Proposition Replicated
Proposition XI.25
If a parallelepipedal solid be cut by a plane parallel to opposite planes, then, as the base is to the base, so will the solid be to the solid.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XI.25
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (3)
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- XI.17Proposition XI.17If two straight lines be cut by parallel planes, they will be cut in the same ratios.
- XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
Required by (dependents) (3)
- XI.28Proposition XI.28If a parallelepipedal solid be cut by a plane through the diagonals of the opposite planes, the solid will be bisected…
- XI.31Proposition XI.31Parallelepipedal solids which are on equal bases and of the same height are equal to one another.
- XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
Discussion
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