Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
s
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xml:space
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">Nam ſi hæ Parabolæ non fuerint baſibus proportionales, erit altera Para-
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bolarum minor quàm opus eſt ad hoc vt huiuſmodi magnitudines ſint pro-
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portionales. </
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<
s
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xml:space
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">Eſto igitur ſi poſſibile eſt minor ABC, & </
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<
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xml:space
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">eius defectus ſit O;
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</
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<
s
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xml:space
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">ita vt baſis AC ad DF ſit vt aggregatum Parabolæ ABC cum magnitudine O
<
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ad Parabolen DEF. </
s
>
<
s
xml:id
="
echoid-s1071
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xml:space
="
preserve
">Iam iuxta vulgatam methodum Antiquorum circum-
<
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ſcribatur Parabolæ ABC, ſigura ex parallelogrammis conſtans, æqualium
<
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altitudinum, ita vt eius
<
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exceſſus ſupra Parabo-
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<
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fig-0050-01
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<
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="
0050-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0050-01
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len ſit minor O; </
s
>
<
s
xml:id
="
echoid-s1072
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xml:space
="
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">quod
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fiet, nempè ſi ex circũ-
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ſcripto Parabolæ paral-
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lelogrammo A Y; </
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>
<
s
xml:id
="
echoid-s1073
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xml:space
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">per
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biſectionem diametri B
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G in I, auſeratur dimi-
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dium parallelogrammũ
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AL, & </
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>
<
s
xml:id
="
echoid-s1074
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xml:space
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">exreliquo dimi-
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dium, donec ſuperſit pa-
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rallelogrammum CM,
<
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quod minus ſit ſpacio O: </
s
>
<
s
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="
echoid-s1075
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xml:space
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">ſic enim exceſſus circumſcriptæ figuræ ex paralle-
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logrammis, ſupra inſcriptam ex æque altis parallelogrammis erit maximum
<
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/>
parallelogrammum CM, (vt ſatis patet) quod eſt minus ſpacio O, ac ideo ex-
<
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/>
ceſſus circumſcriptæ ſupra ipſam Parabolen erit adhuc minor O; </
s
>
<
s
xml:id
="
echoid-s1076
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xml:space
="
preserve
">quapropter
<
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addita communi Parabola ABC, erit vniuerſa figura circumſcripta minor
<
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aggregato Parabolæ ABC cum ſpacio O: </
s
>
<
s
xml:id
="
echoid-s1077
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xml:space
="
preserve
">itaque circumſcripta ABC ex pa-
<
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rallelogrammis ad Parabolen DEF minorem habebit rationem, quam hu-
<
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iuſmodi aggregatum ad eandem Parabolen DEF, ſed prædictũ aggregatum
<
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/>
ad DEF Parabolen ponitur eſſe vt baſis AC ad DF, vel vt circumſcripta
<
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ABC ad circumſcriptam DEF, quæ per æquidiſtantium baſibus interſectio-
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nem deſcripta, ex æquè altis, & </
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>
<
s
xml:id
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echoid-s1078
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">numero æqualibus, ac proportionalibus pa-
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rallelogrãmis conſtabit (cum ſit quadratum A C ad QX, vt recta GB ad BN,
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vel vt HE ad EP, vel vt quadratũ DF ad quadratum TZ;</
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>
<
s
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="
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xml:space
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">vnde & </
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>
<
s
xml:id
="
echoid-s1080
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">recta AC ad
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QX, vel parallelogrammum CM ad QS, vt recta DF ad TZ, vel vt paralle-
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logrammum DR ad TV, & </
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<
s
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xml:space
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">ſic de reliquis ſingula ſingulis, vnde vniuerſa cir-
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cumſcripta ABC, ad vniuerſam DEF, eſt vt vnum CM ad vnum DR, vel vt
<
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baſis AC ad baſim DF) quare circumſcripta ABC ad Parabolen DEF mino-
<
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rem habebit rationem, quam eadem circumſcripta ad circumſcriptam DEF,
<
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hoc eſt circumſcripta ex parallelogrammis erit minor ei inſcripta Parabola
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DEF, totum parte; </
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<
s
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">quod eſt abſurdum: </
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<
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">inter has ergo Parabolas non datur
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minor quàm ſit opus ad hoc vt ipſæ ſint baſibus proportionales: </
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>
<
s
xml:id
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xml:space
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">erit ergo Pa-
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rabole ABC ad DEF, vt baſis AC ad DF baſim. </
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<
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">Quod erat demonſtrandum.</
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<
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">QVod oſtenſum eſt de integris Parabolis æquè altis, idem penitus con-
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ſimili conſtructione, eademque ratiocinatione demonſtrabitur de
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duobus trilineis ABG, CBG ab eadem diametro BG abſciſſis;
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</
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<
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xml:space
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">item de duobus trilineis Parabolicis ABG, DEH æqualium altitudinum, </
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