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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10365Conicor. Lib. V. eorundẽ differen-

82[Figure 82] tias in ellipſi ſci-
licet C L ad C E
erit vt D F ad D
E, & propterea
K F ad E I erit,
vt D F ad D E,
11Lem. 3.& cõparando ho-
mologorum ſum-
mas in hyperbola,
& eorundem dif-
ferentias in elli-
pſi, K D ad D I
erit, vt D F ad D E, & iterum comparando antecedentes ad differentias ter
22Lem. 1. minorum fiet D K ad K I, vt D F ad F E, ſeu vt latus tranſuer ſum ad rectum;
igitur B I eſt linea breuiſsima.

33Ex 9. 10.
huius.

Si autem componamus proportionem in hyperbola deinde abſcinda-
44d mus, & reijciamus oppoſitum ab oppoſito in ellipſi, deinde inuertamus
fiet K D ad K I, vt D F ad F E, & c. Sed textum mendoſum corrigi debere,
vt ſupra factum eſt conſtat ex præcedenti nota.

Notæ in Propoſit. LX.

DEinde ſit perpendicularis ex C, & c. Siex puncto C extra hyperbolen po-
55a ſito perpendicularis ad axim ducta ad centrum eius D pertingat, duci de-
bet pariter ex puncto C recta linea ad ſectionem, cuius portio inter axim D F,
& ſectionem A B ſit linea breuiſsima; fiat C E ad E D, vt latus tranſuer ſum ad
rectum, & ex E ducatur E B par allela axi, ſecans hyperbolen in B, & ex B du-
catur B H perpendicularis ad axim, ſecans eum in H.

Et quia C E ad E D, nempe C B ad B G,

83[Figure 83]66b& c. Quia propter parallelas B E, F D eſt C E ad
E D, vt C B ad B G, & propter parallelas D C,
H B, eſt D H ad H G, vt C B ad B G, quare D H
ad H G erit, vt C E ad E D: poſita autem fuit C
E ad E D, vt latus tranſuer ſum ad rectum; igi-
tur D H ex centro hyperboles ad H G eandem
proportionem habet, quàm latus tranſuerſum ad
rectum, & propterea G B erit linea breuiſsima.

779. huius.

Notæ in Propoſit. LXI.

SIt poſtea punctum C, & perpendicularis C F, & c. Si à puncto C extra
88a hyperbolen A B poſito, C F perpendicularis ad axim efficiat F A ſegmentũ
tranſuerſi axis maius ſemiſse eius D A, & ponantur C E ad E F, atque D

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