Full text: Clavius, Christoph: Christophori[i] Clavii Bambergensis Ex Societate Iesv In Sphaeram Ioannis De Sacro Bosco Commentarivs

Comment. in 1. Cap. Sphæræ

86. COROLLARIVM.


E x omnibus ijs, quæ demonſtrata ſunt, peſpicuum eſt circulum
ab ſolute omnium figurarum recti linearum ſibi iſoperimetrarum
maximum eſſe.

Q voniam enim ex propoſitione 5. habetur, regularium figurarum iſoperime-
trarum eam, quæ plura latera continet, eſſe maiorem. Rurſus ex propoſitione 12.
constat, inter omnes figuras iſoperimetras æqualia numero latera habentes, eam
maximam eſſe, quæ regularis eſt. Ex hac denique 13. propoſitione perſpicuum eſt,
circulum omnium figurarum iſoperimetrarum regularium eſſe maximum: Mani-
feste concluditur, circulum abſolute, ac ſimpliciter omnium figurarum rectilmea-
rum ſibi iſoperimetrarum maximum eſſe quod eſt propoſitum.

87. THEOR 12. PROPOS. 14.


A rea cuiuslibet pyramidis æqualis est ſolido rectangulo con-
tento ſub perpendiculari a vertice ad baſim protracta, & tertia parte
baſis.

S it pyramis, cuius baſis quotcunque laterum A B C D E, & vertex F. So-

[figure]

lidum autem rectangulum G N, cuius baſis
G H I K, æqualis ſit tertiæ parti baſis A B C
D E, altitudo vero, ſiue perpendicularis
G L, æqualis altitudini pyramidis, ſiuæ per-
pendiculari à vertice pyramidis ad eius ba-
ſim productæ. Dico ſolidum rectangulum
G N, æquale eſſe pyramidi A B C D E F. Du-
cantur enim ab omnibus angulis baſis G H-
I K, ad aliquod punctum baſis oppoſitæ, ni-
mirum ad L, lineæ rectę, ita vt conſtituatur
pyramis G H I K L, eandem habens baſim
cum ſolido G N, eandem\'que altitudinem &
cum eodem ſolido G N, & cum pyramide
A B C D E F. Quoniam igitur pyramis
A B C D E F, tripla eſt pyramidis G H I K L,
vt in ſcholio popoſ. 6. lib. 12. Eucl. demon-
ſtrauimus. Etſolidum G N, triplum quo-
que eſt, ex coroll. propoſ. 7. lib. 12. Eucl.
eiuſdem pyramidis G H I K L; erit ſolidum
G N, pyramidi A B C D E F, æquale. Qua-
propter area cuiuslibet pyramidis æqualis eſt
ſolido rectangulo, &c. quod erat oſtenden-
dum.

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