Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Itaque, quoniam rectangulum BKC ad quadratum AK eſt vt LF ad FH
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per conſtrutionem, vel vt XN ad NH, & </
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<
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">quadratum AK ad rectangulum
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AKC eſt vt AK ad KC, vel HG ad GC, vel HN ad NS, ergo ex æqualire-
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ctangulum BKC ad rectangulum AKC, ſiue recta BK ad KA, ſiue BG ad
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GF, vel RN ad NF, eſt vt XN ad NS, ac propterea rectangulum ſub extre-
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mis RN, NS, hoc eſt quadratum MN æquale rectangulo ſub medijs XN, NF:
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</
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<
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">_linea igitur MN poteſt ſpatium XF, & </
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<
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">primi poſt ea verba _ergo rectangulum PMR æquale eſt_
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_LM quadrato_ legatur ſic.</
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<
s
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">Cumque ſit rectangulum BKC ad quadratum AK ita HE ad ED ex con-
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ſtrutione, vel XM ad MD, & </
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">vt quadratum AK ad rectangulum AKC ita
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AK ad KC, vel DG ad GC, vel vt DM ad MR, erit ex æquo rectangulum
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BKC ad rectangulum AKC, vel BK ad KA, ſiue BG ad GE, vel PM ad ME
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vt XM ad MR, quare rectangulum ſub extremis PM, MR, vel quadratum
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ML æquatur rectangulo XME ſub medijs. </
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<
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_MO &</
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">Sed iam ad propoſitas Apollonij propoſitiones accedamus, quas ſimul ſequenti
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Theoremate amplectemur, itemque ſine compoſita proportione demonſtrabimus.</
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baſi coni non æquidiſtante, quorum communis ſectio conueniat,
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12. 13.
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primi co-
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nic.</
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vel cum vnotantum, vel cum vtroque latere trianguli per axem vl-
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tra, vel infra ſui ipſius verticem, planum verò, in quo eſt baſis co-
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ni, & </
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">ſecans planum, conueniant ſecundum rectam lineam, quæ ſit
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perpendicularis, vel ad baſim trianguli per axem, vel ad eam, quæ
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indirectum ipſi conſtituitur, & </
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diametri ſectionis inter latera, & </
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ptorum, ad rectangulum ſegmentorum baſis, ita ſectionis diameter
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ad aliam: </
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muni ſectioni plani ſecantis, & </
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trum, poterit rectangulum adiacens lineæ quarto loco inuentæ, la-
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titudinem habens lineam, quæ ex diametro abſcinditur inter ipſam,
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& </
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">verticem ſectionis interiectam (ſi tamen ſectionis diameter ęqui-
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diſtet alterutri laterum triãguli per axem) ſed ipſum excedet (ſi cum
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vtroque latere vltra verticẽ conueniat) vel ab eo deficiet, (ſi ijſdem
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lateribus infra verticem occurrat) rectangulo ſimili ſimiliterque po-
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ſito ei, quod continetur prædicto diametri ſegmento, & </
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uenta, iuxta quam poſſunt, quæ ad diametrum applicantur.</
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<
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quod ſectionem faciat triangulum B A C, ſecetur autem & </
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