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

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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230192Apollonij Pergæi huius) atque A N pa-

259[Figure 259] rallela erit L O. Edu-
catur iam R Q bifariã
diuidens A E, L M in
P, Q: quare erit diame
1128. lib. 2. ter ſectionis (32. ex 2.)
& educatur R V paral-
lela A N, quæ ſectionẽ
2217. lib. 1. continget (18. ex 1.) .
Et quia duo ſegmen-
ta L M, A E ſunt ſi-
milia habebit maior
3316. 17.
huius. Q R ad eandem R V
eandem proportionẽ,
quàm habet minor R
P; quod eſt abſurdum.
Quare non ſunt ſimilia
duo ſegmenta A E, C
F alteri ſegmento.
Quod erat oſtenden-
dum.

Notæ in Propoſit. XVIII. & XIX.

QVuoniam vnumquodque corum alteri congruit, nec non congruunt
duo ſegmenta G I, K H in ellipſi (7. 8. ex 6.) at non ſunt ſimilia
44a alteri ſegmento, & c. Ideſt. Sit prius ſectio A B C parabole, vel
hyperbole. Quoniam duæ A C, & E F ordinatim ad axim B D applicatæ ab-
557. huius. ſcindunt ex vtraque parte axis duo ſegmen-

260[Figure 260] ta A E, & C F congruentia, propterea ſi-
milia erunt, atque ſimiliter poſita. Secundo,
in ellipſi ductæ ſint ad axim quatuor ordina-
tim applicatæ, quarum binæ extremæ E F,
& I K æqualiter à centro D diſtent; pari-
terque binæ intermediæ A C, & G H æqua-
668. huius. liter diſtent ab eodem centro: quare quatuor
ſegmenta G I, H K, C F, & A E æqualia
erunt, & ſibi mutuo congruent, & propterea
ſimilid quoque inter ſe erunt.

Erit angulus N æqualis O, vti demõ-
77b ſtrauimus, & c. Quoniam duo ſegmenta L
M, & A E, ponuntur ſimilia, atque eorum
baſes L M, & A E productæ occurrunt axi
in O, & N: igitur vt demonſtratum eſt,
88Prop 16.
17. huius. anguli à contingentibus verticalibus ſegmen-
torum ſimilium L M, & A E cum axi com-
muni B D eiuſdem ſectionis continebunt

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