Proposition Replicated
Proposition I.31
Through a given point to draw a straight line parallel to a given straight line.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:I.31
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige \and Claude \\
\small {(translation after Heath, 1908; encoding new, CC-BY-4.0)}·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (2)
Required by (dependents) (22)
- I.32Proposition I.32
- I.37Proposition I.37
- I.38Proposition I.38
- I.39Proposition I.39
- I.40Proposition I.40
- I.42Proposition I.42
- I.46Proposition I.46
- I.47Proposition I.47
- II.1Proposition II.1
- II.2Proposition II.2
- II.4Proposition II.4
- I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
- 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.
- I.40Proposition I.40Equal triangles which are on equal bases and on the same side are also in the same parallels.
- I.42Proposition I.42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
- I.46Proposition I.46On a given straight line to describe a square.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- 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.2Proposition II.2If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the…
- 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…
Discussion
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