Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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angulo per D adſcripta, cum eodem tranſuerſo
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latere DE, ſed cum recto, quod minus ſit recto
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adſcriptæ DAEC, eſt ipſa minor,
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roll. 19. h.</
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verò cum recto maiori, eſt quidem maior ea-
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dem, ſed omnino ſecat anguli latera BA, BC,
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vt ſatis conſtat. </
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<
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">Ampliùs, Ellipſis, quæ per
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D ſupra applicatam FG eidem angulo contin-
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genter inſcribitur, cum tranſuerſo latere ęqua-
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li ipſo DE, vel dato R (ſi tamen interceptum
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diametri ſegmentum DB maius fuerit DE) eſt
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omnino minor prædicta ADCE: </
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eſt _MAXIMA_ inſcripta quæſita. </
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<
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">Notandum eſt autem, quod ſi ABC fuerit
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quælibet coni- ſectio, vel circulus, eadem penitùs conſtructione, ac demon-
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ſtratione inſcribetur ei _MAXIMA_ Ellipſis ADCE, cum dato tranſuerſo R,
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quod tamen in Ellipſi, vel circulo, non excedat maius diametri ſegmentum.</
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<
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">SI verò data ſit Ellipſis ADCE, & </
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">per punctum B extra ipſam datum cir-
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cumſcribendus ſit ei _MINIMV S_ angulus rectilineus. </
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conic.</
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lipſim contingentes BA, BC; </
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ſcriptus quæſitus: </
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">quoniam ducta AC, ac bifariam ſecta in M, iunctaque
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BME, ipſa erit Ellipſis diameter, ſimulque dati anguli ABC, cum
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conic.</
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ipſi AC æquidiſtanter ductæ ab eadem BM bifariam ſecentur: </
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ABC erit datæ Ellipſi ADCE circumſcriptus: </
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quæcunque recta, quæ ex B intra angulum ABC ducitur, cum altera con-
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tingentium minorem angulum conſtituens, neceſſariò ſecat datam Ellipſim
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ADC: </
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">Si duæ rectæ AB, CD ſe mutuò ſecent in E, ſitque AE æqualis
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EB, ſed CE maior ED, dico iunctas CA, BD, ſi producantur, con-
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uenire ſimul ad partes A, D, vt in F, & </
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rallela ad AE, eſſe FC ad CA, vt FG ad GA.</
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ior ED, & </
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">iuncta BH, in triangulis BEH, AE
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C erunt latera circùm æquales angulos ad E, æ-
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qualia: </
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vnde BH parallela ad CA, hoc eſt anguli BAG,
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ABH duobus rectis æquales, ideoque duo BAG,
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ABD minores duobus rectis: </
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cum CA producta ad partes D, A; </
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ſus in F, ex quo ducatur FI parallela ad DG, vel
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ad AE.</
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<
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">Cum ſint ergo triangula FDI, BDE ſimilia, erit
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FI ad EB, vel ad AE, hoc eſt FC ad CA, vt FD
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ad DB, vel vt FG ad GA. </
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