Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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xml:space
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<
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">Hyperbolæ congruentes, per diuerſos vertices ſimul adſcriptæ,
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ſunt inter ſe nunquam coeuntes, & </
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xml:space
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<
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ad interuallum nunquam perueniunt æquale cuidam dato inter-
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uallo.</
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<
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<
s
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">SInt duæ congruentes Hyperbolæ ABC, DEF per diuerlos vertices B, E
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ſimul adſcriptæ, quarum recta latera ſint BG, EH (quæ inter ſe æqua-
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lia erunt) & </
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<
s
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">ipſarum tranſuerſa ſint BI, EL (quæ item æqualia erunt
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roll. 19. h.</
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ſectiones ponantur congruentes.) </
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<
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inter ſe conuenire.</
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<
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<
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<
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">Nam producta contingente HE donec ſectioni ABC occurrat in A, & </
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<
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">C,
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ipſa quoque erit ordinata in ſectione ABC (cum ſint ſectiones ſimul adſcri-
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ptæ) & </
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">ſectio DEF tota cadet infra contingentem AEC; </
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">ſumptoque in ipſa
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ED quocunque puncto D, applicetur SDO, quæ iunctis regulis IG, LH oc-
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currat in K, R; </
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<
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xml:space
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">& </
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<
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">cum ſit triangulum IBG ſimile triangulo LEH (habent
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enim circa æquales angulos B, E, æqualia latera, vtrunque vtrique) erit
<
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angulus BIG æqualis angulo ELH, vnde regulæ IGK, LHR æquidiſtant,
<
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ideoque IK cadit extra LR, cum ſit punctum I ſupra L, ergo OK maior eſt
<
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OR, ſed eſt OB maior OE, igitur rectangulum BOK ſiue quadratum
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1. huius.</
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maius eſt rectangulo, EOR ſiue quadrato DO; </
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<
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xml:space
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">hoc eſt punctum D cadit
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">ibidem.</
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tra ſectionem ED, & </
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">ſic de quocunque alio puncto eiuſdem ſectionis infra
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contingentem EA: </
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<
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xml:space
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">quapropter huiuſmodi Hyperbolæ inter ſe nunquam
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conueniunt. </
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<
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<
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">c.</
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