Proposition Replicated
Proposition X.77
If from a straight line there be subtracted a straight line incommensurable in square with the whole which with the whole makes the sum of squares medial but twice the rectangle rational, the remainder is irrational; let it be called that which produces with a rational area a medial whole.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.77
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (2)
Required by (dependents) (5)
- X.78Proposition X.78If from a straight line there be subtracted a straight line incommensurable in square with the whole which with the…
- X.83Proposition X.83Only one straight line can be annexed to the line producing with a rational area a medial whole.
- X.106Proposition X.106A straight line commensurable with the line producing with a rational area a medial whole is itself such a line.
- X.108Proposition X.108If from a rational area a medial area be subtracted, the side of the remaining area arises as one of four irrationals:…
- X.109Proposition X.109If from a medial area a rational area be subtracted, two other irrational straight lines arise, namely a first apotome…
Discussion
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