Proposition Replicated
Proposition III.3
If in a circle a straight line through the centre bisect a straight line not through the centre, it also cuts it at right angles; and if it cut it at right angles, it also bisects it.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:III.3
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 (5)
- III.1Proposition III.1To find the centre of a given circle.
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…
- I.13Proposition I.13If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two…
- I.26Proposition I.26If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely either…
Required by (dependents) (7)
- III.4Proposition III.4If in a circle two straight lines cut one another which are not through the centre, they do not bisect one another.
- III.9Proposition III.9If a point be taken within a circle, and more than two equal straight lines fall from the point on the circle, the…
- III.14Proposition III.14In a circle equal straight lines are equally distant from the centre, and those which are equally distant from the…
- III.15Proposition III.15Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the centre is always greater than…
- III.25Proposition III.25Given a segment of a circle, to describe the complete circle of which it is a segment.
- III.35Proposition III.35If in a circle two straight lines cut one another, the rectangle contained by the segments of the one is equal to the…
- III.36Proposition III.36If a point be taken outside a circle and from it there fall on the circle two straight lines, and if one of them cut…
Discussion
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