Proposition Replicated

Proposition VIII.12

Between two cube numbers there are two mean proportional numbers, and the cube has to the cube the ratio triplicate of that which the side has to the side.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VIII.12

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.17 VII.18

PropositionProposition VIII.12

Outgoing (5+)

VIII.15 VIII.19 VIII.23 VIII.25 IX.8

Full neighborhood

Depends on (2)

VII.17Proposition VII.17If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the…
VII.18Proposition VII.18If two numbers by multiplying any number make certain numbers, the numbers so produced will have the same ratio as the…

Required by (dependents) (5)

VIII.15Proposition VIII.15If a cube number measure a cube number, the side will also measure the side; and if the side measure the side, the cube…
VIII.19Proposition VIII.19Between two similar solid numbers there fall two mean proportional numbers, and the solid number has to the solid…
VIII.23Proposition VIII.23If four numbers be in continued proportion, and the first be cube, the fourth will also be cube.
VIII.25Proposition VIII.25If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the…
IX.8Proposition IX.8If as many numbers as we please beginning from a unit be in continued proportion, the third from the unit will be…

Discussion

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