Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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partes d. </
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<
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">in pyramide igitur inſcripta erit quædam figura,
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ex priſmatibus æqualem altitudinem habentibus
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cõſtans
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,
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ad partes e: & altera circumſcripta ad partes d. </
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<
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">Sed unum
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quodque eorum priſmatum, quæ in figura inſcripta conti
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nentur, æquale eſt priſmati, quod ab eodem fit triangulo in
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figura circumſcripta: nam priſma pq priſmati po eſt æ
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quale; priſma st æquale priſmati sr; priſma xy priſmati
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xu; priſma
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grc
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priſmati
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z; priſma
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priſmati
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priſ
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ma
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priſmati
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& priſma
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priſmati
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æquale. </
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<
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">re
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linquitur ergo, ut circumſcripta figura exuperet
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inſcriptã
">inſcriptam</
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priſmate, quod baſim habet abc triangulum, & axem ef. </
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<
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">Illud uero minus eſt ſolida magnitudine propoſita. </
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Eadẽ
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ratione inſcribetur, & circumſcribetur ſolida figura in py
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ramide, quæ quadrilateram, uel
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plurilaterã
">plurilateram</
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baſim habeat.</
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<
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">PROBLEMA II. PROPOSITIO XI.</
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<
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">DATO cono, fieri poteſt, ut figura ſolida in
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ſcribatur, & altera circumſcribatur ex cylindris
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æqualem habentibus altitudinem, ita ut circum
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ſcripta ſuperet inſcriptam, magnitudine, quæ ſo
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lida magnitudine propoſita ſit minor.</
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">SIT conus, cuius axis bd: & ſecetur plano per axem
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ducto, 'ut ſectio ſit triangulum abc:
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intelligaturq;
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cylin
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drus, qui baſim eandem, & eundem axem habeat. </
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<
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id
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s.000401
">Hoc igi
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tur cylindro continenter bifariam ſecto, relinquetur cylin
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drus minor ſolida magnitudine propoſita. </
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<
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id
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">Sit autem is cy
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lindrus, qui baſim habet circulum circa diametrum ac, &
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axem de. </
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<
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id
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">Itaque diuidatur bd in partes æquales ipſi de
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in punctis fghKlm: & per ea ducantur plana conum ſe
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cantia; quæ baſi æquidiſtent. </
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<
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">erunt ſectiones circuli, cen
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tra in axi habentes, ut in primo libro conicorum, </
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