Proof
Drop a chord through the point parallel to the plane; drop a
perpendicular from the chord to its foot in the plane; the
constructed line, being perpendicular to two intersecting lines at
the foot, is perpendicular to the plane (XI.4).
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Depends on (3)
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.12Proposition I.12To draw a perpendicular straight line to a given infinite straight line from a given point not on it.
- XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…
Required by (dependents) (5)
- XI.12Proposition XI.12To set up a straight line at right angles to a given plane from a given point in it.
- XI.35Proposition XI.35If there be two equal plane angles, and on their vertices there be set up elevated straight lines containing equal…
- XIII.13Proposition XIII.13To construct a pyramid (regular tetrahedron), to comprehend it in a given sphere, and to prove that the square on the…
- XIII.14Proposition XIII.14To construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
- XIII.15Proposition XIII.15To construct a cube and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
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