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

Table of contents

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[101.] PROPOSITIO LXXII.
[102.] MONITVM.
[103.] LEMMA IX.
[104.] LEMMA X.
[105.] LEMMA XI.
[106.] Notæ in Propoſ. LXIV. & LXV.
[107.] Notæ in Propoſ. LXVI.
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
[109.] Notæ in Propoſ. LXVII.
[110.] COROLLARIVM PROPOSIT. LXVII.
[111.] Notæ in Propoſit. LXXII.
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
[113.] PROPOSITO LXXIV.
[114.] PROPOSITO LXXV.
[115.] PROPOSITIO LXXVI.
[116.] PROPOSITIO LXXVII.
[117.] Notæ in Propoſit. LXXIII.
[118.] LEMMA XII.
[119.] Notæ in Propoſ. LXXIV.
[120.] Notæ in Propoſit. LXXV.
[121.] Notæ in Propoſ. LXXVI.
[122.] Notæ in Propoſit. LXXVII.
[123.] COROLLARIVM.
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
[125.] PROPOSITO XXXXII.
[126.] PROPOSITIO XXXXIII.
[127.] Notæ in Propoſ. XXXXI.
[128.] Notæ in Propoſ. XXXXII.
[129.] Notæ in Propoſit. XXXXIII.
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
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page |< < (45) of 458 > >|
8345Conicor. Lib. V.
Et cum B I intercipiatur inter illas patebit etiam, & c. Et cum B I intercipia-
22l tur inter duos ramos breuiſecantes E K, qui ducuntur ex punctis K, in quibus hy-
perbole
K T L ſecat parabolen A B L, cadet punctum T hyperboles intra parabolen;
quare rectangulum B G F maius erit rectangulo T G F, ſeu K M F, quod æquale eſt
rectangulo
E D F, vt dictum eſt, quare E D ad B G, ſeu D I ad I G (propter ſimili-
33Lem. 5.
præmiſ
.
tudinem triangulorum E D I, B G I) habebit minorem proportionem, quàm G F ad
F
D, &
componendo, eadem D G ad G I minorem proportionem habebit, quàm ad
F
D, ſiue ad A C, &
ideo I G maior erit, quàm A C.
Deinde ex con-
44m60[Figure 60] curſu E ad ſectio-
nem
, &
c. Deinde
ex
concurſu E ad ſe-
ctionem
A B parabo-
len
educantur duo ra-
mi
E X ſupra breui-
ſecantem
E K in pri-
ma
figura, &
infra
eamdem
in figura ſe-
cunda
, &
ex punct is
X
ducantur due X Y
perpendiculares
ad
axim
, ſecantes axim
in
Y, &
hyperbolen K
T
in a exiſtẽte extra
parabolen
;
cumque
duæ
rectæ a Y, necnõ
T
G parallelæ ſint cõ-
tinenti
F V, &
inter-
ponātur
inter hyper-
bolẽ
K T, &
reliquã
continentem
F A eritrectangulum a Y F æquale rectangulo T G F, quod factum
5512. lib. 2. eſt æquale rectangulo E D F, eſtque X Y portio ipſius a Y;
igitur rectangulum E D F
maius
erit rectangulo X Y F, &
ideo E D ad X Y, ſeu D b, ad b Y (propter ſimilitu-
66Lem. 5.
præmiſ
.
dinem triangulorum E D b, X Y b) maiorem rationem habet, quàm Y F ad F D, &

componendo
eadem D Y ad Y b maiorem proportionem habebit, quàm ad D F, ſeu
C
A.

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