Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſunt æqualia. </
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<
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xml:space
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">In ſecunda verò figura, aggregatum triangulorum ex G ma-
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ius eſt aggregato triangulorum ex F, vt ſatis patet (cum illud, ipſum poly-
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gonum excedat) quare, & </
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<
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xml:space
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">aggregatum baſium triangulorum ex G, (quæ
<
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ſuntipſæ perpendiculares ex G) maius eſt aggregato baſium triangulorum
<
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ex F, (quæ ſunt perpendiculares ex F.) </
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<
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<
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s
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">HInc eſt, quod aggregatum perpendicularium ex centro dati polygoni
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ſuper eius latera eductarum, ſemper eſt non maius quolibet ex alio
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puncto perpendicularium aggregato, vbicunque aſſumptum ſit punctum
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hoc, velintra, vel in perimetro, vel extra perimetrum dati polygoni.</
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<
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xml:space
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">In quocunque polygono regulari, aggregatorum linearum ex
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punctis vbicunque aſſumptis ad ipſius angulos eductarum, MINI-
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MVM eſt, quod ex centro.</
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<
s
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xml:space
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">SIt polygonum regulare A B C D E, cuius centrum P, à quo ad angulos
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eductæ ſint rectę P A, P B, P C, P D, P E, ſumptoq; </
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<
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xml:space
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">vbicunque alio
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puncto O, vei intra polygonum A B C D E, vel in eius perimetro, vel ex-
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tra, iungantur item O A, O B, O C, O D, O E. </
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<
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ctarum ex centro P, minus eſſe aggregato ductarum ex O.</
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</
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<
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<
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xml:space
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">Ex punctis enim A, B, C, D, E, erigan-
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turipſis P A, P B, P C, P D, P E perpen-
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diculares L I, I H, H G, G F, F L vtrinq;
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<
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polygonum L I H G F dato ſimile conſti-
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tuere circa idem centrum P, ad cuius late-
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ra ex puncto O ducantur perpendiculares
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O R, O Q, O N, O M, O S.</
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<
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<
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">præcedentis Lemmatis
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in polygono I H G F L aggregatum per-
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pendicularium, quæ ex centro P eſt non
<
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maius aggregato perpendicularium, quæ
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ex puncto O vbicunq; </
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<
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">aſſumpto, ſed aggregatum perpendicularium ex O,
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minus eſt aggregato obliquarum O A, O B, O C, O D, O E, ſuper ijſdem
<
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lateribus circumſcripti polygoni eductarum, (eſt enim perpendicularis O
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R, minor obliqua O A, & </
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O D, & </
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<
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xml:space
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">O S minor O E) ergo aggregatum perpendicularium ex P, hoc eſt
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ad angulos dati polygoni A B C D E eductarum, eſt omnino minus aggre-
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gato obliquarum ex O, nempe eductarum ad eoſdem angulos dati poly-
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goni à puncto O, vbicunque ſit ipſum O. </
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<
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centro ad angulos polygoni regularis _MINIMVM_ eſt. </
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