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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189151Conicor. Lib. VI.

In ſestione A B C ducatur ramus breuiſe-

202[Figure 202] cans ſingularis I L ſecans axem in G, ſitque
1151. 52. 53.
lib. 5, I punctum concur ſus perpendicularis I K, &
breuiſecantis; & à quolibet puncto B inter
L, & verticem A ducatur alius ramus bre-
uiſecans B M, qui occurret L I vltra axim
in M, & inter puncta G, & I; coniungatur-
2228. lib. 5.
8. Addir.
lib. 5. que recta linea B 1. Quoniam angulus L G A acutus eſt, erit angnlus G M N
internus, & oppoſitus in triangulo G M N minor illò, & ideo acutus, & pro-
3313. 14. 15.
lib. 5. pterea qui deinceps eſt angulus B M I erit obtuſus, & ideo in triangulo I B M
latus I B ſubtendens maximum angulum obtuſum maius erit latera B M; ſedra-
mus I L maior eſt, quàm I B, propterea quod remotior eſt à vertice A, igitur
4467. lib. 5. ramus I L maior erit, quàm B M: Secari ergo poterunt æquales rectæ lineæ L R,
B S, quæ ſint minores quidẽ, quàm I L, ſed maiores, quàm M B; & deſcribantur
duo circuli, quorum radij ſint S B, & R L æquales, atque centra ſint S, & R;
55Ex 12.
Addit.
lib. 5. Manifeſtum eſt circulum, cuius radius B S contingere coniſectionem A C in
puncto B, & extrinſecùs incedere, propterea quod radius B S maior eſt maximo
breuiſecantium M B à concurſu M educto; è contra circulus radio R L deſcri-
668. Addit.
lib. 5.
Ibidem. ptus intrinſecùs continget eandem coniſectionem in L cum ramus M L minor ſit
ſingulari breuiſecante L I. Tandẽ in ſectione D E F ſecetur axis abſcißa D H
æqualis A N, & in angulo D H P æquali angulo A N B ducatur radius γ H P,
qui fiat æqualis S B, & cẽtro γ radio verò γ P circulus deſcribatur. Et quia in
ſectionibus æqualibus abſciſſæ, breuiſecantes, anguli ab eis contenti, & circu-
li deſcripti ſunt æquales, & congruentes; igitur circulus radio γ P deſcriptus,
contingit coniſectionem D E F extrinſecùs; ſicuti circulus radij S B tangebat
ſectionem A B C in B extrinſecùs. Vterat propoſitum.

Hoc demonſtrat o oſtendetur, quod in duabus coniſectionibus A B C,
77PROP. 1.
Addit. D E F æqualibus, quarum axes A G, D H duæ portiones B C, &
E F non æquè ab axium verticibus remotæ non erunt ſibi congruentes.

Si enim poſſibile eſt B C, & E F ſibi mutuò congruant, & ſumatur interme-
dium punctum commune, vel duo puncta coincidentia L, & P, & quia portio-
nes B C, E F inæqualiter diſtant à verticibus, ergo puncta coincidentia L, P
non erunt æquè à verticibus remota; ſit ergo P propinquius vertici D, quàm eſt
L vertici A, & per L, & P ducantur rectæ

203[Figure 203] lineæ L O, P Q tangentes ſectiones, & ex lẽ-
8833. 34.
lib. 1. matæ præcedenti deſcribantur duo circuli æ-
quales Z P T, & V L X radijs I L & S
P, quorum Z T extrinſecus tangat ſectionẽ
in P, & V X intrinſecus in L, cumque eo-
rum radij I L, S P ſint breuiſecantes, erunt
perpendiculares ad L O, P Q contingentes
9929. 30.
lib. 5. ſectionem in L, & P; atque portiones B C, E F ſibi mutuò congruunt, ideſt
101035. 36.
lib. 1. conſtituunt vnicam communem peripheriam, ergo rectæ lineæ L O, P Q
contingentes eandem ſectionem ſibi mutuò congruent, pariterque breuiſe-
cantes æquales L I, P M ad illas perpendiculariter inſiſtentes crunt congruentes
quoque; & propterea circuli V X, Z T ab ĳs radĳs geniti erunt quoque

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