1verticem æqualia alterum alteri: eademque ratione, &
triangulum EKH, triangulo BCK: & triangulum FKH,
triangulo BDK; erit pyramis KEFH, ſimilis, & æqua
lis pyramidi KBCD: habent autem tria latera tribus
lateribus homologis, ideſt æ
qualibus, in directum, prout
inter ſe reſpondent, conſtituta;
duarum igitur pyramidum KE
FH, KBCD, ſimul centrum
grauitatis erit K: non aliter
duarum pyramidum KGFH,
KBDA, ſimul centrum gra
uitatis erit K; totius igitur com
poſiti ex quatuor pyramidibus;
ideſt duabus oppoſitis ABC
DK, EFGHK, centrum gra
uitatis erit idem K. Eadem
ratione tam duarum pyrami
37[Figure 37]
dum AEHDK, BCGFK, ſimul, quàm duarum AB
FEK, CDHGK, ſimul centrum grauitatis erit K. To
tius igitur parallelepipedi ABCDEFGK, centrum
grauitatis erit K. Quod demonſtrandum erat.
triangulum EKH, triangulo BCK: & triangulum FKH,
triangulo BDK; erit pyramis KEFH, ſimilis, & æqua
lis pyramidi KBCD: habent autem tria latera tribus
lateribus homologis, ideſt æ
qualibus, in directum, prout
inter ſe reſpondent, conſtituta;
duarum igitur pyramidum KE
FH, KBCD, ſimul centrum
grauitatis erit K: non aliter
duarum pyramidum KGFH,
KBDA, ſimul centrum gra
uitatis erit K; totius igitur com
poſiti ex quatuor pyramidibus;
ideſt duabus oppoſitis ABC
DK, EFGHK, centrum gra
uitatis erit idem K. Eadem
ratione tam duarum pyrami
37[Figure 37]dum AEHDK, BCGFK, ſimul, quàm duarum AB
FEK, CDHGK, ſimul centrum grauitatis erit K. To
tius igitur parallelepipedi ABCDEFGK, centrum
grauitatis erit K. Quod demonſtrandum erat.
PROPOSITIO XXVI.
Si parallelepipedum in duo parallelepipeda
ſecetur, ſegmenta axis à centris grauitatis totius
parallelepipedi, & partium terminata ex contra
rio parallelepipedi partibus reſpondent.
ſecetur, ſegmenta axis à centris grauitatis totius
parallelepipedi, & partium terminata ex contra
rio parallelepipedi partibus reſpondent.
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib