Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ta ADC: </
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">oportet ex C, infra ADC, ſecantem ducere CEF, ita vt
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ſi ex E, & </
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">F applicentur EH, FG ipſi ADC parallelæ, quadratum
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HE ad rectangulum DEG, datam habeaa
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t rationem O ad P.</
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<
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<
s
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">SVmatur Q media proportionalis inter O, & </
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">& </
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">ex D, niſi DA ſit dia-
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metro BD perpendicularis, erigatur DL, & </
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">fiat vt O ad Q, ita DA ad
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DL, iunctaque BLM, ſumatur LM æqualis LD, & </
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pendicularis ipſi BDE: </
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<
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">dico per punctum E quæſitam ſecantem tranſire.</
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<
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">Nam iuncta MD, ductaque MN ipſi BM
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perpendiculari cum ſint anguli L M N,
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LDN recti, erũt anguli NMD, NDM duo-
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bus rectis minores; </
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">quare MN ipſi DE oc-
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curret in N; </
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<
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">cumque angulus LMD, ęqua-
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lis ſit angulo LDM, erunt reſidui ex rectis
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DMN, MDN æquales, hoc eſt ND æqua-
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lis NM, facto igitur centro N, interuallo
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ND, deſcribatur circulus DMG, qui vtrã-
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que LD, LM, continget in D, M, cum an-
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guli ad D, M ſint recti: </
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<
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EH parallela ad DA.</
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<
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<
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">Iam cum BM circulum DMG contingat
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in M, ſitque ME diametro DG perpendi-
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cularis erit GB ad BD, vt GE ad ED, &</
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mi conic.</
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permutando BG ad GE, vt BD ad DE, ſed
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eſt BG maior GE, ergo & </
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eſtque AD æqualis DC, & </
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<
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BA, CE, productę, conuenient ſimul ad partes A, E, vt in F eritque FB
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BA, vt FH ad HA, & </
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<
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DE, vel vt BG ad GE, & </
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<
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xml:space
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">diuidendo BH ad HF, vt BE ad EG, quare iuncta
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FG ipſis EH, DA æquidiſtabit. </
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& </
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<
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">BE ad EM, vt BD ad DL (ob triangulorum ſimilitudinem) erit ex æquo
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HE ad EM, vt AD ad DL, & </
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<
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">quadratum HE ad quadratum EM, hoc eſt ad
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rectangulum DEG, vt quadratum AD ad DL, vel vt quadratum O ad qua-
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dratum Q, vel vt linea O ad P. </
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