Proposition Replicated

Proposition V.12

If any number of magnitudes be proportional, as one of the antecedents is to one of the consequents, so will all the antecedents be to all the consequents.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:V.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)

V.1 V.2

PropositionProposition V.12

Outgoing (5+)

V.15 V.24 VI.20 XII.1 XII.6

Full neighborhood

Depends on (2)

V.1Proposition V.1If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in…
V.2Proposition V.2If a first magnitude be the same multiple of a second that a third is of a fourth, and a fifth also be the same…

Required by (dependents) (5)

V.15Proposition V.15Parts have the same ratio as the same multiples of them taken in corresponding order.
V.24Proposition V.24If a first magnitude have to a second the same ratio as a third has to a fourth, and also a fifth have to the second…
VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…
XII.1Proposition XII.1Similar polygons inscribed in circles are to one another as the squares on the diameters.
XII.6Proposition XII.6Pyramids which are of the same height and have polygonal bases are to one another as the bases.

Discussion

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