Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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axium vertices contingat recta A E, cui intra ſectionem ducta ſit perpen-
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dicularis A D, quæ priùs maiori axi occurret, vt in D. </
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mih.</
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D A, & </
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ctionis peripheriam A B C, ex punctis D, vel F.</
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<
s
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xml:space
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">Nam facto centro D, inter-
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uallo D A, ac circulo deſcripto
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A C G, ipſe cadet totus
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mi h.</
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fectionem A B C, in duobus tan-
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tùm punctis A, C, eam contin-
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gens: </
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<
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">quare quę ducentur ex D
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ad ſectionis peripheriam, pręter
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ad puncta A, C, interuallo D A
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maiores erunt: </
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<
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xml:space
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">exquo ipſa D A,
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vel D C erit _MINIMA_, &</
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verò interuallum F A minus ſit
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ipſo D A. </
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<
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G ipſum F A diametri ſegmen-
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tum, in quo centrum non repe-
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ritur, ſit rectarum _MINIMA_ ad
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circuli peripheriam ducibilium,
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eò magis eadem F A _MINIMA_
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erit ducibilium ex F, ad peri-
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pheriam circumſcriptę ſectionis
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A B C. </
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<
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<
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pſis A B C, circa minorem axim B D, & </
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<
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quod non ſit axium vertex, ſit A E, cui ex contactu A, ducta ſit intra.
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<
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">fectionem recta A D, quę poſt occurſum cum maiori axe, occurret quo-
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que minori, vt in D. </
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<
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<
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mi huius.</
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D A maiorem, _MAXIMAM_ eſſe ducibilium ex D, vel F, ad Ellipſis peri-
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pheriam A B C.</
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<
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">Deſcripto enim circulo A C G ex radio D A, ipſe cadet totus
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mihuius.</
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Ellipſim A B C hanc tantùm contingens in duobus punctis A, C; </
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propter, quæ ducentur ex D ad Ellipſis peripheriam, præter ad puncta
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A, C, diſtantia D A minores erunt: </
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A C G in diametri ſegmento F A ſit circuli centrum, ipſam F
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A, erit _MAXIMA_ ad circuli peripheriam A C G ducibi-
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lium, & </
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<
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ex F, ad peripheriam inſcriptæ Ellipſis A B C. </
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Quod erat vltimò demonſtrandum.</
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