Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Datæ Ellipſi, vel circulo, per terminos cuiuſcunque in ipſo ap-
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plicatę MINIMAM Ellipſim circumſcribere, cuius tranſuerſum la-
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tus æquale ſit dato, quod tamen maius ſit tranſuerſa diametro datæ
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Ellipſis.</
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quædam ad eam applicata AC: </
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">oportet per terminos A, C, cum tranſ-
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uerſo DE, quod excedat BO _MINIMAM_ Ellipſim circumſcribere.</
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">Ducatur ex A contingens AK productæ
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diametro occurrens in K, & </
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ſecetur in puncto G, quod cadet iuter B, & </
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K, vt in 83. </
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">& </
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lineam DE applicetur parallelogrammum,
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æquale quadrato GF, excedens figura
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quadrata, ſitque rectangulum DHE, & </
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ſumpta HI media proportionali inter DH,
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HE, erit rectangulum DHI, ſiue quadra-
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tum GF, ęquale quadrato HI, hoc eſt linea
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GF æqualis HI: </
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HE, erit reliqua LF æqualis EI, & </
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L cadet extra B: </
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KB, vt AF ad FB, ſitque KF bifariam
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mi conic.</
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cta in G, erit rectangulum OGB æquale quadrato GF, ſiue quadrato
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ſiue rectangulo DHE; </
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erit maior HE, ſiue maior GL; </
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<
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">itaque punctum L cadet extra Ellipſim
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CO. </
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itemque punctum N cadet extra Ellipſim ABCO: </
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DHE, ſiue NGL æquale quadrato HI, ſiue GF, ſitque rectangulum OGB,
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æquale eidem quadrato GF, vt ſupra oſtendimus, erunt rectangula OGB,
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NGL inter ſe æqualia, & </
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">ideo vt OG ad GN, ita LG ad GB, ſed eſt LG mi-
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nor GB, vt ſuperiùs demonſtrauimus, vnde, & </
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punctum N cadet extra Ellipſim ABCO. </
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NL, quod æquale eſt datæ lineæ DE, circa applicatam AC
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57. h.</
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Ellipſis ALCN. </
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<
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">Quoniam cum ſit rectangulum NGL æquale quadrato GF, erit NG ad
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GF, vt GF ad GL, & </
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">componendo, NG cum GF, ſiue NK, erit ad GF, vt
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FG cum GL, ſiue vt KL ad GL, & </
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vel vt NG ad GF, vel vt NF ad FL, ergo recta KAM Ellipſim ALCN
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12. h.</
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tingit in A, ſed eadem KAM contingit quoque ad idem punctum A
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pſim ABCO: </
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At ipſa erit _MINIMA_: </
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terminos communis applicatæ AC, & </
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LN, _licet maior ſuerit eadem ALCN_, inſcriptam ABCO omnino ſecat; </
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