333147
ſunt æqualia.
In ſecunda verò figura, aggregatum triangulorum ex G ma-
ius eſt aggregato triangulorum ex F, vt ſatis patet (cum illud, ipſum poly-
gonum excedat) quare, & aggregatum baſium triangulorum ex G, (quæ
ſuntipſæ perpendiculares ex G) maius eſt aggregato baſium triangulorum
ex F, (quæ ſunt perpendiculares ex F.) Quapropter, & c. Quod erat, & c.
ius eſt aggregato triangulorum ex F, vt ſatis patet (cum illud, ipſum poly-
gonum excedat) quare, & aggregatum baſium triangulorum ex G, (quæ
ſuntipſæ perpendiculares ex G) maius eſt aggregato baſium triangulorum
ex F, (quæ ſunt perpendiculares ex F.) Quapropter, & c. Quod erat, & c.
COROLL.
In quocunque polygono regulari, aggregatorum linearum ex
punctis vbicunque aſſumptis ad ipſius angulos eductarum, MINI-
MVM eſt, quod ex centro.
punctis vbicunque aſſumptis ad ipſius angulos eductarum, MINI-
MVM eſt, quod ex centro.
SIt polygonum regulare A B C D E, cuius centrum P, à quo ad angulos
eductæ ſint rectę P A, P B, P C, P D, P E, ſumptoq; vbicunque alio
puncto O, vei intra polygonum A B C D E, vel in eius perimetro, vel ex-
tra, iungantur item O A, O B, O C, O D, O E. Dico aggregatum edu-
ctarum ex centro P, minus eſſe aggregato ductarum ex O.
eductæ ſint rectę P A, P B, P C, P D, P E, ſumptoq; vbicunque alio
puncto O, vei intra polygonum A B C D E, vel in eius perimetro, vel ex-
tra, iungantur item O A, O B, O C, O D, O E. Dico aggregatum edu-
ctarum ex centro P, minus eſſe aggregato ductarum ex O.
Ex punctis enim A, B, C, D, E, erigan-
264[Figure 264] turipſis P A, P B, P C, P D, P E perpen-
diculares L I, I H, H G, G F, F L vtrinq;
productæ. Patet has ſimul conuenire, &
polygonum L I H G F dato ſimile conſti-
tuere circa idem centrum P, ad cuius late-
ra ex puncto O ducantur perpendiculares
O R, O Q, O N, O M, O S.
264[Figure 264] turipſis P A, P B, P C, P D, P E perpen-
diculares L I, I H, H G, G F, F L vtrinq;
productæ. Patet has ſimul conuenire, &
polygonum L I H G F dato ſimile conſti-
tuere circa idem centrum P, ad cuius late-
ra ex puncto O ducantur perpendiculares
O R, O Q, O N, O M, O S.
Iam per Coroll.
præcedentis Lemmatis
in polygono I H G F L aggregatum per-
pendicularium, quæ ex centro P eſt non
maius aggregato perpendicularium, quæ
ex puncto O vbicunq; aſſumpto, ſed aggregatum perpendicularium ex O,
minus eſt aggregato obliquarum O A, O B, O C, O D, O E, ſuper ijſdem
lateribus circumſcripti polygoni eductarum, (eſt enim perpendicularis O
R, minor obliqua O A, & O Q minor O B; O N minor O C; O M minor
O D, & O S minor O E) ergo aggregatum perpendicularium ex P, hoc eſt
ad angulos dati polygoni A B C D E eductarum, eſt omnino minus aggre-
gato obliquarum ex O, nempe eductarum ad eoſdem angulos dati poly-
goni à puncto O, vbicunque ſit ipſum O. Quare aggregatum ductarum ex
centro ad angulos polygoni regularis _MINIMVM_ eſt. Quod erat, & c.
in polygono I H G F L aggregatum per-
pendicularium, quæ ex centro P eſt non
maius aggregato perpendicularium, quæ
ex puncto O vbicunq; aſſumpto, ſed aggregatum perpendicularium ex O,
minus eſt aggregato obliquarum O A, O B, O C, O D, O E, ſuper ijſdem
lateribus circumſcripti polygoni eductarum, (eſt enim perpendicularis O
R, minor obliqua O A, & O Q minor O B; O N minor O C; O M minor
O D, & O S minor O E) ergo aggregatum perpendicularium ex P, hoc eſt
ad angulos dati polygoni A B C D E eductarum, eſt omnino minus aggre-
gato obliquarum ex O, nempe eductarum ad eoſdem angulos dati poly-
goni à puncto O, vbicunque ſit ipſum O. Quare aggregatum ductarum ex
centro ad angulos polygoni regularis _MINIMVM_ eſt. Quod erat, & c.