Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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cum duplo rectanguli LGM, ſed duplum rectanguli K F I, maius eſt duplo
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rectanguli LGM, vt ſuperiùs oſtenſum fuit; </
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<
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">quare his demptis, erunt reli-
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qua quadrata EF, FI ſimul, maiora reliquis ſimul EG, GM, ſed quadratum
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FI minus eſt quadrato GM, cum ſit linea FI minor GM, ergo reliquum qua-
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dratum EF maius erit reliquo EG, ſiue ſemi-diameter EF maior ſemi-dia-
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metro EG. </
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<
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">Quod ſecundò erat, &</
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<
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<
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<
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<
s
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">Dico tandem, in vno quoque Ellipſeos rectangulo quadrante, nempe
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in quadrante ABE, reperiri aliam ſemi-diametrum ipſi EG æqualem.</
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<
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<
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">Producta enim applicata GL ad N, & </
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<
s
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">iuncta EN, in triangulis ELG,
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ELN, eſt NL æqualis LG, & </
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<
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">LE communis, & </
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<
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">anguli ad L recti, quare ba-
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ſes EG, GN æquales erunt, & </
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">ſic in quolibet alio quadrante; </
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<
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ſemi-diametrorum vnica eſt in eodem quadrante, cum quę ad partes maio-
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ris axis ducuntur, maiores ſint, & </
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">quæ ad partes minoris, minores: </
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pter à centro Ellipſeos quatuor tantùm (in rectangulis quadrantibus inter ſe-
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mi-axes) ſemi-diametri æquales ad eius peripheriam duci poterunt. </
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<
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vltimò demonſtrandum erat.</
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">HInc eſt, quod _MAXIMA_ diametrorum, in Ellipſi, eſt axis maior, _MINI-_
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_MA_ verò axis minor; </
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">eadem enim eſt ratio de duplis, ac de ſubduplis.</
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xml:space
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">COROLL. II.</
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">PAtet etiam, quod ſi ex Ellipſeos centro ad interuallum cuiuſcunque ſe-
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mi-diametri, quæ non ſit axis, circulus deſcribatur, ipſum ad partes
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maioris axis cadere intra, ad partes verò minoris cadere extra, & </
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<
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tantùm punctis Ellipſim ſecare.</
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">THEOR. XLII. PROP. LXXXVII.</
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">Si ad extremum axis datæ coni-ſectionis ducta fuerit contingens
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linea, quæ cum alia ad alterum ſectionis punctum contingente
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conueniat; </
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">axem intercipitur
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(qui tamen in ſectione Ellipſis, ſit axis maior) minor eſt altera con-
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tingente: </
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">in Ellipſi tantùm, contingens ex minori axe altera
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contingente maior eſt.</
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">SIt coni-ſectio AB, cuius axis BC (quitamen in Ellipſi ſit axis maior) & </
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Hyperbola, ac Ellipſi ſit centrum D, ſitque ex vertice B contingens li-
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nea BE; </
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">ſumptoque in ſectione quolibet alio puncto A (quod tamen in Elli-
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pſi non ſit alterum axis extremum; </
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conic. </
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">inter ſe æquidiſtarent) ab eo ducatur contingens AE quæ
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cum BE conueniet in E. </
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di conic.</
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diametrum, cumtranſeat per occurſum tangentium, ſecare AB tactus iun-
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gentem biſariam in F.</
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