1tripla: ſed vt AF, ad FE, ita eſt CF, ad FL; tripla igi
tur erit CF, ipſius FL. Similiter oſtenderemus rectas
AE, BM, ſecare ſe ſe in eaſdem rationes, ita vt ſegmen
ta, quæ ad angulos, ſint tripla eorum, quæ ſunt ad centra
E, M, quorum AF, eſt tripla ipſius FE: in puncto igitur
F, ſecant ſe rectæ lineæ AE, BM. Eadem ratione & re
ctæ AE, DN, ſecent ſe in puncto F, neceſse erit: quare
vt AF ad FE, ita erit DF ad FN. Quatuor igitur
axes pyramidis ABCD, ſecantſe ſe in puncto F, in eaſ
dem rationes, ita vt
ſegmenta ad angulos,
ſint reliquorum tripla.
Rurſus, quia compo
nendo, & conuerten
do, eſt vt FE ad EA,
ita FL ad LC: hoc
eſt, vt pyramis BCD
F, ad pyramidem A
BCD, ita pyramis
ABDF, ad pyrami
dem CBDA, (pro
pter baſium commu
nitatem, & vertices in
eadem recta linea) erit
14[Figure 14]
pyramis ABDF, æqualis pyramidi BCDF. Eadem ra
tione tam pyramis ACDF, quàm pyramis ABCF, æqua
lis eſt pyramidi BCDF. Quatuor igitur pyramides, qua
rum communis vertex punctum F, baſes autem triangula,
quæ ſunt circa pyramidem ABCD, inter ſe æquales erunt,
& vnaquæque pyramidis ABCD, pars quarta. Dico in
nullo alio puncto à puncto F, quatuor rectas, quæ ab an
gulis ad triangula oppoſita pyramidis ABCD, ducantur,
ſecare ſe in eaſdem rationes. Si enim fieri poteſt ſecent
ſe tales rectæ in eaſdem rationes in alio puncto S. Simi
tur erit CF, ipſius FL. Similiter oſtenderemus rectas
AE, BM, ſecare ſe ſe in eaſdem rationes, ita vt ſegmen
ta, quæ ad angulos, ſint tripla eorum, quæ ſunt ad centra
E, M, quorum AF, eſt tripla ipſius FE: in puncto igitur
F, ſecant ſe rectæ lineæ AE, BM. Eadem ratione & re
ctæ AE, DN, ſecent ſe in puncto F, neceſse erit: quare
vt AF ad FE, ita erit DF ad FN. Quatuor igitur
axes pyramidis ABCD, ſecantſe ſe in puncto F, in eaſ
dem rationes, ita vt
ſegmenta ad angulos,
ſint reliquorum tripla.
Rurſus, quia compo
nendo, & conuerten
do, eſt vt FE ad EA,
ita FL ad LC: hoc
eſt, vt pyramis BCD
F, ad pyramidem A
BCD, ita pyramis
ABDF, ad pyrami
dem CBDA, (pro
pter baſium commu
nitatem, & vertices in
eadem recta linea) erit
14[Figure 14]pyramis ABDF, æqualis pyramidi BCDF. Eadem ra
tione tam pyramis ACDF, quàm pyramis ABCF, æqua
lis eſt pyramidi BCDF. Quatuor igitur pyramides, qua
rum communis vertex punctum F, baſes autem triangula,
quæ ſunt circa pyramidem ABCD, inter ſe æquales erunt,
& vnaquæque pyramidis ABCD, pars quarta. Dico in
nullo alio puncto à puncto F, quatuor rectas, quæ ab an
gulis ad triangula oppoſita pyramidis ABCD, ducantur,
ſecare ſe in eaſdem rationes. Si enim fieri poteſt ſecent
ſe tales rectæ in eaſdem rationes in alio puncto S. Simi
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