Firstly, there are four number systems in Irish:
1) Na Maol-Uiṁreaċa; these are mainly just used when counting or when numbering things off. Here are some Irish examples: a h-aon, a dó, a trí 'one, two, three'; bád a h-aon, bád a dó 'boat one, boat two'
2) Na Bun-Uiṁreaċa; these are used when counting non-human things. Usually these nouns are in the singular, but can be in the plural under certain circumstances. Here are some Irish examples: (aon) bád aṁáin, ḋá ḃád, trí ḃád 'one boat, two boats, three boats'
3) Na hUiṁreaċa Pearsanta; these ar used when counting humans. Here are some Irish examples: bean (aṁáin), beirt ban, triúr ban 'one woman, two women, three women'
4) Na hOrd-Uiṁreaċa; these are basically the equivalent of 'first, second, third' in English: céad, tarna, tríú
In the quote that you provided, both Bun-Uiṁreaċa (in ceithre ríchathaoir fichead) and hUiṁreaċa Pearsanta (in ceathrar seanóirí fichead) ar seen. The reason that the forms of the word ceaṫair are different is because the form can change depending on which type of number system is being used. So ceiṫre is used for counting the thrones and cearṫar for the elders.
As for ceithre ríchathaoir fichead, as a broad rule, whenever you have a compound number (a number with two parts), the first part of the number goes in front of the noun and the second part goes after the noun (like in ḋá ḃád déag 'eleven boats'). Nowadays, however, it's more common to hear ceiṫre rí-ċathaoir a's fiċe, literally 'four thrones and twenty' instead.
_________________ I'm an intermediate speaker of the Corca Dhuibhne dialect of Irish and also have knowledge on the old spelling Soir gaċ síar, fé ḋeireaḋ thíar
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