1erit axis DE, pyramidis ABCD, cuius axis ſegmentum
DP eſt triplum ipſius PE: igitur P centrum erit pyra
midis ABCD. Et quoniam tres rectæ FK, KH, HF,
ſunt parallelæ tribus BD, DC, CB, pro vt inter ſe reſpon
dent, vt KH, ipſi LG, quoniam vtraque lateri DC, ob
latera triangulorum ſecta proportionaliter in punctis K, H,
L, G: & ſic de reliquis; erit pyramis AKFH, ſimilis toti
pyramidi ABCD. Similiter vnaquæque trium aliarum
pyramidum abſciſſarum, videlicet FLBG, GHMC,
KDLM, ſimilis erit pyramidi ABCD, atque ideo in
ter ſe ſimiles. Rurſus,
quoniam pyramidum
ſimilium latus AD eſt
duplum lateris AK, ho
mologi; pyramis AB
CD, octupla erit py
ramidis AKFH, ob
triplicatam laterum ho
mologorum proportio
nem. Similiter vna
qunæque trium reliqua
rum pyramidum abſciſ
ſarum erit octaua pars
pyramidis ABCD;
15[Figure 15]
quatuor igitur pyramides abſciſſæ ſimul ſumptæ dimi
dium erit pyramidis ABCD: & reliquum igitur ſoli
dum demptis quatuor pyramidibus, dimidium pyramidis
ABCD. Dico reliquum ſolidum LKMGFH, eſſe
octaedrum. Nam octo triangulis ipſum contineri mani
feſtum eſt. bina autem oppoſita eſſe parallela, & æqualia,
& ſimilia, ſic oſtendimus. Quoniam enim triangulum
FGH, eſt in plano trianguli ABC, plano trianguli KLM
parallelo; erit triangulum FGH, parallelum triangu-
DP eſt triplum ipſius PE: igitur P centrum erit pyra
midis ABCD. Et quoniam tres rectæ FK, KH, HF,
ſunt parallelæ tribus BD, DC, CB, pro vt inter ſe reſpon
dent, vt KH, ipſi LG, quoniam vtraque lateri DC, ob
latera triangulorum ſecta proportionaliter in punctis K, H,
L, G: & ſic de reliquis; erit pyramis AKFH, ſimilis toti
pyramidi ABCD. Similiter vnaquæque trium aliarum
pyramidum abſciſſarum, videlicet FLBG, GHMC,
KDLM, ſimilis erit pyramidi ABCD, atque ideo in
ter ſe ſimiles. Rurſus,
quoniam pyramidum
ſimilium latus AD eſt
duplum lateris AK, ho
mologi; pyramis AB
CD, octupla erit py
ramidis AKFH, ob
triplicatam laterum ho
mologorum proportio
nem. Similiter vna
qunæque trium reliqua
rum pyramidum abſciſ
ſarum erit octaua pars
pyramidis ABCD;
15[Figure 15]quatuor igitur pyramides abſciſſæ ſimul ſumptæ dimi
dium erit pyramidis ABCD: & reliquum igitur ſoli
dum demptis quatuor pyramidibus, dimidium pyramidis
ABCD. Dico reliquum ſolidum LKMGFH, eſſe
octaedrum. Nam octo triangulis ipſum contineri mani
feſtum eſt. bina autem oppoſita eſſe parallela, & æqualia,
& ſimilia, ſic oſtendimus. Quoniam enim triangulum
FGH, eſt in plano trianguli ABC, plano trianguli KLM
parallelo; erit triangulum FGH, parallelum triangu-