Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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233 plano, quorum communis ſectio F G vel alterutri laterum trianguli per
axem, nempe AC æquidiſtet, vt in prima figura, vel cum vtroque latere in
F, H, extra verticem coni, vt in ſecunda;
ſiue infra verticem, vt in tertia, &
quarta conueniat, &
ſecans planum baſi non æquidiſtet, faciatque ſectio-
nem in ſuperficie coni lineam MFT, &
communis ſectio plani ſecantis, atq;
eius in quo eſt baſis coni ſit DGE perpendicularis ad baſim trianguli per axẽ
BC, vel ad eam, quæ indirectum ipſi conſtituitur, vt in quarta figura;
& fiat
in prima figura, vt quadratum FG, in reliquis verò, vt rectangulum HGF,
2[Figure 2] ad rectangulum BGC, ita linea HF, ſegmentum diam etri ſectionis, ad aliam
FL, quæ (facilitatis, &
commoditatis gratia tantùm ad ea, quæ à nobis in po-
ſterum ſunt pertractanda, non quod hanc, vel aliam poſitionem requirat
propoſiti demonſtratio, poteſt enim ipſa FL cum diametro FH, ad quemcun-
que angulum conſtitui) concipiatur applicari ex F, ſectionis vertice,

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