Proposition Replicated
Proposition VI.2
If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle proportionally; and if the sides of the triangle be cut proportionally, the line joining the points of section will be parallel to the remaining side of the triangle.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VI.2
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 (6)
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- I.37Proposition I.37Triangles which are on the same base and in the same parallels are equal to one another.
- I.38Proposition I.38Triangles which are on equal bases and in the same parallels are equal to one another.
- I.39Proposition I.39Equal triangles which are on the same base and on the same side are also in the same parallels.
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- V.11Proposition V.11Ratios which are the same with the same ratio are also the same with one another.
Required by (dependents) (8)
- VI.3Proposition VI.3If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the…
- VI.4Proposition VI.4In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which…
- VI.9Proposition VI.9From a given straight line to cut off a prescribed part.
- VI.10Proposition VI.10To cut a given uncut straight line similarly to a given cut straight line.
- VI.11Proposition VI.11To two given straight lines to find a third proportional.
- VI.12Proposition VI.12To three given straight lines to find a fourth proportional.
- VI.24Proposition VI.24In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.
- XI.17Proposition XI.17If two straight lines be cut by parallel planes, they will be cut in the same ratios.
Discussion
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