Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Videatur figura Propoſ. 16. huius, in qua conicus, ATDF, in-
telligatur ſectus plano vtcumque per verticem, A, ducto efficiente
triangulum, ſiue triangulos, ADC, AEF, intra, extra autem trian-
gulum, ACE, & qui ex illis integratur, ADF, ſecetur autem alio
plano baſi parallelo, quod in conico producat figuram, VBO, & ſint earum, & plani per verticem communes ſectiones, BR, DC,
IO, EF. Dico eaſdem eſſe lineas homologas earundem figurarum,
VBO, TDF. Intelligantur in baſi ductæ oppoſitæ tangentes, T
H, SP, per quas, & verticem, A, extendantur plana, quæ pariter
tangent conicum, ATDF, ſint autem eorum, & plani figurę, VB
O, producti communes ſectiones, VK, XN, quas, vt ibi, oſten-
demus eſſe oppoſitas tangentes ipſius, VBO, reſpectu, BO, ſum-
ptas, accipiatur deinde in, TH, vtcumq; punctum, H, à quo vſq; ad aliam oppoſitam tangentem, SP, ducatur vtcumque, HP, & peripſam, & punctum, A, extendatur planum, quod ſecet tangen-
tia plana in rectis, AH, AP, & planum parallelarum, VK, XN,
in recta, KN, erunt ergo ipſæ, KN, HP, parallelæ, extendatur
planum trianguli, ADF, ita vt ſecet triangulum, APH, in recta,
AG, & planum figuræ, TDF, productum, ſi opus ſit, in recta, D
G, Eodem modo igitur, quo vti ſumus in Propoſ. 19. quia, KN,
HP, ſunt parallelæ, oſtendemus ipſas, KN, HP, eſſe ab ipſis, B
M, DG, (quę ſunt communes ſectiones trianguli, ADF, & ęqui-
diſtantium planorum, VBO, TDF, & ideò ſunt parallelæ) ſimi-
liter diuiſas, & ad eandem partem in punctis, M, G, vnde, vt ibi
oſtendemus figuras, VBO, TDF, eſſe ſimiles, & earum, & tan-
gentium oppoſitarum, XN, VK; SP, TH, incidentes eſſe ipſas,
KN, HP, & tangentes eſſe regulas homologarum earundem, qua-
rum duæ ſunt ipſæ, BRIO, DCEF, coniunctæ, ſiue ipſæ, BR,
DC; IO, EF. Eodem modo, ſi propoſitus conicus fuiſſet, cuius
vertex, A, baſis altera figurarum a bafi, TDF, per rectam, DF,
abſciſſarum, vt ipſa, DTF, oſtenſum eſſet ipſas, BR, DC; IO,
EF, communes ſectiones plani conicum tangentis in triangulis, A
DC, AEF, & planorum æquidiſtantium, BVO, DTF, eſſe ea-
rundem homologas, erunt autem in hoc caſu latera homologa, ve-
lut cum ſunt intra figuras ſunt lineæ homologæ earumdem, quode-
rat oſtendendum.

87.1.

Coroll.1.
huius.
18. Huius.
Sed hoc
etiam per
modũ Co-
rollar. ex
Prop. 19.
deducipo
tuiſſet.

88. COROLLARIVM.

_H_Inc habetur, ſi propoſitum fuiſſet fruſtum conici, BTF, quod eius
omnia latera producta coincidiſſent in vno puncto, A vnde,
oſtenſum pariter fuiſſet communes ſectiones plani per eius latera tran-

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