The question Translation: that which was to have been made deals with grammatical aspects of the expression quod erat demonstrandum, but I am interested in a detailed break-down of the meaning attributed to each word. Generally this is translated as which was (necessary) to be demonstrated, but how is this meaning broken down according to each of the three individual words? More specifically, is the "necessity" aspect inherent in the gerundive "demonstrandum" or in "erat" ? Since "erat" is just past tense of "to be", it seems likely that the meaning of "necessity", if any, would be in the gerundive. Do gerundives generally carry such a connotation of necessity?

  • Of the European languages, its a problem in Englisch, Dutch and Low German, reduced set of constructions. But substantivation of whole phrases are now common at least in modern American (Bloomberg) English. In German it simply translates into "What was the to be made visible". Funnily, it is a religous fomula, to make the monster visible down here. In a sense, the Romans, like many ancient and some modern philologists, thought about (Greek) mathemata as a form of black magic.
    – Roland F
    Nov 21, 2023 at 12:20

1 Answer 1


Yes. In Quod erat demonstrandum the sense of necessity can be attributed completely to the gerundive. As in our case, often the gerundive is coupled with the verb esse (to be) - most famously in Censeo Carthaginem esse delendam ("I think Carthage must be destroyed").

However, the gerundive can bear a similar sense of necessity without being coupled with the verb esse, as it can be used adjectively.

So it seems that saying that the "necessity" aspect is inherent in the gerundive is a fair statement - and that usage is general indeed. This does not mean, however, that a gerundive forces a necessity as there are some other constructions in Latin where gerundive do not necessarily bear the "necessity" sense.

As for the word-breakdown. Quod=what, erat=was, demostrandum=to be demonstrated.

  • Thanks! That's very helpful. You write that other gerundives "do not necessarily bear the 'necessity' sense." I am specifically interested in a comment by Leibniz where the gerundive "Aliter" is used. Leibniz writes: "Aliter demonstrandum quod neque majus quia non potest inveniri pars ejus finita aequalis." et cetera. Would one expect "Aliter" to have the "necessity" sense here? Nov 21, 2023 at 13:09
  • @MikhailKatz, Not sure I get what it means the adverb ""Aliter" to have the "necessity" sense here?. Do you ask if "Aliter demostrandum" means "it must be shows in another way?" Also note that "demostrandum" here is probably not gerundive but rather gerund (though still bears the necessary sense); My remark was about constructions where gerundive can use to signal "purpose", and not such as given by this Leibniz quote. You might try post here another question about this specific quote.
    – d_e
    Nov 21, 2023 at 13:58
  • Yes, sorry, I was referring to "Aliter demonstrandum". Nov 21, 2023 at 14:01
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    Your initial statement "In Quod erat demonstrandum the sense of necessity can be attributed completely to the gerundive" is not evident. I'd rather say that this meaning is a property of the construction esse +gerundive and related ones rather than a property of the verbal adjective. See also Danesi et al (2017: 148) for a similar view: "The locus of deontic modality is not attributable to any specific lexical item or category found in the construction, but rather must be attributed to the construction as a whole. That is, the GER+(NOM+)DAT construction is semantically non-compositional".
    – Mitomino
    Nov 21, 2023 at 16:24
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    @Mitomino, I created a relevant question to our discussion:
    – d_e
    Nov 21, 2023 at 17:52

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