PROPOSITIO VII.
Pyramides ſimilibus, & æqualibus triangulis
comprehenſæ inter ſe ſunt æquales.
comprehenſæ inter ſe ſunt æquales.
Sint pyramides ABCD, EFGH, ſimilibus, & æqua
libus triangulis comprehenſæ, & ſi ſint ſimiliter poſitæ, qua
rum vertices A, E, baſes autem triangula BCD, FGH.
Dico pyramidem ABCD, pyramidi EFGH, æqualem
eſse. A punctis enim A, E, manantia latera inferius pro
ducantur, & prædictis lateribus maiores, inter ſe autem
æquales abſcindantur AK, AL, AM, EN, EO, EP,
13[Figure 13]
& conſtruantur pyramides AKLM, ENOP: pyramides
igitur hæ æqualibus, & ſimilibus triangulis comprehenden
tur, vt colligitur ex ipſa conſtructione; triangulis igitur inter
ſe æquilateris, & æquiangulis KLM, NOP, inter ſe con
gruentibus non congruat, ſi fieri poteſt, pyramis ENOP,
pyramidi AKLM, ſed cadat vertex E, pyramidis ENOP,
extra verticem A, pyramidis AKLM, & ex puncto A,
libus triangulis comprehenſæ, & ſi ſint ſimiliter poſitæ, qua
rum vertices A, E, baſes autem triangula BCD, FGH.
Dico pyramidem ABCD, pyramidi EFGH, æqualem
eſse. A punctis enim A, E, manantia latera inferius pro
ducantur, & prædictis lateribus maiores, inter ſe autem
æquales abſcindantur AK, AL, AM, EN, EO, EP,
13[Figure 13]& conſtruantur pyramides AKLM, ENOP: pyramides
igitur hæ æqualibus, & ſimilibus triangulis comprehenden
tur, vt colligitur ex ipſa conſtructione; triangulis igitur inter
ſe æquilateris, & æquiangulis KLM, NOP, inter ſe con
gruentibus non congruat, ſi fieri poteſt, pyramis ENOP,
pyramidi AKLM, ſed cadat vertex E, pyramidis ENOP,
extra verticem A, pyramidis AKLM, & ex puncto A,
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