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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[311.] PROPOSITIO XXXIX.
[312.] PROPOSITIO XXXX.
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
[314.] LEMMA VII.
[315.] LEMMA VIII.
[316.] LEMMA IX.
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
[318.] Notæ in Propoſit. XXXX.
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
[320.] PROPOSITIO XXXXVI.
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
[322.] LEMM A XI.
[323.] LEMM A XII.
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
[325.] Notæ in Propoſit. XXXXVI.
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
[327.] PROPOSITIO XXXXI.
[328.] PROPOSITIO XXXXVII.
[329.] PROPOSITIO XXXXVIII.
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
[331.] LEMMA XIV.
[332.] LEMMA XV.
[333.] Notæ in Propoſit. XXXXI.
[334.] Notæ in Propoſit. XXXXVII.
[335.] Notæ in Propoſit. XXXXVIII.
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
[338.] LEMMA XVII.
[339.] LEMMA XVIII.
[340.] Notæ in Propoſit. XXXXIX.
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336297Conicor. Lib. VII. indirectum additur S C,
388[Figure 388] erit rectangulum M C S
cum quadrato ex A S, ſeu
ex Q R æquale quadrato
ipſius A C;
ergo rectangu-
lum M C S æquale eſt dif-
ferentiæ quadrati A C à
quadrato Q R:
pariratione
rectangulum K L T vna
cum quadrato N O æquale
erit quadrato I L:
ergo ſi-
militer rectangulum K L T æquale eſt differentiæ quadratorum ex I L, &
ex
N O;
eſtquè quadratum I L maius quadrato A C, cum diameter I L in hyper-
bola maior ſit, quàm axis C A;
igitur rectangulum K L T vna cum quadrato
N O maius erit rectangulo M C S vna cum quadrato Q R:
eſt verò rectangu-
lum M C S æquale rectangulo K L T (cum ſint differentiæ quadratorum ex con-
11Prop. 12.
huius.
iugatis diametris, quæ in hyperbola oſtenſæ ſunt æquales);
ergo quadratum N
389[Figure 389] O, ſcilicet reſiduum maioris ſummæ, maius erit quadrato Q R, quod eſt reſi-
duum ſummæ minoris:
& propterea N O maior erit, quàm Q R: erat autem
I L maior quàm C A;
igitur I L cum N O, ſeu K L maior erit, quàm A C,
&
Q R ſimul, ſiue quàm M C: ſed in rectangulis M C S, & K L T æquali-
bus, vt K L ad M C, ita reciprocè C S ad L T;
igitur C S, ſeu differentia
ipſarum A C, &
Q R maior eſt, quàm L T, ſeu differentia ipſarum I L, &
N O in hyperbola.
Si poſtea præter I L ponatur alia diameter ab axe remotior cum ſua coniu-
gata erit ſimiliter differentia quadratorum ex diametris coniugatis remotiori-
bus ab axi æqualis differentiæ quadratorum axium A C, &
Q R, &

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