Proposition Replicated
Proposition II.9
If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double of the square on the half and of the square on the straight line between the points of section.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:II.9
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 (8)
- 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.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.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
- 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.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
Discussion
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