# Full text: Clavius, Christoph: Christopheri Clavii Bambergensis ex Societate Iesv In Sphaeram Ioannis de Sacro Bosco commentarius

Comment. in I. Cap. Sphæræ diculari, & medietate baſis A B, (ꝑ 1. propoſ. huius) æquale eſt triangulo A B G; ſi ſumantur tot huiuſmodi rectangula, in quot triangula diuiſa eſt figura regu-
laris, erunt omnia ſimul ſiguræ A B C D E F, æqualia; propterea quòd omnia
triangula oſtenſa ſint æqualia triangulo A B G. Cum igitur eadem ſimul æ-
qualia ſint rectangulo I K L M; propterea quòd K L, æqualis ponitur dimidio
ambitus A B C D E F, hoc eſt, omnibus medietatibus baſium ſimul, & recta
I K, perpendiculari G H; erit figura regularis A B C D E F, æqualis rectangu
lo I K L M. Area igitur cuiuslibet figuræ regularis æqualis eſt, & c. quod erat
demonſtrandum.

8. primi.

## 75.THEOR. 3. PROPOS. 3.

Regularis
figura quæ
cunque cui
triangulo
rectangulo
æqualis ſit.

Area cuiuslibet figuræregularis æqualis eſt triangulo rectangulo,
cuius unum latus circa angulum rectum æquale eſt perpendiculari à centro
figuræ ad unum latus ductæ, alterum uero æquale ambitui eiuſdem figuræ.

Sit rurſus figura regularis A B C, cuius centrum D, à quo perpendicula-
ris ad latus A B, ducta ſit D E; triangulum uero rectangulum D E F, habens
angulum E, rectum, & latus D E, æquale perpendiculari D E, latus autẽ E F,
æquale ambitui figuræ A B C. Dico triangulum D E F, figuræ A B C, æquale
eſſe. Compleatur enim rectangulum D E F G; & diuiſa E F, bifa@iam in pun-
cto H, ducatur H I, æquidiſtans rectæ D E. Erit igitur (per 2. propoſ. huius)
rectangulum D E H I, contentum ſub D E, perpendiculari, & ſub E H, dimi-
dio ambitus figuræ, æquale figuræ A B C: At rectangulo D E H I, æquale eſt
triangulum D E F. Nam rectangulum D E H I, eſt dimidium rectanguli
D E F G; propterea quod æqualia ſunt rectangula D E H I, I H F G; Triangu-
lum quoque D E F, dimidium eſt eiuſdem rectanguli D E F G. Igitur & trian-
gulum D E F, æquale erit figuræ A B C. Area ergo cuiuslibet figuræ regula
ris æqualis eſt triangulo rectangulo, & c. quod demonſtrandum erat.

38 [?] . primi.
41. primi.

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