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