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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257219Conicor. Lib. VI. dem nulla ratione rectæ lineæ inter ſe æquidiſtantes, inter curuas interceptæ de-
terminare poſſunt prædictarum curuarum diſtantias;
quandoquidem inæquali-
ter ſemper inclinantur ad quamlibet prædictarum curuarum, &
rectæ lineæ in-
terceptæ, quæ ſunt perpendiculares ad vnam ipſarum, non erunt inter ſe æqui-
diſtantes.
Et quia, vt dictum eſt, prædictæ perpendiculares ſunt diſtantiarum
legitimæ menſuræ, nunquàm concludi poteſt certo, quod prædictæ ſectiones ſint
æquidiſtantes.
vel ſibi ipſis ſucceſſiuè viciniores ſiant, niſi conſiderentur rectæ
lineæ interceptæ ad vnam ſectionum perpendiculares:
quod quidem hucuſque
quod ſciam factum non eſt, neque forſan huiuſmodi ſpeculatio inuentu facilis
erit, aut iniucunda.
In parabola, vel hyperbola A B C ad eius axim E A I ducere ra-
11PROP. 6.
Addit.
mum breuiſſimum æquidiſtantem alicui rectæ lineæ E F, quæ oportet,
vt efficiat cum axi ad partes ſectionis angulum A E F acutum, ſed in
hyperbola ſit minor ſemiße vnius recti, &
angulus F E X ab vna
asymptoto, &
recta linea E F contentus ſit acutus.
Fiat angulus A E D æqualis an-
298[Figure 298] gulo A E F, &
ex vertice A du-
catur recta linea A B efficiens an-
gulum I A B, qui ſimul cum an-
gulo A E F vnum rectum angulũ
compleat;
ſed in hyperbola, quia
vterq;
angulus X E A, & A E F
deficit à ſemirecto erũt ambo mino-
res ſumma præcedentium, ſcilicet
vno angulo recto;
ergo ablato cõmuni
angulo A E F, erit angulus I A B
maior angulo A E X.
Poſtea, quia
tam A E F, quàm A E D minor eſt ſemiſſe vnius anguli recti, &
A E F cum
angulo I A B vnum rectum angulum complent;
ergo angulus I A B maior erit
angulo D E A:
& propterea recta linea A B producta neceſſario ſecabit vtram-
que rectam lineam E D, &
E X asymptotum extra ſectionem cadentem ad par-
tes D, X;
ideoque A B hyperbolen ſecabit in aliquo alio puncto B. In parabola
verò, quia recta linea A B axim
299[Figure 299] ſecat in vertice A non ad angulos
rectos (cum anguli I A B, &
A
2217. 27.
lib. I.
E F rectum compleant) ergo A B
ſectioni occurrit in duobus pun-
ctis.
Secetur iam A B bifariam
in L, &
per L ducatur diameter
ſectionis L G ſectioni occurrens in
3335. 36.
lib. I.
5. lib. 2.
G, &
per G ducatur contingens G
H, ſeu parallela A B ſecans axim
in H, &
per G ducatur I G O per-
pendicularis ad G H.
Dico I G
problema efficere.
Quoniam

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