Proposition Replicated

Proposition XII.18

Spheres are to one another in the triplicate ratio of their respective diameters.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XII.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 (4)

X.1 XII.8 XII.12 XII.17

PropositionProposition XII.18

Outgoing (0)

none

Full neighborhood

Depends on (4)

X.1Proposition X.1Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and…
XII.8Proposition XII.8Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
XII.12Proposition XII.12Similar cones and cylinders are to one another in the triplicate ratio of the diameters in their bases.
XII.17Proposition XII.17Given two spheres about the same centre, to inscribe in the greater sphere a polyhedral solid which does not touch the…

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