Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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rectangulum AKF ad rectangulum DKE, vt quadratum AK ad KD (ob la-
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terum proportionalitatem) vel vt quadratum IO ad OE (ob triangulorum
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AKD, IOE ſimilitudinem) vel vt rectangulum IOL ad EOM (ob homolo-
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gorum laterum proportionalitatem) erit, ex æquali, rectangulum GKH,
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vel quadratum GK ad rectangulum DKE, ſiue vt rectũ latus Ellipſis GEHD
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ad eiuſdem tranſuerſum, vt rectangulum POQ, ſiue quadratum PO, ad re-
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ctangulum EOM, vel vt rectum Ellipſis PMQE ad ipſius tranſuerſum: </
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ergo huiuſmodi Ellipſes habeant latera proportionalia, ſintque æqualiter
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defin. h.</
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inclinatæ, erunt inter ſe ſimiles. </
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">Præterea, cum ſit AD´ ad DK, vt IE ad EO, ſitque AD maior IE,
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63. h.</
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DK maior EO. </
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">Item, cum ſit FE ad EK, vt LM ad MO, ſitque FE maior
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LM, erit EK maior MO, ergo integra tranſuerſa diameter DE, maior toto
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tranſuerſo latere EM; </
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">ſed tranſuerſum DE ad tranſuerſum EM, eſt vt rectum
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vnius ad rectum alterius, vt ſuperiùs demonſtrauimus, eſtq; </
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maios EM, quare rectum recto maios erit, ſiue Ellipſis GEHD maiorum la-
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terum, maior erit Ellipſi PMQE minorum laterum, quæ tùm in
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roll. 19. h.</
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tùm in ſectione, aut ſemi-Ellipſi, vel ſemi-circulo vertici B propior eſt.
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">Problematis, concipiantur methodo ſuperiùs
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allata, per datum punctum inſcribi Ellipſes ad partes verticis, vel angu-
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li, vel ſectionis, quæ ſimiles ſint alijs ad oppoſitas partes per idem punctum
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inſcriptis (ſi tamen ſectionis, vel circuli portio, quæ ab applicata per datum
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punctum terminatur, huius Ellipſis ſit capax, quod accidet, quando in ſe-
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cunda præcedentium figurarum, diagonalis IL, quæ ex I ducitur diagonali
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AF æquidiſtans, & </
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