arithmetic in Irish

Eólas ar Áireamh (arithmetical tables in Irish) is a fascinating booklet by Peadar Ua Laoghaire.

From this book I have learned the following:

* Zero or nought: PUL used the word neamhnídh; he did not have the word náid. Neamhnídh, a haon, a dó, a trí, etc.
* He lists tríochad (not triocha) alongside deich a’s fiche, and accepts caogad (not caoga) alongside deich a’s dachad, but does not have non-vigesimal figures for 60, 70, 80 or 90.
* He state that the a in counting may be used or left out before fiche, tríochad, dachad, caogad and céad (which he spells ceud), which are substantivized by the particle’s omission; the a in counting may not be used before míle.
* In discussion of place value, “units, tens and hundreds” are aoin, deichniúbhair, ceuda, where aoin is the plural of aon, and ceuda is the plural of ceud used only in the abstract; ceudta is used with hundreds of individuals.

* Asking questions on addition: cuir a trí le n-a trí, 7 cad a bhéidh agat? A sé. Cuir a sé i mbun a dódheug, 7 an mór a bhéidh agat? A h-ochtdeug. Cuir a sé le n-a ceathair, 7 cad a thiocfaidh as? A deich. Cá mheud a dhéinean a seacht 7 a cúig? A dódheug. Sums of addition can be so stated: a h-aon ‘s a h-aon, sin a dó.

* Asking questions on subtraction: bain aon ó n-a deich agus cad fhanfaidh? A naoi. Bain a dó uaidh agus cad a fágfar? A h-ocht. Bain a sé ó n-a sé agus cad e bheidh ann? Neamhnídh. Bain a sé ó n-a naoi agus cad tá ‘na dhiaidh? A trí. Sums of subtraction can be so stated: a h-aon ó n-a h-aon, fágtar neamhnídh.

* Asking questions on multiplication: meudaigh a dó fó thrí? A sé. Meudaigh fó cheathair é? A h-ocht. An mór a dhéinean trí cheathair? A dódheug. A cúig, cúig uaire, an mór é? A cúig a’s fiche. Cá mheud a dhéinean ocht gcúig? Dachad. Sums of multiplication can be so stated: a dó aon uair, sin a dó; a dó faoi dhó, sin a ceathair; a dó fó thrí, sin a sé. (It seems is used to multiply by 3-11, faoi is used to multiply by 2 and compounds of 2, just as 12.)

* Asking questions on division: An mó uair atá a cúig i bhfichid? Ceithre h-uaire. Cá mheud uair atá a trí ann? Sé h-uaire, agus a dó fairis [=six, with two over]. An mó ceathair i sédeug? Ceithre cheathair. Cá mheud naoi i dtríochad? Trí naoi, agus a trí d’fhuighlach [=three, remainder three]. Cé mheud deich i gcaogad? A cúig. Cé mheud deich i gcúig a’s dachad? Ceithre deich, agus a cúig fuighlaigh. Cá mheud dó i n-aondeug? Cúig cínn agus aon i n-a fhuighlach. Sums of division can be so stated: tá a dó i gceathair, dhá uair [=two into four goes twice]; tá a dódheug i gceathair 7 dachad 7 ceud, dhá uair deug.

* The equal sign = is cómh, of which the plural is cómha.

* 2.5 may be read as a do agus leath; a half only becomes go leith after a noun.

* I was familiar with fiche neómat tar éis a dódheug, 20 minutes past 12, but I thought 20 minutes to was with chun, but PUL has fiche neómat d’á h-aon. Buile chlog sa ló: one o’clock in the afternoon.

* A rhyme for the days in the months depends on referring to June, normally An Mitheamh, as Mithiomh an tSamhraidh, and September as Mithiomh an Fhóghmhair, and collectively the two are na Mithimh teó, the hot Mitheamh months. Mithiomh an Gheimhridh and Mithiomh an Earaig are na Mithimh fuara, December and March. The rhyme is:

NA LAETHEANTA INS GACH MÍ

Tríochad lá a bheirid leó
Samhuin, Abrán, na Mithimh teó.
Lá sa mbreis ag gach mí eile,
Acht an Feabhra thiar ar deire,
Gan aige acht ocht lá fhichid –
Naoi lá fhichid, i mbliaghain bhisig.

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