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

5. EXTRACT from PAPPUS’s Preſace to his Seventh Book
in Dr. HALLEY’s Tranſlation.

DE TACTIONIBUS II.

HIS ordine ſubnexi ſunt libri duo DE Tactionibus , in
quibus plures ineſſe propoſitiones videntur; ſed & ex
his unam etiam faciemus, ad hunc modum ſe habentem. “ E
punctis rectis & circulis, quibuſcunque tribus poſitione
datis, circulum ducere per ſingula data puncta, qui, ſi fieri
poſſit, contingat etiam datas lineas. ” Ex hac autem ob mul-
titudinem in Hypotheſibus datorum, tam ſimilium quam diſſi-
milium GENERUM , fiunt neceſſario decem propoſitiones di-
verſæ; quia ex tribus diſſimilibus generibus fiunt diverſæ
triades inordinatæ numero decem. Data etenim eſſe poſſunt
vel tria puncta; vel tres rectæ; vel duo puncta & recta; vel
duæ rectæ & punctum; vel duo puncta & circulus; vel duo
circuli & punctum; vel duo circuli & recta; vel punctum,
recta & circulus; vel duæ rectæ & circulus; vel tres circuli. Horum duo quidem prima problemata oſtenduntur in libro
quarto primorum Elementorum. Nam per tria data puncta,
quæ non ſint in linea recta, circulum ducere, idem eſt ac
circa datum triangulum circumſcribere. Problema autem in
tribus datis rectis non parallelis, ſed inter ſe occurrentibus,
idem eſt ac dato triangulo circulum inſcribere. Caſus vero
duarum rectarum parallelarum cum tertiâ occurrente, quaſi

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