Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

389. THEOR. II. PROP. IV.

Si quotcunque rectæ lineæ terminatæ (non minus verò quam
tres) cuiuslibet longitudinis, ad vnum idemque punctum occur-
rant, totidem angulos inter ſe æquales conſtituentes, & quatuor
rectos complentes. Erit aggregatum harum ſimul omnium occur-
rentium, MINIMVM aggregatorum rectarum, à quibuſcunque
alijs aſſumptis punctis, ad eoſdem datarum terminos eductarum.

SInt quotcunque rectę A B, A C, A D, A E, A F, A G terminatę, quę
ad punctum A ſimul occurrant, conſtituantque angulos B A C, C A
D, D A E, E A F, F A G, G A B inter ſe æquales, & ſimul ſumpti ęquales
quatuor rectis: dico aggregatum harum omniũ minus eſſe aggregato linea-
rum, quæ ex quolibet alio puncto I ad eoſdem terminos B, C, D, E, F, G,
educi poſſunt, quales ſunt I B, I C, I D, I E, I F, I G.

Sit enim A G _MAXIMA_ ductarum ex A, ſuper qua ſumatur A P ipſa A
G non minor, cui demantur æquales A H, A L, A M, A N, A O, & com-
pleatur polygonum H L M N O P, quod erit æquilaterum, & æquiangulũ,
ſiue regulare, cum anguli ad A ſint æquales, eiuſque centrum erit A; deni-
que iungantur I H, I L, I M, I N, I O, I P.

0334-01

Iam aggregatum ductarum A H, A L, A M, A N, A O, A P ex centro
A ad angulos polygoni, cum ſit _MINIMVM_, erit minus aggregato ducta- rum I H, I L, I M, I N, I O, I P ex puncto I, ſed harum aggregatum mi-
nus eſt aggregato binarum I B, B H; I C, C L; I D, D M; I E, E N; I F,
F O; I G, G P; nam I B, B H maiores ſunt I H, & I C, C L maiores I
L, & c. quare eò magis aggregatum, ex A ductarum, A H, A L, A M, A
N, A O, A P minus erit aggregato binarum I B, B H; I C, C L; I D, D
M; I E, E N; I F, F O; I G, G P; demptis ergo communibus ſegmentis B
H, C L, D M, E N, F O, G P, erit reliquum aggregatum datarum A B,
A C, A D, A E, A F, A G minus reliquo aggregato ductarum I B, I C,

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