 The works of Apollonius of Perga were partly unknown or lost

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 tarix 17.11.2018 ölçüsü 1,07 Mb. #80160 • During the 16th and 17th centuries interest in ancient works on mathematics increased and several mathematicians tried to restore and reconstruct works that had been lost, drawing upon the quotations and references in other works of ancient mathematicians. • The preface to the seventh book of Mathematical Collection by Pappus outlined the contents of Apollonius’s treaties On Tangencies and On Inclinations. • Given 3 things, each of which may be either a point, a straight line or a circle, to draw a circle which shall pass through each of the given points (so far as it is points that are given) and touch the straight lines or circles.  • The particular case of drawing a circle to touch three given circles attracted the interest of Viete and Newton. • Vieta thereupon proposed a simpler construction (by means of only compass and ruler), and restored the whole treatise of Apollonius in a small work, which he entitled Apollonius Gallus (Paris, 1600).     • If EAEB = EC2, then EC is tangent to the circle ABC. • By the lemma previously proved, the circle ABC touches  at C • Construct the circle ALM • NMH  NOI  MN = NO • Construct circle DBG • Their circumscribed circles are mutually tangent to each other • Exegetics (solution by derivations) • 2001 Eppstein Tangent Spheres and Tangent Centers • Wikipedia Yüklə 1,07 Mb.

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