Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Ducatur EF Ellipſim contingens, cui ex E perpendicularis erigatur ED,
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maiori axi occurrens in L, minori verò in D: </
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lo DE circulus deſcribatur EGHI. </
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<
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<
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<
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<
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">quoniam quilibet alius
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0170-01
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circulus, cuius radius, maior ſit ipſo
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DE, eſt omnino maior circulo EG-
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HI, & </
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<
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">cuius radius minor ſit D E,
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eſt quidem minor, ſed vel totus ca-
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dit intra Ellipſim, vel eius periphe-
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riam neceſſariò ſecat. </
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<
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trum fuerit in perpendiculari ED,
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& </
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<
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quæ cadit inter contactum E, &</
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maiorem axim, circulus cadet totus
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intra, & </
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<
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qualis eſt EP, tunc eius circulus ca-
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det totus intra circulum EGHI, ſed
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licet ipſius peripheria ad partes G,
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B, ſtatim ac diſcedit ab E, cadat in-
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ter peripheriam circuli AGH, & </
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<
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">perip heriam Ellipſis EBH, cum tamen in
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ſe ipſum redeat, neceſſariò Ellipticam peripheriam EBH ſecabit, nam ſpa-
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tium EGHB eſt vndique occluſum.</
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<
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">Si verò centrum fuerit extra perpendicularem ED, vt in Q: </
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<
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">iuncta QE
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cum contingente SEF inæquales angulos efficiet, quorum alterum, videli-
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cet SEQ obtuſus erit, quare ſi ipſi EQ erigatur perpendicularis ER, hæc
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omninò ſecabit Ellipſim: </
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<
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">quare ſi cum centro Q, interuallo QE
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mi conic.</
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deſcribatur XEV, ipſæ ad partes ſecantis ER ſecabit omnino Ellipſis peri-
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pheriam, vt per ſe patet. </
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<
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ptus quæſitus. </
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mutuò contingentes, ſunt inter ſe in continua, eademque ratione
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geometrica, quæ progreditur iuxta quadrata tangentium, ex ver-
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tice dati anguli ductarum.</
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<
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contactus ſint G, H, &</
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<
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Dico hos circulos inter ſe eſſe in continua, eademque ratione geometrica,
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ipſamque incedere iuxta quadrata contingentium BL, BM, BC, &</
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<
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<
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anguli BLD, BCF ſint recti, & </
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