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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10466Apollonij Pergæi ad G F, vt latus tranuer ſum ad

84[Figure 84] rectum, & ducatur ex E recta
E H parallela F A, quæ ſecetur
à rectis D K, G I ad axim per-
pendicularibus in K, & I, &
per D ducatur hyperbole D B
114. lib. 2. circa aſymptotos H I G, occur-
ret hyperbole A B (vt in Prop.
59. 62. 63. oſtenſum eſt) ali-
cubi, vt in B, coniungatur rect a
linea B C, quæ occurrat axi in
L, & ipſi E H in M, duca-
turque ex B perpendicularis ad
axim eum ſecans in N, & re-
ctam E M in H. Dico, quod B L eſt linea breuiſsima.

C E ad E F, nempe K D eſt, vt D G ad G F, & c. Quoniam ex conſtru-
22b ctione C E ad E F, ſeu ad ei æqualem K D, in parallelogrammo D E, eſt vt
D G ad G F, ſcilicet vt latus @ anſuerſum ad rectum, eſtque K I ad I E, vt D
G ad G F propter parallelas D K, G I, F E; ergo vt prima C E ad ſecundam
D K, ita eſt tertia K I ad quartam I E, & propterea rectangulum C E I ſub
extremis contentum æquale eſt rectangulo D K I ſub intermedĳs compræhenſo;
eſt vero rectangulum B I æquale rectangulo D I cum compræhendantur ab hyper-
bole D B, & aſymptotis H I G; ergo rectangulum C E I æquale eſt rectangulo
3312. lib. 2. B H I; & propterea B H ad C E, nempe H M ad M E (propter ſimilitudinem
triangulorum B H M, C E M) eandem proportionem habebit, quàm E I ad I
H, & componendo eadem H E ad H I, atque ad E M eandem proportioner
habebit; & ideo H I ſeu ei æqualis N G æqualis erit E M, quare eadem
L F ad N G, atque ad E M eandem proportionem habebit: ſed propter ſimi-
litudinem triangulorum L C F, M C E eſt F C ad E C, vt F L ad M E,
ſeu ad N G, & erat C E ad E F, necnon D G ad G F in eadem propor-
tione lateris tranſuerſi ad rectum, & ſummæ terminorum ad antece-
44Lem. 1. dentes terminos, ſcilicet F C ad E C, necnon F D ad D G ean-
dem proportionem habent; quare L F ad N G eandem
proportionem habet, quàm F D ad D G, & compa-
rando homologorum differentias L D ad D N
55Lem. 3. eandem proportionem habebit, quàm F D
ad D G, & comparando conſe-
quentes ad differentias termi-
66Lem. 1. norum D N ad L N erit,
vt D G ad F G,
ſcilicet
vt latus tranſuer ſum ad rectum;
quapropter B L eſt linea
779. huius.breuiſsima.

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