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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212174Apollonij Pergæi I, O L remanebunt I E, L K inæquales. Quod eſt abſurdum: oſtenſæ enim fue-
runt prius æquales inter ſe.

In figura autem tertia ducamus duas perpendiculares, & c. In quarto
11e caſu ſupponuntur baſes A C, & D F per centra circulorum tranſire, eo quod
anguli A B C, & D E F recti ſupponuntur, atque rectæ lineæ B H, E I non
ſunt perpendiculares ſuper eaſdem baſes, licet intra circulos efficiant angulos B
H C, & E I F inter ſe æqua-
les: perſecta igitur conſiru-

235[Figure 235] ctione, vt prius ad diame-
trũ D F, ducãtur ex punctis
E, & K perpendiculares E
Q, K S, quæ diuidẽtur bi-
fariã, & ad angulos rectos
in P, & R. Et quoniam
(vt in præcedenti caſu oſtẽ-
ſum eſt) G E ad E I ean-
dem proportionem habet,
quàm M K ad K L, cum-
que latera I E, L K ſint
parallela, pariterque P E, & K R æquidiſtent, atque baſes I P, L R in dire-
ctum poſitæ ſint, erunt triangula I E P, & L K R æquiangula, & ſimilia: &
propterea I E ad E P erit, vt. L K ad K R: eſt verò P E ad eius duplam E Q,
vt R K ad eius duplam K S (cum diameter ſecet eas bifariam, quas perpendi-
culariter prius ſecabat) ergo, ex æquali ordinata, erit G E ad E Q, vt M K ad
K S; ſuntq; anguli verticales G E Q, & M K S æquales, propterea quod conti-
nẽtur à rectis lineis quæ binæ binis ſunt æquidiſtantes; ergo triangula G E Q, &
M K S ſimilia ſunt inter ſe: & propterea angulus E G Q æqualis erit angulo K M S.

Et propterea ſegmentum E F Q maius ſimile erit ſegmento K F S mi-
22f nori: quod eſt abſurdum, & c. Legendum puto. Et propterea periheriæ E F
Q, & K F S, quibus inſiſtunt æquales erunt: quod eſt abſurdum. Eſt enim E
F Q maior, quàm K F S.

Notæ in Propoſit. Præmiſſ. VI.

DEinde ſint duo anguli B, E qualeſcumque; ſed angulus A B H, vel
33a C B H æqualis angulo D E I vel F E I, & condictiones, vti dixi-

236[Figure 236]

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