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Comment by Y_Y | Hacker News Reader

Homo is third declension masculine, hominum is plural genitive ("of men"). Here you need accusative, so ad hominem.

    Case  Singular  Plural
    Nominative  homō  hominēs
    Genitive  hominis  hominum
    Dative  hominī  hominibus
    Accusative  hominem  hominēs
    Ablative  homine  hominibus
    Vocative  homō  hominēs

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From a French education, I have learned a different order of cases for Latin declension tables (NVAGDA: Nominative, Vocative, Accusative, Genitive, Dative, Ablative). I was curious to know where it comes from, and apparently the order you used is more common in the US: https://en.wikipedia.org/wiki/Latin_declension#Order_of_the_...

I learnt your way in school too, but the table is copied from wiktionary.

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