Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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043/01/027.jpg
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tripla: ſed vt AF, ad FE, ita eſt CF, ad FL; tripla igi
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tur erit CF, ipſius FL. </
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<
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>Similiter oſtenderemus rectas
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AE, BM, ſecare ſe ſe in eaſdem rationes, ita vt ſegmen
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ta, quæ ad angulos, ſint tripla eorum, quæ ſunt ad centra
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E, M, quorum AF, eſt tripla ipſius FE: in puncto igitur
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F, ſecant ſe rectæ lineæ AE, BM. </
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<
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>Eadem ratione & re
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ctæ AE, DN, ſecent ſe in puncto F, neceſse erit: quare
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vt AF ad FE, ita erit DF ad FN. </
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>
<
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>Quatuor igitur
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axes pyramidis ABCD, ſecantſe ſe in puncto F, in eaſ
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dem rationes, ita vt
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ſegmenta ad angulos,
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ſint
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abbr
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reliquorũ
">reliquorum</
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tripla.
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</
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<
s
>Rurſus, quia compo
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nendo, & conuerten
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do, eſt vt FE ad EA,
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ita FL ad LC: hoc
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eſt, vt pyramis BCD
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F, ad pyramidem A
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BCD, ita pyramis
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ABDF, ad pyrami
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dem CBDA, (pro
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pter baſium commu
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nitatem, & vertices in
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eadem recta linea) erit
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<
figure
id
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pyramis ABDF, æqualis pyramidi BCDF. </
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>
<
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>Eadem ra
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tione tam pyramis ACDF, quàm pyramis ABCF, æqua
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lis eſt pyramidi BCDF. </
s
>
<
s
>Quatuor igitur pyramides, qua
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rum communis vertex punctum F, baſes autem triangula,
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quæ ſunt circa pyramidem ABCD, inter ſe æquales
<
expan
abbr
="
erũt
">erunt</
expan
>
,
<
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/>
& vnaquæque pyramidis ABCD, pars quarta. </
s
>
<
s
>Dico in
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nullo alio puncto à puncto F, quatuor rectas, quæ ab an
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gulis ad triangula oppoſita pyramidis ABCD, ducantur,
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ſecare ſe in eaſdem rationes. </
s
>
<
s
>Si enim fieri poteſt ſecent
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ſe tales rectæ in eaſdem rationes in alio puncto S. </
s
>
<
s
>Simi</
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