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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11678Apollonij Pergæi

MONITVM.

ANtequam huius Decimætertiæ Sectionis explicationes, atque
emendationes aggrediamur, vt Notæ breuiores, clarioreſque
reddentatur, & teſtus Arabici menda facilius corrigi poſſent, operæ
pretium duximus (amice lector) Lemmata ſequentia præmittere.

LEMMA IX.

Si ad coniſectionem, atque ad vnum quadrantem ellipſis A B C à
concurſu D nullus ramus duci poſsit, qui ſit breuiſecans; Dico, quod
quilibet ſecans ramus D B cum tangente H B G per eius terminum B
ducta efficit angulum D B H ad partes verticis A acutum, & D B
G, qui deinceps eſt, obtuſum.

Quoniam nullus ramus ex concurſu

98[Figure 98] D ad ſectionem A C ductus eſt breui-
ſecans, erit (ex conuerſa propoſitionis
49. 50. 51. 52. huius) menſura A E
aut non maior ſemiſſe lateris recti, aut
perpendicularis D E maior Trutina,
quæ ſit F, & ideo quilibet ramus ſe-
cans D B cadit ſupra breuiſsimam ex
puncto B ad axim ductam, eſt verò
breuiſsima ex puncto B ad axim ducta
perpendicularis ad G B H tangentem
1129. 30.
huius. ſectionem in B; ergo angulus D B H,
verticem A reſpiciens eſt acutus, & qui deinceps eſt D B G erit obtuſus.

LEMMA X.

Iiſdem poſitis, ſi à concurſu D vnicus tantum ramus D B breuiſe-
cans ad ſectionem A B duci poteſt; Dico, quod quilibet alius ramus
ſecans D 1 ſupra, vel infra breuiſecantem D B poſitus efficit cum recta
L I H tangente ſectionem in I angulum D I L, verticem reſpicien-
tem, acutum, & D I H, qui deinceps eſt, obtuſum.

Nam ex conuerſa propoſitione 51. & 52. huius perpendicularis D E æqualis
crit Trutinæ F, & ideo quilibet ramus D I poſitus ſupra, velinſra

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