Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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<
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">Dato angulo rectilineo, per punctum in qualibet eius diametro
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datum, MAXIMAM Ellipſim inſcribere, cuius latera datam ha-
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beant rationem.</
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<
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<
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xml:space
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<
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">datum punctum D, per quod
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oporteat Ellipſim inſcribere, cuius tranſuerſum latus ad rectum, datam
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quamcunque habeat rationem E ad F, & </
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<
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">Applicetur per D, ordinatim GDH, &</
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per H ducatur HIL diametrum ſecans in I, & </
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BA in L, ita vt ex I, & </
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DH parallelis, rectangulum DIM, ad quadra-
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tum AI, rationem habeat E ad F, & </
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uerſo DM, per extrema applicatæ AC, Elli-
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pſis deſcribatur DAMC. </
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57. h.</
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_MAXIMAM_ quæſitam.</
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<
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LA ad AG, ſiue vt MI ad ID, quare BA, BC
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Ellipſim contingent, ideoque ipſa erit
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conic.</
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lo inſcripta, eritque _MAXIMA_, vt in præce-
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dentibus oſtenſum fuit. </
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<
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<
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">Datis medijs proportionalibus, Arithmetica nempe, & </
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metrica inter eaſdem ignotas extremas; </
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<
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geometrica inter duas eaſdem ignotas
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extremas, quarum idem ſit terminus A, & </
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ſimul congruere intelligantur: </
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AB ſuperare ipſam AC, cum media ari-
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thmetica ſit maior media geometrica. </
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oporteat datis AC, AB ignotas extremas
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proportionales inuenire.</
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<
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">Fiat centro A interuallo A C circulus
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CF, cui ex puncto B contingens ducatur
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BF, quæ eum radio FA rectum efficiet an-
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gulum, vnde ſubtenſa BA erit maior ipſa
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BF; </
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deſcribatur ſemi- circulus DFE, ipſæ ſeca-
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bit BA infra A, ſed tamen vltra C (cum ſit
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BC minor BF, eo quod AC æquatur AF,
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&</
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