Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſibus proportionales: </
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re ſemi-Parabole EBC ad
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EDC, ſiue tota ABC ad
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totam ADC, ſuper ea-
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dem baſi AC, & </
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<
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xml:space
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dem diametrum BE, eſt vt
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altitudo FA ad AG. </
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<
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xml:space
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ſi concipiatur altera Para-
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bole QST, cuius baſis QT
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æqualis ſit baſi AC, alti-
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tudo verò SV ſit æqualis
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ipſi GA (quæcunq; </
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<
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clinatio baſis cum diame-
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tro SZ) ipſa, per præcedẽ-
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tem propoſitionem, ęqua-
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lis erit Parabolę ADC, ac
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ideo QST ad ABC eandem habebit rationem, quàm ADC ad ABC, vel
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quàm altitudo GA, ſiue SV ad FA. </
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<
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xml:space
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">Vnde Parabolæ æqualium baſium
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ſunt inter ſe vt altitudines. </
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<
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xml:space
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<
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">Sirecta linea ſemi-Parabolen ad extremum baſis contingens
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cum diametro conueniat, & </
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<
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">intra ipſam ſuper eadem baſi deſcri-
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pta ſit Parabole, cuius diameter ſit dimidium diametri ſemi-Para-
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bolæ, ac ei æquidiſtet; </
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<
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">erit trilineum à contingente, producta dia-
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metro, & </
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<
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xml:space
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">conuexa ſemi-Parabolica linea contentum, æquale tri-
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lineo à diametro, conuexa Parabolica, & </
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<
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lica comprehenſo.</
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</
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<
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<
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xml:space
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">ESto ſemi-Parabole ABC, cuius baſis AC, & </
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<
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CB occurrens in E, & </
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<
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">iuncta AB, ac bifariam ſecta AC in F, agatur F
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GH æquidiſtans CB, & </
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<
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">ſuper baſi AC cum diametro GF, quod eſt dimidium
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CB, deſcripta ſit Parabole AGC, (quæ cadet tota intra ABC:) </
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<
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lineum AEBHA æquale eſſe trilineo AHBCGA.</
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<
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">Sed ad hoc demonſtrandum, videndum eſt primò, quomodo cuilibet tri-
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lineo ex prædictis, circumſcribi poſſint figuræ ex æquè altis, & </
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qualibus parallelogrammis, &</
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<
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<
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">Per continuam igitur biſectionem, diuidatur contingens AE, vel baſis AC
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in quotcunq; </
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cta D, L, M, F, &</
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ſemi-Parabolen ſecent in Q, R, K, H &</
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& </
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<
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intra ſemi-Parabolen ABC cadent (cum ſint contingenti æquidiſtantes) vel
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extra trilineum AEBHA. </
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<
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ra EBYZ&</
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