Greetings gentlemen & ladies ! There was this Greek gentleman by the name of Archimides . Can someone break-up and translate the name ? Does the Arch come from Archios meaning ancient ? How should one best pronounce it - as Ark, or Arch or Arsh ?
sinhakumara. 
As for the pronounciation: Arkhimēdēs.
kh should be pronounced like an aspirated k. Put an emphasis on the first e when saying it.
In English that is toward “chief thinker” (archi-= “chief” + medes, related to medesthai “to think, to scheme”.)
Looking in “The Dictionary of Indo-European Roots” that second part is related to many of the med- (medicus, meditari, mederi) and mod- (modus, moderari, modestia) words in Latin, and to English mete and meet (the adjective).
ευρεκα - first person aorist active indicative. I have found.
Just a slight correction: εὕρηκα.
Also, is that not the first person perfect active indicative, and not the first person aorist active indicative? As far as I know, the first person aorist active indicative is εὗρον.
it’s definitely the perfect indicative. the use of perfect in his case is fitting:
“I’ve found it and now i have the solution” as oppose to “I found it (but it could be that now I do not hold the solution anymore)”.
Scribo may have put aorist for the perfect unintentionally.
Yeah sorry, pretty new to greek and “I found” seems very aoristy, yeah looking at my book (Alpha to Omega) which has the full conjugation laid out Eureka behaves pretty oddly…
as regards the pronounciation - does the X in Greek sound closer to “kh” as in sakhar (russian) or khuda (persian) ; or does it sound more like H as in hungry or hell ? Also do the Greek phonetics carry a universality through all its dialects ?
sinhakumara.
It is a “breathed” k sound (not an h). Many native english speakers can’t hear the difference, and it is commonly pronounced simply as a hard “K” sound. There are (not including rho) three “breathed” letters: theta, chi, and phi. Generally, these are now pronounced “th” as in “then” or “thin,” a hard K, and f. However, it is likely that the actual sounds were: theta= th in outhouse, phi=ph as in uphill, ect.