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I am reading a French geometry textbook that says the following:

Pour ce qui va nous intéresser ici, deux droites qui ne se rencontrent pas (ou sont confondues) sont dites parallèles.

My English translation of this is as follows:

For what interests us, two straight lines who never meet (or are combined) are said to be parallel.

I'm wondering how the "(ou sont confondues)" should be interpreted in the context. Two lines that "combine" are not parallel, so it seems to me that this should be interpreted as saying that two straight lines who never meet, or are never combined, are said to be parallel. Is this interpretation correct?

I would appreciate it if people would please clarify this.

  • Comments are not for extended discussion; this conversation has been moved to chat. – Evpok Jan 10 at 17:52
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Confondues doesn't mean "combined", it's closer to "confused" when it means indistinguishable.

So deux droites confondues means two straigth lines that are impossible to distinguish from each other, i.e. two straight lines that might have different definitions but that share all of their points.

See the TLFi:

CONFONDRE, verbe trans.
I.− [L'accent est mis sur l'idée de non-distinction]
A.− Mêler si étroitement (soit plusieurs choses ou personnes, soit une chose ou une personne à un ensemble) qu'il n'est plus possible de les distinguer.

Etymologically, confondre means fondre ensemble, i.e. melt together.

Note: In geometry, the definition of parallel lines is the set of lines that share the very same direction (vecteur directeur). That means any given line is parallel with itself.

When we want to exclude that case, we say droites strictement parallèles.

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  • The technical term in English is "coincident lines". It exists in French too but "confondu" is more common, it seems. – Teleporting Goat Jan 10 at 13:04

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