Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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DA, & </
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ſerua.</
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s
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">Iam ſi ſectio primæ figure ABC fuerit Parabole, cum AE ſit ei contingens
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erit EB æqualis BF, ergo rectangulum EDF cum quadrato FB
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conic.</
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quadrato BD, quare
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ſolum rectangulũ EDF,
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ſiue quadratum DA mi-
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nus erit quadrato DB,
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ſiue linea D A minor
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DB.</
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<
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Hyperbolen reprefen-
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tet, reperto eius centro
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Q, erit rectangulum
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FQE ęquale
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mi conic.</
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QB, ergo FQ ad QB, vt
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QB ad QE, vel vt
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12. h.</
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ad BE, ſed FQ maior eſt QB, ergo FB erit maior BE, ſiue pluſquam dimi-
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dium ipſa FE, diuiſa ergo FE bifariam in V, erit FV minor FB, eritque re-
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ctangulum EDF cum quadrato FV æquale quadrato DV, igitur ſolum re-
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ctangulum EDF, hoc eſt quadratum DA minus quadrato DV, ſeu linea DA
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minor DV, & </
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">eò minor ipſa DB.</
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">Amplius in Ellipſi ſecundæ figuræ, dum perpendicularis AD conuenit
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cum axe maiori, eſt rectangulum ENF æquale quadrato NB, & </
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mi conic.</
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proportionali NF dempta eſt pars ND, ergo per Lemma præcedens erit re-
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ctangulum EDF, ſiue quadratum DA minus quadrato DB, hoc eſt perpen-
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dicularis DA maiori axi occurrens, minor eiuſdem axis portione DB.</
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nali NR addita eſt NI, ergo per idem Lemma erit rectangulum LIR, ſiue
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quadratum IA maius quadrato IH, ſiue perpendicularis AI minori axi oc-
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currens maior eiuſdem axis portione HI. </
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ctum, quod non ſit axis vertex, à quo ductæ ſint duæ rectæ lineæ,
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altera contingenti, altera autem axi perpendicularis; </
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<
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bola ea axis portio inter perpendiculares inrercepta æqualis, in
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Hyperbola verò maior, ſed in Ellipſi minor dimidio recti lateris
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eius axis, cui perpendiculares occurrunt.</
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<
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punctum ſit A, à quo ducta ſit contingens AE cum axe
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pr. eonic.</
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in E, atque ex A erecta ſit AD ipſi AE perpendicularis (quæ cum axe con-
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ueniet in D) & </
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primæ figuræ, interceptam axis portionem DF dimidio recti lateris æqua-
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lem eſſe.</
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