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While I was reading translated into Korean version of Thomas Heath Euclid Elements, I found something weird. And I am doubting whether that translation is wrong. I will retranslate it so you guys can rate it. Before, please read the original text of Thomas Heath Elements.

https://archive.org/details/EuclidsElementsBooksIIIVolume1Heath/page/n164 (liked above, book page 155, definition 1)

Now I will recite Korean version below, which I will retranslate it. Bold sentences are different sentences compare to original text.

Definition 1: A point is that which is indivisible into parts.

The original text says "A point is that which has no part." But this is incorrect translation. It is better to say "A point is that which is indivisible into parts." An exactly parallel use of (greek word) in the singular is found in Aristotle, literally "There is a part even of the form"; Bonitz translates as if the plural were used, "even the form is divisible(into parts)." So in this case, it is reasonable to say "A point is that which is indivisible into parts." Capella(5th C.A.D) alone or almost alone translated differently. "a point is that a part of which is nothing." Simon has adopted this translation, but this does not make sense. If point does not have part, Euclid might as well have said that a point is itself "nothing" , which of course he does not to.

Now, I will write down my understanding below.

Thomas Heath

  • A point is that which has no part right
  • A point is that which is indivisible into parts right
  • A point is that a part of which is nothing wrong

Korean translator

  • A point is that which has no part wrong
  • A point is that which is indivisible into parts right
  • A point is that a part of which is nothing wrong

So what Korean translator think is, A point is that which has no part and A point is that a part of which is nothing, these two sentences are same. But I don't think it is same in view of Thomas Heath's original purpose. Am I wrong? If so, please help me to understand it.

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    $\begingroup$ I think you are safe to follow Heath's original. I cannot comment on what a Korean translator had in mind. If you reading for your own education, I suggest reading the English version. If you are teaching a class in Korean, you may have to supplement the Korean translation with your own comments. I also suggest reading a more modern version of foundations of geometry, say, Greenberg's book. $\endgroup$ – Moishe Kohan Dec 18 '19 at 19:09
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    $\begingroup$ Many scholars believe that definitions of Book 1 are later insertions for didactic purposes, see What made Euclid/Heron define line as a length without breadth and point as that which has no part? The part-whole axiom of Euclid ("the whole is greater than its part") agrees well with Heath's translation. Medieval Aristotelians, like Duns Scotus, accepted points as something (not nothing) with no extension, and hence no part. "Indivisible into parts" is different. To Aristotle, objects can have parts without being divisible into them. $\endgroup$ – Conifold Dec 19 '19 at 1:40
  • $\begingroup$ You seem to be fluent in English, and Heath is considered a good, respectable translator/commentator of Euclid. Why do you bother about Korean translation? $\endgroup$ – Alexandre Eremenko Dec 19 '19 at 3:28
  • $\begingroup$ @Alexandre Eremenko As I told, that Korean translation is based on Heath version so I thought my translation may be wrong. Because that Korean translator is expert in translating. $\endgroup$ – Vito Dec 19 '19 at 3:53
  • $\begingroup$ @Conifold Then does it mean "having no part" is sufficient condition and "indivisible into parts" is necessary condition? $\endgroup$ – Vito Dec 19 '19 at 4:11

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