Proposition Replicated

Proposition XI.34

In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciprocally proportional to the heights are equal.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XI.34

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 (3)

VI.14 XI.32 XI.33

PropositionProposition XI.34

Outgoing (1)

XI.36

Full neighborhood

Depends on (3)

VI.14Proposition VI.14In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular…
XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
XI.33Proposition XI.33Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.

Required by (dependents) (1)

XI.36Proposition XI.36If three straight lines be proportional, the parallelepipedal solid formed out of the three is equal to the…

Discussion

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