Proposition Replicated

Proposition III.7

If on the diameter of a circle a point be taken which is not the centre, and from the point straight lines fall upon the circle: that will be greatest on which the centre is, the remainder of the same diameter will be least, and of the rest the nearer to the diameter through the centre is always greater than the more remote.

type · theoreticalevidence · argumentextracted by · author

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

I.5 I.20 I.24

PropositionProposition III.7

Outgoing (1)

III.8

Full neighborhood

Depends on (3)

I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…
I.20Proposition I.20In any triangle two sides taken together in any manner are greater than the remaining one.
I.24Proposition I.24If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the…

Required by (dependents) (1)

III.8Proposition III.8If a point be taken outside a circle and from the point straight lines be drawn through to the circle, one of which is…

Discussion

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