Proof
Draw two perpendicular diameters of the given circle (I.11). Through
each endpoint draw the tangent to the circle (III.16). Each tangent
is perpendicular to its diameter (III.18); the four tangents thus form
a quadrilateral with all sides parallel and all angles right (I.28,
I.29). Equal radii combined with I.34 force the sides equal, hence a
square circumscribes the circle.
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Depends on (6)
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.28Proposition I.28If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on…
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
- III.16Proposition III.16The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle,…
- III.18Proposition III.18If a straight line touch a circle, and a straight line be joined from the centre to the point of contact, the straight…
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