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BSHM Bulletin: Journal of the British Society for the History of Mathematics Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t741771156 The tangency problem of Apollonius: three looks

To cite this Article: , 'The tangency problem of Apollonius: three looks', BSHM Bulletin: Journal of the British Society for the History of Mathematics, 22:1, 34 - 46 To link to this article: DOI: 10.1080/17498430601148911 URL: http://dx.doi.org/10.1080/17498430601148911

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Franc BH ` D epbihdhssltosin solutions his published te aigpoint Having en hi on ftnec,point tangency, of point their Being F HFE )( ¸ i Vie ois h iethrough line The . B BD n e titretcircle intersect it let and ) r qa atraeitro nls aalllns.Angles lines). parallel angles, interior (alternate equal are ¼ ` e(1540–1603) te ( BJ BD )( DGB H loat also E BK ol epbigaotteslto.Cntutascn line secant a Construct solution. the about bring help would B and ) . and A F H n agn ocircle to tangent and Construct . 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These tangency. in poles. eight of the circles, here. points of solution the shown each at two of to about circles each centre brings to corresponding radical similitude respect the the radical with from pole the intersect line its Construct lines construct a them. and Draw by similitude circles. defined of given similitude line of one Pick lines centre. four the and homothety w ouin.Gvntesm he ice,ltcircles let circles, three same or zero the has tangent group homogeneously each Given is cases, it special solutions. Excepting or be group). groups) fourth two three can tangent (the of circles homogeneously circles one three either given into all is to (falling three circle pair The solution one Each them. exactly ways. to seeing different even three without in paired solutions the for groups the encloses sphere one since are plane circles tangent the them. common When no two. produce though. is other will there here three construction spheres, these apply into Consider not Gergonne’s rolled one. does and only reasoning exist, the three-dimensional not solutions The certainly eight conflict, All one is circles. 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