Proof
Lay the two segments end-to-end as , on a single line; on
as diameter describe a semicircle (Postulate 3, III.31 implicit).
Erect the perpendicular at to the diameter; then , , and are similar by VI.8, so
, making the required mean proportional.
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Depends on (4)
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- III.31Proposition III.31In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less…
- VI.8Proposition VI.8If in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the…
- 3Postulate 3To describe a circle with any centre and distance.
Required by (dependents) (3)
- VI.25Proposition VI.25To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal…
- X.10Proposition X.10To find two straight lines incommensurable, the one in length only, the other in square also, with an assigned straight…
- X.115Proposition X.115From a medial straight line there arise irrational straight lines infinite in number, and none of them is the same with…
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