Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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0030
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<
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">PROBL. I. PROP. II.</
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<
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xml:space
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">Datæ Parabolæ per punctum in ea datum lineam contingentem
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ducere.</
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</
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<
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">SIt Parabole, cuius diameter AB, & </
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tet ex C Parabolæ contingentem rectam lineam ducere.</
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<
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">Prop. 33.
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primi co-
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nic.</
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">Applicetur ordinatim recta CD, & </
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natur EA, iungaturque ACF. </
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<
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">Dico ipſam eſſe tangentem quæſitam.</
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<
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0030-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0030-01
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<
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">Sumpto enim in ſectione quolibet puncto G, per eum applicetur BGF
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rectam AC ſecans in F, diametrum verò in B, & </
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<
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">iuncta DF ex E vertice.
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</
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<
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">ducatur EHM parallela ad AF ſecans DF in H, & </
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">CD in M, ſitque HL ipſi
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FB æquidiſtans. </
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<
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">Iam cum ſit AE æqualis ED, erit FH æqualis HD, ob pa-
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rallelas AF, EH; </
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">itemque BL æqualis LB ob æquidiſtantes BF, LH: </
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">quare
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fumpta EI media geometrica inter DE, & </
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arithmetica EL. </
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<
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">Ampliùs quadratum GB ad CD eſt vt linea EB ad
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mi conic.</
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vel vt quadratum mediæ geometricæ EI ad quadratum ED, ergo & </
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</
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<
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ſiue GB ad CD, minorem rationem quam EL ad ED, vel quàm EH ad EM,
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ſeu quam AF ad AC, vel quàm FB ad eandem CD, ergo GB minor eſt FB: </
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quare punctum F cadit extra Parabolen, & </
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ACF. </
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<
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<
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cta AB bifariam in H, cum eadem quoque in æqualiter ſecta ſit in E (nã
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cum ſit DE æqualis EA, erit in prima figura BE maior EA, & </
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<
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minor EA) erit rectangulum AHB maius rectangulo AEB, ac propterea.
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</
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<
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