THE ELEMENTS OF EUCLID

Translation into Iirsh commence dby

JOHN O'DONOVAN.

II.

9.

Is é is cúinne dron-líneach plánálda
ann, claonadh dhá líne dhíreach chum a chéile
noch theagmhas le chéile acht nach bhfuil 'san
dron-líne chéadna.

[The word cúinne, "a corner," is chosen to translate
"angle." In older Irish the use of uille (gen., uilleann,
dat., uillinn), lit. "elboW," is established in the sense of
"angle;" tre-uillech, "triangular." Dron-líneach,
"rectilinear." Teagmhaim, I meet, now usually teang-
mhaim. O'D. here still wavers between líne dhíreach and
dron-líne.]

10.
An uair sheasas dron-líne ar dhron-líne
eile, agus do ghní na cúinní ar gach taobh de
coimhionann, gairthear dron-uille de gach
cúinne dhíobh, agus gairthear ingear de'n dron-
líne sheasas ar aroile.

[Coimhionann, "equal." Dron-uille, "right-angle."
Uille here adopted as well as cúinne. O'Reilly gives
ingear, "a perpendicular," ingearach, "vertical." Ar
aroile = ar a chéile, ar an gceann eile.]

11.
Gairthear leathan-uille de'n chúinne sin
atá níos mó ná dron-uille.

12.
Agus géar-uille dhi sin atá níos lugha
ná dron-uille.

13.
Is é is teóra ann, fóirimeall aon neith.

14.
Is é is fioghair ann, an nídh timchealltar
le haon teórainn no níos mó.

[Leathan-uille, obtuse angle. The usual word for
"obtuse" is maol. Géar-uille, acute angle. Teóra,
boundary, circumference. Fioghair, figure.]

15.
Is é is crios no cearcal ann .i. fioghair
cuimsighthear fá aon líne amháin ar a
ngairmthear an timcheallaidhe nó an fóiri-
meall, is an gcuma go bhfuil gach uile líne
tarraingthear ó phonc áirithe ar thaobh de'n
fhioghair chum an timcheallaidhe coimh-ionann
le n-a chéile.

[Crios, cearcal = circle. The words cró and buaile,
both metaphors taken from the circular-shaped cattle-
fold, were formerly used to mean "circle." There is an
evident difficulty in adapting common words, like crios,
cró, cuairt, to a special technical use. It is like substi-
tuting "ring" or "hoop" for the geometrical term circle
in English. Only a pedant coudl object to the use of a
borrowed but thoroughly naturalized term like cearcal,
about which there could be no confusion. Timcheallaidhe,
circumference. We may reject fóirimeall, already used
in a far wider sense. Ar thaobh de'n fhioghair seems to
obsure the true meaning.]

16.
Agus gairthear ceart-lár an chreasa de'n
phonc so.

[Ceart-lár, centre. I have heard the word used
popularly in this sense. Ceart-mheadhón is also found.]

17.
Is é is lár-líne an chreasa ann .i. dron-
líne (.i. líne dhíreach) tarraingthe tré n-a
cheart-lár agus críochnuighthe ar gach taobh leis
an timcheall-líne.

[Lár-líne, diameter. Timcheall-líne here substituted
for timcheallaidhe. No term is given for "radius," but
ga has been used in that sense. Note that O'D. does
not use taoibh in the dative.]

18.
Is é is leath-chrios ann .i. fioghair teoruigh-
thear leis an lár-líne agus an pháirt sin de'n
timcheall-líne gearrtha amach leis an lár-
líne.

[Leath-chrios, semi-circle (leath-chearcal would be better).
The latter half of this definition is weak both in meaning
and in idiom. The circumference is cut in two equal halves
by the diameter. An pháirt sin … gearrtha amach is
English-Irish. We might say fioghair teoruighthear
fá'n lár-líne agus fá'n gcuid de'n timcheall-líne atá ar
aon taobh de'n lár-líne.]

19.
Is é is mír de chearcal ann .i. an fhioghair
coimsighthear fá dhron-líne agus (fá) an pháirt
de'n timcheall-líne ghearras sé amach.

[Better fá dhron-líne agus fá aon-chuid de'n timcheall-
líne. The part "cut off" and the part off which it is
cut are equally capable of bounding a segment (mír).
Coimsighthear = teoruighthear, is bounded.]

20.
Fioghairí dron-líneacha umorro .i. iad so
coimsighthear fá líntibh direcha.

[Umorro, an obsolete particle, used in passing from
one subject to another. Fioghracha is used as plural of
fioghair.]

21.
Fioghairí trí-thaobhacha, nó teoruilleanna,
fá thrí líntibh díreacha.

[Trí-thaobhach, trilateral. Teoruille, triangle.]

22.
Fioghairí ceathar-thaobhacha fá cheithre líntibh
díreacha.

[Ceathar-thaobhach, quadrilateral.]

23.
Fioghairí ioltaobhacha, nó iolchúinní, fá
níos mó ná ceithre línte díreacha.

[Ioltaobhach, multilateral. Iolchúinne, a polygon: not
a good term, as its form implies a kind of angle rather
than a figure. Iolchúinneach, polygonal, or a polygon,
might be used.]

24.
I measg fioghairí trí-thaobhach, gairthear
teoruille chomhthaobhach di sin ag a bhfuil trí
thaobha coimhionanna.

[Comhthaobhach, equilateral.]

25.
Teoruille chomhchosach is ainm do'n fhio-
ghair ag a bhfuil dá thaobh amháin coimhionann.

[Comhchosach, equal-legged, isosceles.]

26.
Teoruille neamhchomhshliosnach ainm na
fioghrach ag a bhfuil trí thaobha neimhionanna.

[Neamhchomhshliosnach, unequal-sided, scalene. A rather
unwieldy term. Slios, a side.]

27.
Teoruille dhron-uilleannach .i. teoruille
ag a bhfuil dron-uille.

28.
Teoruille leathan-uilleannach .i. teor-
uille ag a bhfuil cúinn leathan.

29.
Teoruille ghéar-uilleannach .i. í sin ag a
bhfuil trí cúinní géara.

[Instead of teoruille, the derivative teoruilleannach
might be substituted in the foregoing definitions, as the
compound word usually denotes a special kind of the
thing denoted by its last part, here uille, angle. Teor-
uille, a triple angle, teoruilleannach (a thing) having
three angles. Teora is an old inflected form of trí,
three.]

Mac Léighinn.