Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ALCO eſt _MINIMA_ circumſcripta datæ Ellipſi ABCO, per terminos ap-
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plicatæ AC, cum dato tranſuerſo DE: </
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<
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ditionibus circumſcriptibilis. </
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<
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">ad finem, dicatur _licet minor fue-_
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_rit eadem ALCN_ in hac verò, _licet maior fuerit eadem ALCN_ (perinde ac
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ſi, per terminos A, C, cum diametro æquali ipſi LN alia in ea deſcribi poſſit
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Ellipſis minor ALCN, in hac verò alia maior ALCN) vtrunq; </
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merè dixiſſe ex ſequéti Theoremate manifeſtum fiet, à quo habebitur quam-
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libet aliam Ellipſim per A, C, adſcriptam, cum tranſuerſo ęquali ipſi LN, ſed
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cuius ſegmenta ab applicata AC abſciſſa, ſint magis inæqualia quàm ſint ſe-
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gmenta NF, FL, minorem eſſe ipſa ALCN; </
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minus inæqualibus, quàm ſint NF, FL, eadem ALCN maiorem eſſe.</
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rum, & </
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">quarum tranſuerſa latera ſint æqualia, MINIMA eſt ea,
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cuius communis ordinatim ducta ſit diameter coniugata: </
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verò illa, cuius ſegmenta diametri ſunt minùs inæqualia, minor eſt
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ea, cuius diametri ſegmenta ſunt magis inæqualia.</
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ſimul adſcriptæ, & </
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coniugata diameter Ellipſis ABCD, ſiue G eius centrum. </
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hanc minorem eſſe altera AECF, ſiue eſſe _MINIMAM_, &</
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bifariam ſecta in G, erit EF in pũcto Ginæ-
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qualiter ſecta, vnde rectangulum BGD ma-
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ius erit rectangulo EGF, cum ſit
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_MVM_; </
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dratum AG, ſiue tranſuerſum BD ad
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mi conic.</
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ctum Ellipſis ABCD, maiorem habebit ra-
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tionem quàm rectangulum EGF ad idem
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quadratum AG, ſiue quàm
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EF ad rectum Ellipſis AECF: </
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BD, EF ſunt æqualia, ergo rectũ Ellipſis AB
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CD, minus erit recto AECF:</
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huiuſmodi Ellipſes (cum ſint ęqualiter incli-
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natæ) concipiantur eſſe per eundem verticem ſimul adſcriptæ, ita vt tranſ-
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uerſæ diametri ſimul congruant, ipſa ABCD, cuius rectum minus eſt, inſcri-
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pta erit, ſiue minor AECF, cuius rectum maius eſt, & </
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roll. 19. h.</
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alia, cuius diametri ſegmenta ſint inæqualia: </
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_MA_, &</
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