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.

74.1.

119-01
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.

75.1.

120-01
38 [?] . primi.
41. primi.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer