Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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& </
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<
s
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xml:space
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">ex puncto A in ſectione extra verticem ſumpto ipſam contingat
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">2.4. h.</
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AE, quæ cum axe SB, conueniet, & </
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<
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">in Ellipſi cum vtraque axe SB, TH;</
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<
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xml:space
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<
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xml:space
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">24. 25.
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pr. conic.</
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ſintque occurſus E, L, & </
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<
s
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xml:space
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</
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<
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xml:space
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">Dico primùm hanc cum axe conuenire, & </
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<
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">in Ellipſi cum vtraque axe, ſed
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priùs cum maiori.</
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</
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<
s
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0159-01
"/>
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AF axi ordinatim appli-
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cata, quæ cum axe re-
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ctum angulum AFE cõ-
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ſtituet, ac ideo angulus
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AEF acutus erit, ſed eſt
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rectus EAD, quare AD
<
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conuenit cum EBD, vt-
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puta in D. </
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<
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tione in Ellipſi demon-
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ſtrabitur ipſam AD con-
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uenire quoque cum mi-
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nori axe HT, ſi ex A or-
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dinatè ei applicetur AR: </
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<
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xml:space
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">nam cum angulus ARL ſit rectus, angulus ALR
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acutus erit, ſed LAD rectus ponitur, quare AD conuenit quoque cum axe
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minori HT, vt in I. </
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<
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">Quod autem priùs cum maiori axe conueniat, ita oſten-
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detur. </
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<
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">Etenim cum recta AF ſit ad axim applicata, & </
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<
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">contingens AE cum
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axe in E conueniat, N verò ſit centrum Ellipſis, erit rectangulum EFN ad
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quadratum AF, vt tranſuerſum latus ad rectum, ſed quadratum AF
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mi conic.</
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tur rectangulo EFD, ergo rectangulum EFN ad rectangulum EFD, ſiue li-
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nea FN ad FD, erit vt tranſuerſum latus ad rectum, hoc eſt vt quadratum
<
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BS ad quadratum HT (nam ſecunda diameter HT media proportionalis eſt
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inter tranſuerſum BS, & </
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<
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">latus rectum) ſed quadratum BS maius eſt quadra-
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to HT, cum ſit BS axis maior, ergo & </
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<
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dicularis ergo AD ſecat priùs maiorem axem, quàm minorem.</
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<
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">Dico inſuper in vtraque ſigura interceptam DA minorem eſſe intercepto
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axis ſegmento DB.</
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</
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<
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<
s
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xml:space
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">_Ducta enim ex B recta BG_ ordinatim ductæ FA æquidiſtant, ipſa quidem
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ſectionem continget, & </
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<
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mi conic.</
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GD: </
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<
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">cumque anguli GAD, GBD ſint recti, erunt duo quadrata DA, AG
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quadrato DG itemque duo quadrata DB, BG eidem quodrato DG æqua-
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lia, ergo duo ſimul DA, AG duobus ſimul DB, BG æqualia erunt, ſed AG
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quadratum maius eſt quadrato BG cum ipſa tangens AG, ſit maior
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te BG, ergo quadtatum DA minus erit quadrato DB, ſiue perpendicularis
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DA minor maioris axis ſegmento DB. </
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<
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">Cum verò in Ellipſi tangens AL occurret minori axi TH, vt in L. </
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terceptam perpendicularem AI maiorem eſſe axis ſegmento IH.</
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<
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">Si enim ex H ducatur HM ordinatim applicatæ NB æquidiſtans hæc Elli-
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pſim continget, & </
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<
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">alteritangenti AL occurret vt in M; </
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<
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">iuncta ergo M
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mi conic.</
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erunt duo triangula rectangula MAI, MHI, quorum anguli ad A, & </
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ſunt; </
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<
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">quare duo quadrata MA, AI vnico MI, & </
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qualia erunt, ergo duo ſimul MA, AI duobus ſimul MH, HI ſunt </
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