Céadnithe an Chruinne-thómhais

Céadnithe an Chruinne-thómhais
(The Elements of Geometry.)

Sloínnte
(Definitions.)

1. (a point), .i. ionad gan méid.
2. Líne, .i. faid gan leithead.
Críoch líne eó, & cómhghearradh línte eó.
3. Líne díreach .i. líne gan casadh ann.
4. Uachtar (a surface), .i. ní ag á bhfuil faid agus leithead gan raímhre.
Críoch uachtair líne, & cómhghearradh dhá uachtar líne.
5. Clár (a plane), .i. uachtar ’na luíonn díreach idir aon dá eó ann.
Ní fhéadfadh dhá líne dhíreach luí ar a chéile, i gcuid díobh, gan luí ar a chéile ar fad, ná slí do chómhdhúnadh. Ní lú ná fhéadfadh dhá chlár.
6. Taibhse (a solid), .i. ní ag á bhfuil faid & leithead & raímhre, in éineacht.
Teóranna taibhse uachtair.
7. Oscall (an angle), .i. gabhal, .i. cómhrac (meeting) dhá líne.
8. Oscall dírlíneach (rectilinear angle), .i. oscall is de chómhrac dhá líne dhírigh1.
9. Díoroscall (right angle), .i. nuair ’ chómhracaid dhá líne dhíreacha & do-níd dhá chómhoscall 2 in aice a chéile, is díoroscaill an dá chómhoscall san, & is cómhdhíreacha3 dá chéile an dó líne sin.
10. Móroscall (obtuse angle), .i. oscall is leithe ná díoroscall.
11. Caoloscall (acute angle), .i. oscall is caoile ná díoroscall.
12. Línte díreacha cómhfhana (parallel straight lines), .i. línte díreacha in aon chlár & fan a chéile, i dtreó, pé faid do leantar iad, ar aghaidh nú siar, nách féidir dóibh dúnadh ar a chéile.

Nótaí

Do-níd: PUL here uses the traditionally correct absolute form of the verb déanamh, corresponding here to deinid.
Dhá chómhoscall: note the failure to use the correct dual form, oscaill, here. T. F. O’Rahilly comments in Papers on Irish Idiom, in which he transcribes PUL’s Euclid, that in the meaning of “angle”, PUL usually had oscall as a masculine noun, thus creating a contrast with oscall, meaning “armpit”. But he often had oscaill in the dative or dual, which O’Rahilly adjusted in his editing to oscall in line with the generally masculine declension of oscall when meaning “angle”. (The editing approach adopted by O’Rahilly seems flawed, as inconsistencies in the original manuscript should be retained and discussed, but that is another question.) Consequently, without checking the original manuscript, it is difficult to know if PUL had oscall or oscaill here.
An dó líne sin: is given in the original (i.e., the text as edited by T. F. O’Rahilly), where would be expected.

Foclóirín

ag: “at, by”. Note the combination ag á, where the CO has ag a.
caoloscall: “acute angle”, or géaruillinn in the CO.
céadní: “element, a basic part of something”. This may be an ad hoc word produced by PUL to translate “element”, as the word is not given in dictionaries. Possibly eilimint in the CO.
cómhdhíreach: “perpendicular”. This appears to be an ad hoc word produced by PUL, as the word is not given in dictionaries. Ingear is used in the CO where “perpendicular” is a noun, and ingearach where it is an adjective.
cómhdhúnaim, cómhdhúnadh: this word is not given in dictionaries, but slí do chómhdhúnadh appears to mean “to close the gap, to come together with no space left between”.
cómhfhan: “parallel”. This appears to be an ad hoc word produced by PUL to translate “parallel”, as the word is not given in dictionaries. Parailéalach is used in the CO.
cómhghearradh: “concision, curtailment”. Cómhghearradh dhá uachtar líne, “where two surfaces meet is a line”.
cómhoscall: “equal angle”. This appears to be an ad hoc word; the CO for “equal angles” is uillinneacha ar cóimhéid.
cómhracaim, cómhrac: “to meet, encounter”, or comhraicim, comhrac in the CO. Cómhrac dhá líne, “the juncture/confluence of two lines”.
cruinne-thómas: “geometry”, or geoiméadracht in the CO. Cruinne-thómas appears to be an ad hoc word produced by PUL, along the same lines as the word given in Dinneen’s dictionary, cruínn-eólas, “geography”.
díoroscall: “right angle”. This appears to be an ad hoc word; the CO has dronuillinn.
dírlíneach: “rectilinear”. This appears to be an ad hoc word; the CO has dronlíneach.
eó: “point”, especially the point of a blade. PUL uses this word to refer to a geometrical point, where the CO would have pointe or ponc.
faid: “length”, or fad in the CO.
gabhal: “fork”.
ionad: “unit”. PUL normally uses inead, but here the CO form ionad is found.
leath: “broad”. Listed in Dinneen’s dictionary as an obsolete word (more usually found as leathan), although the comparative leithe is sometimes found.
móroscall: “obtuse angle”. This appears to be an ad hoc word; the CO has maoluillinn.
oscall: “armpit”, or ascaill in the CO. PUL’s use in the meaning of “angle” here appears to be an attempt to create new geometrical terminology. Uillinn is the word used in the CO for “angle”.
sloinne: “surname”, but also “definition”.
taibhse: “solid”. This word generally means “ghost” or “appearance”, but Dinneen’s dictionary shows it can also mean “size, bulk”, and maybe by extension from here, “solid”. The CO form is solad.
teóra: “border, limit, boundary”, with teóranna in the plural. The CO has teorainn and teorainneacha.

1De chómhrac dhá líne dhírigh: dhírigh is as given in the original, although it is unclear to me that dhírigh is the right form to qualify a feminine noun in the genitive dual. More research required here.

2PUL: cómhoscall, an equal angle.

3PUL: cómhdhíreach: a perpendicular.