Proposition Replicated
Proposition X.73
If from a rational straight line there be subtracted a rational straight line commensurable with the whole in square only, the remainder is irrational; and let it be called apotome.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.73
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
Required by (dependents) (7)
- X.74Proposition X.74If from a medial straight line there be subtracted a medial straight line commensurable with the whole in square only,…
- X.79Proposition X.79Only one rational straight line can be annexed to an apotome which is commensurable with the whole in square only.
- X.85Proposition X.85To find the first apotome.
- X.103Proposition X.103A straight line commensurable in length with an apotome is itself an apotome and the same in order.
- 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.111Proposition X.111The apotome is not the same as the binomial.
- XIII.6Proposition XIII.6If a rational straight line be cut in extreme and mean ratio, each of the segments is the irrational straight line…
Discussion
No replications, contradictions, or comments registered yet for this claim.