Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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265227Conicor. Lib. VI. ipſi C A D circa communem axim A G. Et quoniam hyperbolæ H G 1 ſemiaxis
tranſuer ſus B G maior eſt tranſuer ſo ſemiaxe B A, hyperboles C A D, pariter-
què latus rectum illius maius erit buius latere recto (cum later a figurarum ſint
1112. huius. proportionalia in hyperbolis ſimilibus:)
igitur hyperbole H G I maior eſt hyper-
bola M G N (quod ab alijs oſtenſum eſt), &
conſiſtunt circa communē axim A G,
&
vertex G eſt communis; igitur hyperbole H G I compræbendit hyperbolen M
G N;
& ideo hyperbole H G I cadit inter duas hyperbolas G M, & A C : &
propterea hyperbole G H multo magis ſucceſſiuè vicinior efficitur hyperbolæ A C,
quàm hyperbole G M;
ſed duæ hyperbole æquales, & ſimiliter poſitæ A C, & G
22Propoſ. 7.
addit.
M ſemper magis, ac magis ad inuicem approximantur, igitur multo magis hy-
perbolæ concentricæ A C, &
G H ſemper magis, ac magis ad ſe ſe ipſas appro-
33lib. 7.
prop. 208.
29. 30.
lib. 5.
pinquantur, &
inter ſe non conuenient vt Pappus demonſtrauit. Tandem, quoniã
lineæ breuiſſimæ, quæ perpendicularis eſt ad tangentem hyperbolem G H portio
ab asymptoto E B, &
ſectione H G compræ henſa effici poteſt minor quacunque
recta linea propoſita;
cadit verò hyperbole A C inter ſectionem G H, & continen-
44Propof. 4.
lib. 2.
tem B E;
igitur multo magis diſtantia inter hyperbolas G H, & A C minor
erit quacunque recta linea propofita.
Quod erat oſtendendum.
Si in duobus conis ducta fuerint duo triangula per axes A B C, D E
55PROP.
10. Add.
F ſimilia, &
ſimiliter poſita, atq; ſectionum I G H, & N L M dia-
metri G O, L K æque ad baſes inclinatæ intercipiant cũ triangulorum la-
teribus A B, D E eiſdem G O, L K parallelis, portiones O B, K E æquales;
vel cum axibus conorum Aγ, D Z diametris æquidiſtantibus intercipiant
portiones O Y, K Z æquales, &
efficiant angulos A Y C, D Z F
aquales :
erunt conicæ ſectiones inter ſe æquales, & in qualibet earum,
duplum interceptæ poterit figuram ſectionis.
312[Figure 312]
Primò in parabolis, quia triangula A B C, D E F ſunt ſimilia, erit B C
ad C A vt E F ad F D, &
G O, L K ſunt parallelæ homologis A B, D E;
ergo O C ad C G, & B O ad G A eandem proportionem habebunt, quàm B C
ad C A, ſeu eandem, quàm habet E F ad F D;
eſtque E K ad L D vt E F
ad F D;
ergo B O ad G A eſt vt E K ad L D; ſuntque B O, E K æquales;

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