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.
HInc eſt, quod aggregatum perpendicularium ex centro dati polygoni
ſuper eius latera eductarum, ſemper eſt non maius quolibet ex alio
puncto perpendicularium aggregato, vbicunque aſſumptum ſit punctum
hoc, velintra, vel in perimetro, vel extra perimetrum dati polygoni.
ſuper eius latera eductarum, ſemper eſt non maius quolibet ex alio
puncto perpendicularium aggregato, vbicunque aſſumptum ſit punctum
hoc, velintra, vel in perimetro, vel extra perimetrum dati polygoni.
THEOR. I. PROP. III.
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.
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.