Proposition Replicated

Proposition VIII.18

Between two similar plane numbers there is one mean proportional number, and the plane number has to the plane number the ratio duplicate of that which the corresponding side has to the corresponding side.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VIII.18

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 (2)

VII.19 VIII.5

PropositionProposition VIII.18

Outgoing (4)

VIII.19 VIII.20 VIII.26 IX.1

Full neighborhood

Depends on (2)

VII.19Proposition VII.19If four numbers be proportional, the number produced from the first and fourth will be equal to the number produced…
VIII.5Proposition VIII.5Plane numbers have to one another the ratio compounded of the ratios of their sides.

Required by (dependents) (4)

VIII.19Proposition VIII.19Between two similar solid numbers there fall two mean proportional numbers, and the solid number has to the solid…
VIII.20Proposition VIII.20If one mean proportional number fall between two numbers, the numbers will be similar plane numbers.
VIII.26Proposition VIII.26Similar plane numbers have to one another the ratio which a square number has to a square number.
IX.1Proposition IX.1If two similar plane numbers by multiplying one another make some number, the product will be square.

Discussion

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