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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142104104 Apollonij Pergæi nem: Dico, quod circumpherentia Z γ ſecat tangentem rectam lineam
x A, & coniſectionem B G in puncto A.

Quoniam perpendicularis D E ponitur ma-

127[Figure 127] ior trutina L; ergo quilibet ramus D A cadit
1151. 52.
huius. ſupra breuiſsimam ex puncto A ad axim B E
ductam: efficit vero breuiſsima cum tangente
A x angulum rectum; ergo angulus D A x eſt
2229. 30.
huius. acutus; & propterea recta A x cadit intracir-
culum A Z; ſed A x cadit extra coniſectio-
3335. 36.
Lib. 1. nem B A, quàm contingit; ergo circumferen-
tia Z A cadit extra ſectionem B A, & extra
tangentem A x: poſtea ducatur quilibet ramus
D G infra ramum D A ſecans circumferentiã
circuli in r: & quia ramus D A propinquior
eſt vertici B, quàm D G, erit D A minor,
4464. 65.
huius. quàm D G; eſtque D γ æqualis D A (cum ſint ambo radĳ eiuſdem circuli) ergo
D γ minor erit, quàm D G: & propterea quodlibet punctum γ peripheriæ cir-
cularis infra punctum A poſitum cadet intra coniſectionem B G; & ideo cir-
cumferentia Z A γ ſecat tangentẽ, & coniſectionẽ in A, quod erat propoſitum.

Iſdem poſitis, ſit perpendicularis D E æqualis Trutinæ L, & ſit D
55PR. 10.
Addit. A ſingularis ille ramus breuiſecans, qui ex concurſu D ad ſectionem
B G duci poteſt; perficiaturque conſtructio, vt antea factum eſt; Dico,
6651. 52.
huius. circulum Z A γ ſecare coniſectionem in A, & contingere rectam Ax.

Ducatur quilibet ramus D F ſupra breuiſe-

128[Figure 128] cantem D A, ſecans circuli peripheriam in Z,
& quilibet alius ramus D G infra D A ſecans
eandem peripheriam in γ. Et quia ex con-
curſu D ad ſectionem B G vnicus tantum bre-
77Ibidem. uiſecans D A duci poteſt; igitur ramus D F
propinquior vertici B minor eſt remotiore D
8867. huius. A, & D A propinquior vertici B minor eſt
remotiore D G: ſuntque rectæ D Z, D γ æ-
quales eidem D A (cum ſint radĳ eiuſdem,
circuli) ergo D Z maior eſt, quàm D F, &
D γ minor, quàm D G; & propterea quodli-
bet punctum Z circuli ſupra A ſumptum ca-
dit extra coniſectionem B F A, & quodlibet
infimum punctum γ eiuſdem circuli cadit intra eandem coniſectionem A G;
quapropter circumferentia circuli Z A γ ſecat coniſectionem B A G in A. Po-
ſtea quia recta A x contingens ſectionem in A perpendicularis eſt ad breuiſe-
cantem D A, cum I A ſit breuiſsima; igitur recta linea x A, quæ perpendicu-
9929. 30.
huius. laris eſt ad radium D A, continget circulum Z Y γ. Quapropter circulus Z
A γ ſecant coniſectionem B A G in A, & tangit eandem rectam lineam A x,
quàm contingit ſectio conica B A G, & in eodem puncto A, quod erat oſtendendũ.

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141	103
142	104
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152	114
153	115
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Scan	Original
141	103
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147	109
148	110
149	111
150	112
151	113
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153	115
154	116
155	117
156	118
157	119
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161	123
162	124
163	125
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170	132

Scan	Original
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
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163	125
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