Apollonius <Pergaeus>; Lawson, John - The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

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68[iii]

EXTRACT from PAPPUS's Preface to his Seventh Book
in Dr. HALLEY's Tranſlation.

DE SECTIONE DETERMINATA II.

HIS ſubjiciuntur libri duo de Sectione Determinatâ,
quas etiam ad modum præcedentium unam pro-
poſitionem dicere liceat, ſed disjunctam: quæ hujuſ-
modi eſt. “ Datam rectam infinitam in uno puncto ſe-
care, ita, ut è rectis interceptis inter illud & puncta
in illâ data, vel quadratum ex unâ, vel rectangulum
ex duabus interceptis, datam habeat rationem, vel ad
contentum ſub aliâ unâ interceptâ & datá quâdum;
vel etiam ad contentum ſub duabus aliis interceptis:
idque ad quam partem velis punctorum datorum. ”
Hujus autem, quaſi bis disjunctæ, & intricatos Dio-
riſmos habentis, per plura neceſſario facta eſt demon-
ſtratio. Hanc autem dedit Apollonius communi methodo
tentamen faciens, ac ſolis rectis lineis uſus, ad exemplum
ſecundi libri Elementorum primorum Euclidis: ac rur- ſus idem demonſtravit ingenioſe quidem, & magis ad
inſtitutionem accomodate, per ſemicirculos. Habet
1

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