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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174136Apollonij Pergæi

IV. Et ſi in eodem ſegmento ducantur or-

172[Figure 172] dinatæ parallelæ baſi B C, atque recta linea
A M ſecet omnes æquidiſtantes ipſi B C bifa-
riam in punctis M, N, & O vocabitur A M:
Diameter eiuſdem ſegmenti.

V. Et terminus eiuſdem diametri A ad
ſectionem poſitus, vocatur Vertex ſegmenti.

Tres prædictæ definitiones ſuperadditæ ab
interprete Arabico fuerunt, vt ego puto, quandoquidem omnino neceſſariæ non
ſunt.

VI. Sicuti in prima definitione ſectiones ſibi mutuò congruentes æquales vo-
cabantur, ſic pariter, ſi ſegmentum B A C ſuperpoſitum ſegmento E D F ſibi
mutuò congruant, ſunt duæ illæ lineæ curuæ æquales inter ſe.

VII. Declarat Apollonius in hac definitio-

173[Figure 173] ne ſeptima, quænam ſegmenta conica ſimilia
inter ſe cenſeri debeant. Vt ſi fuerint dua-
rum conicarum ſectionum ſegmenta B A C,
& E D F, quarum diametri A M, & D L
eſſiciant cum ordinatim applicatis, ſeu cum
baſibus B C, & E F angulos æquales in M,
& L, & in vnaquaque earum ductæ fuerint
pares multitudines applicatarum, quæ ſint ba-
ſibus æquidiſtantes, vt G H, & I K, & in
eis veriſicentur hæ conditiones, vt habeat B
C ad abſciſſam M A eandem proportionem,
quàm E F ad abſcißam L D, & G H ad ab-
ciſſam N A eandem proportionem habeat,
quàm I K ad abciſsam O D, & tandem ab-
ciſsa M A ad abſciſſam A N eandem propor-
tionem habeat, quàm abſcißa L D ad abſciſ-
ſam D O; tunc quidem vocat Apollonius duo
ſegmenta B A C, & E D F ſimilia inter ſe. Et hic primo animaduertendum
eſt, dìfinitionem ſegmentorum ſimilium relatam ab Eutocio Aſcalonita in 3. prop.
lib. 2. æquipond. Archimedis, non eße integram: in ea enim deſiderantur illa
verba, quarum baſes cumdiametris continent angulos æquales, ſine quibus
definitio eſſet erro-

174[Figure 174] nea, vt optime notat
Mydorgius. Hoc au-
tem ita eße verba
textus Arabici aper-
te declarant, habent
enim. Et ſimilia
ſunt quorum baſes
continent cum dia
metris angulos re-
ctos legẽdum

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