Proposition Replicated

Proposition VI.22

If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be proportional; and if the rectilineal figures similar and similarly described upon them be proportional, the straight lines will themselves also be proportional.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VI.22

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (1)

VI.20

PropositionProposition VI.22

Outgoing (3)

X.9 X.14 XI.37

Full neighborhood

Depends on (1)

VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…

Required by (dependents) (3)

X.9Proposition X.9The squares on straight lines commensurable in length have to one another the ratio which a square number has to a…
X.14Proposition X.14If four straight lines be proportional, and the square on the first be greater than the square on the second by the…
XI.37Proposition XI.37If four straight lines be proportional, the similar and similarly described parallelepipedal solids upon them will also…

Discussion

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