Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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<
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<
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">huius, in qua conicus, ATDF, in-
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telligatur ſectus plano vtcumque per verticem, A, ducto efficiente
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triangulum, ſiue triangulos, ADC, AEF, intra, extra autem trian-
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gulum, ACE, & </
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<
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">qui ex illis integratur, ADF, ſecetur autem alio
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plano baſi parallelo, quod in conico producat figuram, VBO, & </
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ſint earum, & </
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<
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">plani per verticem communes ſectiones, BR, DC,
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IO, EF. </
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<
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">Dico eaſdem eſſe lineas homologas earundem figurarum,
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VBO, TDF. </
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<
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echoid-s1039
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">Intelligantur in baſi ductæ oppoſitæ tangentes, T
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H, SP, per quas, & </
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<
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">verticem, A, extendantur plana, quæ pariter
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huius.</
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tangent conicum, ATDF, ſint autem eorum, & </
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<
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">plani figurę, VB
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O, producti communes ſectiones, VK, XN, quas, vt ibi, oſten-
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demus eſſe oppoſitas tangentes ipſius, VBO, reſpectu, BO, ſum-
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ptas, accipiatur deinde in, TH, vtcumq; </
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<
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">punctum, H, à quo vſq;
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</
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<
s
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">ad aliam oppoſitam tangentem, SP, ducatur vtcumque, HP, & </
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<
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peripſam, & </
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<
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">punctum, A, extendatur planum, quod ſecet tangen-
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tia plana in rectis, AH, AP, & </
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<
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">planum parallelarum, VK, XN,
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in recta, KN, erunt ergo ipſæ, KN, HP, parallelæ, extendatur
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planum trianguli, ADF, ita vt ſecet triangulum, APH, in recta,
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AG, & </
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<
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">planum figuræ, TDF, productum, ſi opus ſit, in recta, D
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G, Eodem modo igitur, quo vti ſumus in Propoſ. </
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<
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">19. </
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<
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">quia, KN,
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HP, ſunt parallelæ, oſtendemus ipſas, KN, HP, eſſe ab ipſis, B
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M, DG, (quę ſunt communes ſectiones trianguli, ADF, & </
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<
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diſtantium planorum, VBO, TDF, & </
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<
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">ideò ſunt parallelæ) ſimi-
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liter diuiſas, & </
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<
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">ad eandem partem in punctis, M, G, vnde, vt ibi
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oſtendemus figuras, VBO, TDF, eſſe ſimiles, & </
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<
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gentium oppoſitarum, XN, VK; </
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<
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">SP, TH, incidentes eſſe ipſas,
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KN, HP, & </
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<
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">tangentes eſſe regulas homologarum earundem, qua-
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rum duæ ſunt ipſæ, BRIO, DCEF, coniunctæ, ſiue ipſæ, BR,
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DC; </
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<
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">IO, EF. </
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<
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">Eodem modo, ſi propoſitus conicus fuiſſet, cuius
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vertex, A, baſis altera figurarum a bafi, TDF, per rectam, DF,
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abſciſſarum, vt ipſa, DTF, oſtenſum eſſet ipſas, BR, DC; </
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<
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EF, communes ſectiones plani conicum tangentis in triangulis, A
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etiam per
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modũ Co-
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rollar. ex
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Prop. 19.
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deducipo
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tuiſſet.</
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DC, AEF, & </
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<
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">planorum æquidiſtantium, BVO, DTF, eſſe ea-
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rundem homologas, erunt autem in hoc caſu latera homologa, ve-
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lut cum ſunt intra figuras ſunt lineæ homologæ earumdem, quode-
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rat oſtendendum.</
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<
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">_H_Inc habetur, ſi propoſitum fuiſſet fruſtum conici, BTF, quod eius
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omnia latera producta coincidiſſent in vno puncto, A vnde,
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oſtenſum pariter fuiſſet communes ſectiones plani per eius latera </
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