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History of Science and Mathematics

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  • $\begingroup$ Any (translated) quote in Euclid's Elements to see that? $\endgroup$ Commented Jun 20, 2021 at 15:18
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    $\begingroup$ @QuiqueRuiz: If you read the book, you can see that clearly. It would be instructive if you can provide a quote showing the opposite. $\endgroup$ Commented Jun 20, 2021 at 18:35
  • $\begingroup$ Your answer surprises me, because Greeks tried to avoid infinity, and if one considers a space, a geometric space as a whole, one must think of if as being infinite. I know it is considered that the infinitude of prime numbers is proved in Euclid's Elements, but one can say that what is proved is that if one has a finite list of prime numbres, one can find a new prime number which is not in the list. That's why I asked when in history a geometric space was treated as a whole. Maybe I should say "studied". $\endgroup$ Commented Jun 20, 2021 at 21:27
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    $\begingroup$ @QuiqueRuiz: Euclid does not claim infinitude of the 2- or 3-space anywhere except in Postulate 5: that a line can be continued indefinitely. That is why Postulate 5 was considered suspicious. In the definitions of the circle, he is talking about "plane figures". But there is no doubt, that points and lines live in a plane too. $\endgroup$ Commented Jun 20, 2021 at 21:45
  • $\begingroup$ @QuiqueRuiz: One can claim that Euclid studies the plane and the 3-space in Elements. But he never claims it himself. $\endgroup$ Commented Jun 20, 2021 at 21:48