Proof
Apply I.11 to erect perpendiculars; use I.3 to cut off equal segments;
use I.31 and I.29 to close the square; verify right angles via I.34.
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Full neighborhood
Depends on (5)
- I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
- 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.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
Required by (dependents) (7)
- 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.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…
- II.5Proposition II.5If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole…
- 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…
- II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
- II.14Proposition II.14To construct a square equal to a given rectilineal figure.
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