Proposition Replicated
Proposition II.13
In acute-angled triangles the square on the side subtending the acute angle is less than the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle (namely that on which the perpendicular falls) and the straight line cut off within by the perpendicular.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:II.13
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 (4)
- II.7Proposition II.7If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to…
- II.12Proposition II.12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides…
- I.12Proposition I.12To draw a perpendicular straight line to a given infinite straight line from a given point not on it.
- 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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