84 COMMENT. IN I. C AF. SPH AE RAEæquale ambitui figuræ A B C. Dico triangulum D E F, figuræ A B C, æqualeeſle. Compleatur enim rectangulum D EFG;& diuiſa E E, bifariam in pun-(to H, ducatur HI, ęquidiſtans rectæ D E. Erit igitur(per 2. propoſ. huius)re-

. D 8

1—9 Gangulum DEH, contentum ſub D E, perpendiculari,& ſub EIN, dimidio9 ambitus figuræ, æquale ſiguræ A B C: At rectangulo DE HI, æquale eſt trian-1 gulum D E F. Nam rectangulum D EHI, eſt qimidium rectanguli PE F G;10 36. primi. Propterea quòd æqualia ſunt rectangula DEH, IHF G; Triangulum quo-1 41. Prim. que DE F, dimidium eſt eiuſdem rectanguli DE FG. Igitur& triangulum1 DE F, quale erit figuræ A B C. Area ergo cuiuslibet ſiguræ regularis æqualit9 eſt triangulo rectangulo,& c. quod demonſtrandum erat.9 0 1 54 T NEON 4 PY RO 05. 4

1

0 5 5— 5 N

citculu- A RE A cuiuslibet circuli qualis eſt rectangulo comprehenſo ſub1 du recun. ſemidiamet ro,& dimidiata circumferentia circuli.1 50 0 æqu- ES T O circulus A B C, cuius ſemidlameter DB: Redangulum autemN is ſit.

A 0

4 K2 5 85

DB EF, comprehenſum ſub D B, ſemidiametro circuli,& B E, recta, qutrqualis ſit dimidiatæ eircunferentiæ circuli. Dico aream circuli A B C, 4 655en