Proposition Replicated
Proposition X.9
The squares on straight lines commensurable in length have to one another the ratio which a square number has to a square number; and squares which have to one another the ratio which a square number has to a square number will also have their sides commensurable in length.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.9
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 (4)
- VI.22Proposition VI.22If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be…
- VIII.14Proposition VIII.14If a square measure a square, the side will also measure the side; and if the side measure the side, the square will…
- X.5Proposition X.5Commensurable magnitudes have to one another the ratio which a number has to a number.
- X.6Proposition X.6If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable.
Required by (dependents) (3)
- X.10Proposition X.10To find two straight lines incommensurable, the one in length only, the other in square also, with an assigned straight…
- X.19Proposition X.19The rectangle contained by rational straight lines commensurable in length is rational.
- X.21Proposition X.21The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the…
Discussion
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