Greek Language/Euclid Terms/Augggh!

Trying to come to some understanding of the divine Euclid, I’m stymied by the fact that I don’t read classical Greek. Of course, there are English “translations.” But I don’t want to know the English word that most closely approximates the Latin word that someone once thought meant the same thing as the original Greek word; I want to know the following:
(1) the original Greek word transliterated–ie, not written in Greek letters, but in the English sound-equivalent ( as when we write “hubris” or “chaos” )…
(2) some sense of, not only what the words formally denote, but what they might have connoted at that time. For example: for us the word “line” suggests something drawn or inscribed, but it might be that the word actually used by Euclid suggested an edge (of a sword?) or a length of yarn stretched on a loom.
The terms I am particularly interested in (all from The Elements, Book I, Definitions) are the ones rendered in English as POINT, PART, LINE, LENGTH, and SURFACE.
As a final question: Sohowcome we read “perestroika” in transliterated English and not with cyrillic characters; “Osama Bin Laden” or “Jihad” not in Arabic characters; “karma” not in Hindic; “Beijing” not in Chinese; but words from classical Greece are almost always presented in Greek letters, without transliteration?

The Greek alphabet. Not that you can’t get it in hundreds of other places…

Greece was, of course, regarded as a centre of culture and learning by the Romans… and the Romans influenced the whole of Western European culture… so much so that Latin and Greek were considered, for centuries, amongst the essential requirements for being properly educated. So, the Greek alphabet is almost as important in Western European culture as the Roman one we actually use. Whereas Arabic, Russian, Chinese and so forth would be known only to specialists.

Cheer up. The classical Greek alphabet isn’t so tough to get your head around. (The classical Greek language on the other hand…)

To understand Euclid, two things are required: Heath’s 1925 translation & commentary of the Elements and a blackboard to work out the propositions on. Dover publishes a 3 volume edition of Heath’s translation. Knowledge of Greek and/or mathematics is nice but not required.

Heath will not supply you with transliteration of the Greek. Learning Attic Greek would not be a waste of time.

Heath gives a mathematical, historical, and linguistic context to the concepts Euclid uses. For example, his notes on Definition 2, “A line is breadthless length”, go on for 7 pages; notes for Postulate 5 extend 19 pages; Proposition 47, 18 pages. The Elements is a synthesis of a few hundred years of Greek academic thinking on geometry. Euclid took these thoughts and made them rigorously consistent. Intellectually, he is closer to the 21[sup]st[/sup] century than to the Homeric era. Taking your example, his word for line, [sym]grammh[/sym] (‘gramme’), originates from a less than bucolic word meaning “a scratch”. For possibly more colorful origins of the idea of a line, you need to go back a couple of hundred years to the era of the pythagoreans. Unfortunately, few source materials exist and you pretty much have to settle for some scholar’s learned commentary (and, of course, some other scholar’s learned commentary establishing the exact opposite). If you are interested in the basic etymology of the greek words, a copy of Liddell & Scott’s Greek-English Lexicon will be very useful. For a real fun time, examine the slowly evolving meaning of the word [sym] logos[/sym] (‘logos’) from Heraclitus through Euclid to the New Testament.

As for your final question, some books make the mistaken assumption that their audience is well-educated, in a classical sense. This is a huge mistake, especially in America. Knowledge of Greek, Latin, German, & French cannot be presumed.

To be more accurate, they make the arrogant assumption that anyone worth communicating their ideas to speaks Greek, German, Latin and French. This is no more a mistake in America than in Europe or any other continent.

Reading Euclid is not exactly like reading Plato. He is not exactly one of the great stylists of the Hellenistic world. If you can find yourself a tutor, you should be able to slog through it in a matter of weeks.


Words from classical Greek are not “always” given in Greek letters without transcription. I have any number of books in my bookcase, up to and including at least two fat dictionaries, that give classical Greek words in Roman transcription only.

The Perseus Project at Tufts has both Euclid in Greek and Heath’s translation online. This link takes you to the list of Greek texts. They also have Liddell & Scott online and most words appear to be hyperlinked to it. I’m looking at the English transliteration right now, and you can configure the system to display the Greek characters.

Euclid’s first definition begins with the word [sym]shmeion[/sym] transliterated as “sêmeion”, and it has the basic translation of “a mark, a token”. That is probably the word translated as “point”.