Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Nam quadratum AF æquatur rectangulo ſub FB, & </
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1. h.</
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ſub dupla FB, ſiue ſub EF, & </
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mi conic.</
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Quod primò, &</
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">Amplius in Hyperbola ſecundæ figuræ, dico interceptam portionem FD
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eſſe pluſquam dimidium recti lateris.</
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">Nam reperto eius centro G, erit rectangulum GFE ad quadratum AF,
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vel ad rectangulum DFE, vt tranſuerſum latus ad rectum, ſed
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mi conic.</
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GFE ad DFE, eſt vt linea GF ad FD, ergo GF ad FD eſt vt tranſuerſum la-
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tus ad rectum, vel vt ſemi-tranſuerſum GB ad ſemi-rectum, & </
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GF ad GB, erit vt FD ad ſemirectum, ſed eſt GF maior GB, ergo FD erit
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maior ſemi-recto latere. </
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tertiæ figuræ, in qua
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intercepta axis portio
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DF eſt de maiori axe,
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vel in quarta figura, in
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qua prædicta portio
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DF eſt de minori axe,
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dico item ipſam DF
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minorem eſſe dimidio
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recti lateris eius axis,
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cui ductæ perpendicu-
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lares occurrunt.</
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pſis centro G, eſt re-
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ctangulũ EFG ad qua-
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dratum AF, vel ad re-
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ctangulum E F D,
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tranſuerſum latus ad
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rectum, ſed idem rectangulum EFG ad EFD eſt vt linea GF ad FD quare
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GF ad FD eſt vt tranſuerſum ad rectum, vel vt GB dimidium tranſuerſi ad
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dimidium recti, & </
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GF minor GB, ergo & </
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mò, &</
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ter contactum, & </
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<
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ſectionis. </
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latere DF, ſed DF, vel æqualis eſt (in Parabola) vel maior (in Hyperbola)
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prædicto dimidio, quare perpẽdicularis AD erit omninò maior ipſo dimidio.</
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