Proposition Replicated

Proposition II.7

If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to twice the rectangle contained by the whole and the said segment together with the square on the remaining segment.

type · theoreticalevidence · argumentextracted by · author

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

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)

II.1 II.4

PropositionProposition II.7

Outgoing (1)

II.13

Full neighborhood

Depends on (2)

II.1Proposition II.1If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by…
II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…

Required by (dependents) (1)

II.13Proposition II.13In acute-angled triangles the square on the side subtending the acute angle is less than the squares on the sides…

Discussion

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