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Euclid's Elements: Primary Documents 2017-09-15 12:05:43 Post No. 3383885
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Euclid's Elements: Primary Documents 2017-09-15 12:05:43 Post No. 3383885
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ITT I will conduct a little bit of amateur philology and share my thoughts. My object of study is a page from an edition of Euclid which is about 1100 years old. It is 45, verso (the left page at the link)
http://bodley30.bodley.ox.ac.uk:8180/luna/servlet/detail/ODLodl~8~8~57083~130478:Elementa,-Books-I-XV
The reason why I am interested in this page, is because a facsimile of same is used as the frontispiece for Heath's edition, which is now the modern English-language standard for the complete, annotated Euclid. Clearly, the page was chosen to be an attractive, representative example for what Euclid - on the written page - has looked like throughout history.
The proposition which is shown (top two-thirds of the page) is BOOK III, PROPOSITION 4. The thing being shown is: if two lines in a circle cut each other, and they don't pass through the circle's center, then they don't bisect each other.
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Both script and language are Greek. The script, however, is a sort of stylized cursive Greek used during the medieval period, known as Greek Minuscule:
https://en.wikipedia.org/wiki/Greek_minuscule
The text is Byzantine, and dated C. 888 AD. Given this (and the reference to "uncial" in the above wiki link), it is interesting to contrast the orderly-yet-stylized writing of this codex of the Elements, with another book, produced just a few decades earlier, and clear on the opposite end of Europe, between Scotland and Ireland: the Book of Kells.
Pic related is the example that wiki gives of an "uncial" script, and is a representative example for what the "regular text" pages of Kells look like, notwithstanding the famous stylized picture-pages. With Kells however, the language is not Greek, but Latin - a lavish presentation of (for the most part) the Latin Vulgate.
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The next task, to make sense of the OP page, is to gather together three or four levels of translation: the original, a modern Greek transliteration, a possible intermediate romanization, and finally the English translation. Happily much of this is already online so it's just a matter of putting things in-parallel.
The original is already given. For the modern greek transliteration, this is fastest, but it's missing certain bits:
http://users.ntua.gr/dimour/euclid/book3/postulate4.html
A more thorough and closely-matching transliteration, with the added benefit of already-in-line parallel English translation, is HERE (pp. 73-74 of the PDF):
http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf
And for completeness, an English solo version is given here (which is not letter-perfect Heath, but is as close as makes no material difference):
https://mathcs.clarku.edu/~djoyce/elements/bookIII/propIII4.html
Comparing these to the difficult page of the OP begins to make things make sense at a granular level. A good tactic is to focus in on the CAPITALIZED GEOMETRIC "ABΓ" - style forms, to orient yourself in a given text, and keep pace: I count 22 such items, consitently across the versions that I read (see pic related for a quick grab of these). Notice the bar-forms at tops of each, denoting that they are such-and-such geometric objects.
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elaboration: close parallel comparison of the original with a modern Greek script.
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