Question: am I right to consider Old Trian as a cognate of Latin Trinus? And sharing the same root *tri-(s)no-with it and the Old English þrinen (Middle English threnen) from Old Icelandic þrennr?
Given that Latin Trinus is a form of the distributive numeral three, and that Trianach from Trian was also considered to be the distributive numeral three:
Edward Lhuyd, Archaeologia Britannica, Volume 1 (Oxford 1707)
"TRIANACH, Three by three. Pl."
John O'Brien and Edward Lhuyd, Focalóir Gaoidhilge-sax-bhéarla (Paris 1768):
"TRIANACH, three by three, terni."
William Shaw, A Galic And English Dictionary (London 1780):
"TRIANACH, Three by three, of the third part"
Edward O'Reilly, An Irish-English Dictionary with a Compendious Irish Grammar (Dublin 1821):
"TRIANACH, three by three, of the third part, thirdly"
Robert Archibald Armstrong, A Gaelic Dictionary in Two Parts (London 1825):
"TRIANACH, a. (from trian.) Ir.id. Three by three; of the third part."
Dictionarium Scoto-Celticum (Edinburgh 1828):
"TRIANACH, (Trian), Of the third part: trinus, ternus. "Trianach Iàn." C. S. One third full : plenus usque ad tertiam partem."
Norman Macleod, Daniel Dewar, A Dictionary of the Gaelic Language in Two Parts (Glasgow 1831):
"TRIANACH, adj. (Train,) Of the third"
Edil (online at Edil.qub.ac.uk/dictionary/) accessed 07 24 2007:
"tríanach o, a (1 trían ) threefold, tripartite"
"treinech o, a (trí) In Mod. Ir. trénach. threefold, tripartite"
Then Old Irish Trian is equivalent to the Latin Trinus?