Zeno Rogue
1 min readDec 29, 2021

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Thanks!

Euclid basically wanted to reduce everything he knew about geometry to some set of postulates as simple as possible.

Like, if you teach someone to play a game, you want to state its rules as simple as possible. Then they are easiest to remember.

If something follows from the other rules, you do not need to introduce it. So postulates are not supposed to follow from the other postulates. If they did, it is more elegant to remove the one which does. And things that follow would be stated as theorems (consequences of the main rules).

So he would be more satisfied if he reduced everything to just the first 4 postulates. He probably suspected (or maybe he knew?) that the first four were unavoidable, but it seemed to him that the fifth could be avoided.

(You say "from ones that come before" but the order does not matter here: if Euclid found that, say, 3rd followed from 1st and 5th, he would probably also remove the 3rd postulate and possibly reorder the other ones.)

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Zeno Rogue
Zeno Rogue

Written by Zeno Rogue

Mathematics, game development, art, roguelikes, hyperbolic geometry. Sometimes all at once.

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