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

88. COROLLARIVM.

Ex omnibusiis, quæ demonſtrata ſunt, perſpicuum eſt circu-
lum abſolute omnium figurarum rectilinearum ſibi iſoperimetra-
rum maximum eſſe.

88.1.

@Circul’ om
nibus figu-
@is rectili-
neis ſibi iſo
perimetris
maior eſt.

Qvoniam 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 eſ-
ſe, quę regularis eſt: Ex hac denique 13. propoſitioue perſpicuum eſt, circulum omnium
figurarum iſoperimet rarum regularium eſſe maximum: Manifeſte concluditur, circu-
lum abſolute ac ſimpliciter omnium figurarum rectilinearum ſibi iſoperimetrarum ma-
ximum eſſe quod eſt propoſitum.

89. THEOR. 12. PROPOS. 14.

Area cuiuslibet pyramidis æqualis eſt ſolido rectangulo conten-
to ſub perpendiculari à uertice ad baſim protracta, & tertia parte
baſis.

89.1.

Pyramis
quælibet
cui paralle-
lepipedo ſit
@qualis.

Sit pyramis, cuius baſis quotcu nque laterum A B C D E, & uertex F. Solidum autem rectangulu [?] m G N, cu-
ius baſis G H I K, æqualis ſit tertię par-
ti baſis A B C D E, altitudo uero, ſiue
perpendicularis G L, æqualis altitudini
pyramidis, ſiue perpendiculari à uerti-
ce pyramidis ad eius baſim productæ. Dico ſolidum rectangulum G N, ęqua-
le eſſe pyramidi A B C D E F. Ducan-
tur enim ab oibus angulis baſis G H I K,
ad aliquod punctum baſis oppoſitę, ni-
mirum ad L, lineę rectæ, ita ut conſti-
tuatur pyramis G H I K L, eandem ha-
bens baſim cum ſolido G N, eand emq́ue
altitudinem & cum eodem ſolido G N,
& cum pyramide A B C D E F. Quo-
niam igitur pyramis A B C D E F, tri-
pla eſt pyramidis G H I K L, ut in ſcho-
lio propoſ. 6. lib. 12. Eucl. demonſtraui-
mus: Et ſolidum G N, triplum quoque
eſt, ex coroll. propoſ. 7. lib. 12. Eucl. eiuſdem pyramidis G H I K L; erit ſo-
lidum G N, pyramidi A B C D E F, ęqua
le. Quapropter area cuiuslibet pyrami-
dis ęqualis eſt ſolido rectãgulo, & c. quod
erat oſtendendum.

89.1.

134-01

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