile superabant, atque eo magis, quod in conspectu Caesaris atque omnis exercitus res gerebatur (Caesar, De Bello Gallico, III 14, 8)

The remaining fight depended on courage, by which our soldiers easily carried the day; all the more so because it unfolded in the sight of Caesar and the whole army.

I believe that none of these examples quite covers the case that you are citing, which is a more direct translation of everything implied by a fortiori:

Here are some other options that might work:

  1. Ex quo patet + acc. and inf.: from which it is evident, etc. (Note that I did not find classical examples of this exact phrae)
  2. Constat ergo + acc. and inf.: It is therefore certain, etc.

or, for some good ol' classical hyperbole:

  1. Quid dementius quam + inf.: what could be more insane than (And yes, this is probably inappropriate as a substitution for a fortiori 99.99% of the time.)

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