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Use Calculus to prove a property in Apollonius' book: Let C be a point on a hyperbola. Let CB be the perpendicular from that point

Use Calculus to prove a property in Apollonius' book: Let C be a point on a hyperbola. Let CB be the perpendicular from that point to the diameter. Let G and H be the intersections of the diameter with the curve, and choose A on the diameter, or the diameter extended, so that AH : AG = BH : BG. Then AC will be tangent to the curve at C

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