Proposition XII.16 — Given two circles about the same centre, to inscribe in the …

Proof

Bisect arcs repeatedly (III.30) until the chord-to-arc gap is smaller than the difference of radii; this guarantees that the inscribed polygon avoids touching the smaller circle.

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Depends on (2)

III.30Proposition III.30To bisect a given arc.
X.1Proposition X.1Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and…

Required by (dependents) (1)

XII.17Proposition XII.17Given two spheres about the same centre, to inscribe in the greater sphere a polyhedral solid which does not touch the…

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