Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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reliquo BFC æqualis, qui ſunt anguli ad
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centra D, F: </
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circumferentias, hoc eſt anguli B G L,
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B I C æquales erunt, vnde G L æquidi-
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ſtabit I C: </
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<
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">quare, vt C B ad B L, ita I B,
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ad BG, vel ſumpta communi altitudine
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BH, ita rectangulum IBH, ſiue quadra-
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tum B C, ad rectangulum H B G, vel ad
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quadratum BM: </
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<
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">cum ergo ſit CB ad BL,
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vt quadratum C B ad quadratum B M,
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erunt tres contingentes BC, BM, BL,
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in eadem ratione geometrica, ſed C B
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ad B M, eſt vt C F ad M E, & </
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<
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">M B ad
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B L, vt M E ad L D; </
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<
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">ergo C F, M E,
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L D, vti etiam ipſarum quadrata, ſiue
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_MAXIMI_ circuli ex FC, EM, DL erunt
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in eadem ratione geometrica, quę pro-
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cedit iuxta quadrata contingentium
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B C, B M, B L. </
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<
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">Quod oſtendere pro-
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ponebatur.</
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">HInc elicitur, quod ſi datus angulus fuerit angulus trianguli æquilateri,
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ſiue duæ tertiæ vnius recti, prædicti _MAXIMI_ circuli erunt inter ſe
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in continua progreſſione nonupla. </
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">Tunc enim in triangulo ęquilatero BNO,
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_MAXIMVS_ inſcriptus circulus ex DG ſingula latera ad puncta contactuum
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bifariam ſecabit, quare BL æquabitur LN, ſiue NG, ſiue NM, (cum circu-
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lum contingentes, ex eodem puncto ſint æquales) hoc eſt BM erit tripla
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BL, & </
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<
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">quadratum BM nonuplum quadrati B L, vel circulus ex EM nonu-
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plus circuli ex DL, itemque circulus ex F C nonuplus circuli ex E M, cum
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ſint in eadem proportione geometrica, & </
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<
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modi circuli ſe mutuò, & </
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<
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">Hic autem notandum eſt inter hos _MAXIMOS_ circulos non dari _MAXI-_
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_MVM_, cum infra circulum FC alij infiniti in eadem progreſſione dato angu-
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lo inſcribi poſſint, eò quod ipſe ad partes L ſit infinitæ extenſionis.</
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ad partes verticis B, ſupra circulum DL, reſiduo trilineo, licet terminato,
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alij infiniti circuli perpetuò decreſcentes inſcribi poſſunt.</
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