Full text: Pergaeus, Apollonius: The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus

and DF = the Difference of the ſemidiameters of the 1ſt and 3d, and through A
deſcribe a circle which ſhall touch the two auxiliary ones externally.

Case 2d. If it be required that the circle ſhould touch all the other three
externally; then the circles being the ſame as before in reſpect to their magnitude,
let BG and DF be alſo the ſame as in the 1ſt Caſe, but through A deſcribe a circle
which ſhall touch and include the two auxiliary ones.

Case 3d. If it be required that the circle ſhould touch and include one of the
given circles A, and touch the other two externally; then let BG and DF = the
the ſum of the ſemidiameters of the 1ſt and 2d, and ſum of the ſemidiameters of
of the 1ſt and 3d reſpectively; and through A deſcribe a circle which ſhall touch
the two auxiliary ones externally.

Case 4th. If it be required that the circle ſhould touch externally one of the
given circles A, and ſhould touch and include the other two; then let BG and
DF = the ſums as in Caſe 3d, but through A deſcribe a circle which ſhall touch
and include the two auxiliary ones.

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