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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145107Conicor. Lib. V. culum Z A γ, qui coniſectionem in puncto A ſecat.

Sumatur enim quodlibet punctum G in productione breuiſsimæ A I ſupra,
vel infra punctum D: manifeſtum eſt (ex 8. præcedentium propoſit.) à puncto
G duci poſſe duos breuiſecantes ramos, quorum A G erit infimus, ſi punctum G
cadit ſupra punctum D, & tunc circulus radio G A deſcriptus continget coniſe-
1111.
Additarũ. ctionem intrinſecus in A: ſi vero punctum g cadat infra punctum D, tunc pa-
228.
Additarũ. riter ex g duo breuiſecantes duci poſſunt ad ſectionem, quorum ſupremus erit
g A; & propterea circulus radio g A deſcriptus continget coniſectionem B AC
3311.
Additarũ. extrinſecus in A; quaproptcr circulus radio D A deſcriptus (quem contingit
eadem recta linea X A quæ tangebat ſectionem in A) vnicus erit, qui ſectionem
B C ſecet in A, quod erat oſtendendum.

Circulorum omnium intrinſecus tangentium coniſectionem non in axis
44PROP.
13.
Addit. vertice, aſsignari non poteſt maximus: tangentium vero intrinſecus ſe-
ctionem in termino axis maximus erit, cuius radius æqualis eſt ſemie-
recto.

Repetatur figura, &

132[Figure 132] hypotheſis præcedẽtis pro
poſitionis. Quoniã qui-
libet circulus radio G A
minori, quàm D A de-
ſcriptus ſemper intrin-
ſecus tangit coniſectio-
nem in A (vt in præce-
dẽti propoſitione dictum
eſt) vbicumque ponatur
centrum G ſupra punctũ
D; neque augendo ra-
dium G A efſicitur alius
contactus circuli, & ſe-
ctionis, quàm intrinſe-
cus, & tunc primo cir-
culus deſinit intrinſecus
tangere ſectionem in A,
quando D A efſicitur
radius, ſcilicet quando
non amplius intrinſecus ſectionem tangit, ſed eam ſecat in A; quapropter aſsi-
gnari non poteſt maximus circulorum tangentium intrinſecus ſectionem in A.
Quod verò circulorum intrinſecus tangentium eandem ſectionem in vertice axis
B, ille, cuius radius B K æqualis eſt ſemierecto B H ſit maximus, oſtenſum eſt
à Maurolico propoſ: 5. 8. & 11. libri 5. Conicorum. Patet ergo propoſitum.

Iiſdem poſitis: dico circulorum omnium extrinſecus tangentium coni-
55PROP.
14.
Addit. ſectionem minimum aſsignari non poſſe.

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