Proposition Replicated
Proposition X.21
The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the square equal to it is irrational. Let the latter be called medial.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.21
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
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Required by (dependents) (9)
- X.22Proposition X.22The square on a medial straight line, if applied to a rational straight line, produces as breadth a straight line…
- X.23Proposition X.23A straight line commensurable with a medial straight line is medial.
- X.24Proposition X.24The rectangle contained by medial straight lines commensurable in length is medial.
- X.25Proposition X.25The rectangle contained by medial straight lines commensurable in square only is either rational or medial.
- X.26Proposition X.26A medial area does not exceed a medial area by a rational area.
- X.27Proposition X.27To find medial straight lines commensurable in square only which contain a rational rectangle.
- X.28Proposition X.28To find medial straight lines commensurable in square only which contain a medial rectangle.
- X.36Proposition X.36If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be…
- X.115Proposition X.115From a medial straight line there arise irrational straight lines infinite in number, and none of them is the same with…
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