Proposition Replicated
Proposition II.11
To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:II.11
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 (6)
- I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
- I.10Proposition I.10To bisect a given finite straight line.
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- 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.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
Required by (dependents) (7)
- IV.10Proposition IV.10To construct an isosceles triangle having each of the angles at the base double of the remaining one.
- VI.30Proposition VI.30To cut a given finite straight line in extreme and mean ratio.
- XIII.1Proposition XIII.1If a straight line be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole…
- XIII.2Proposition XIII.2If the square on a straight line be five times the square on a segment of it, then, when the double of the said segment…
- XIII.4Proposition XIII.4If a straight line be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment…
- XIII.5Proposition XIII.5If a straight line be cut in extreme and mean ratio, and there be added to it a straight line equal to the greater…
- XIII.6Proposition XIII.6If a rational straight line be cut in extreme and mean ratio, each of the segments is the irrational straight line…
Discussion
No replications, contradictions, or comments registered yet for this claim.