Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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            <p type="main">
              <s id="s.000678">
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              pyramidem, uel conum, uel coni portionem eandem pro­
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              portionem habet, quam baſes ab, cd unà cum ef ad ba­
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              ſim ab. </s>
              <s id="s.000679">quod demonſtrare uolebamus.</s>
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            <p type="margin">
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              6. 11. duo
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              decimi</s>
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            <p type="main">
              <s id="s.000681">Fruſtum uero ad æquale eſſe pyramidi, uel co
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              no, uel coni portioni, cuius baſis conſtat ex baſi­
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              bus ab, cd, ef, & altitudo fruſti altitudini eſt æ­
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              qualis, hoc modo oſtendemus.</s>
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            <p type="main">
              <s id="s.000682">Sit fruſtum pyramidis abcdef, cuius maior baſis trian­
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              gulum abc; minor def: & ſecetur plano baſibus æquidi­
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              ſtante, quod ſectionem faciat triangulum ghk inter trian­
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              gula abc, def proportionale. </s>
              <s id="s.000683">Iam ex iis, quæ demonſtrata
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              ſunt in 23. huius, patet fruſtum abcdef diuidi in tres pyra
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              mides proportionales; & earum maiorem eſſe
                <expan abbr="pyramidẽ">pyramidem</expan>
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              abcd
                <expan abbr="minorẽ">minorem</expan>
              uero defb. </s>
              <s id="s.000684">ergo pyramis à triangulo ghk
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              conſtituta, quæ altitudinem habeat fruſti altitudini æqua­
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              lem, proportionalis eſt inter pyramides abcd, defb: &
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              idcirco fruſtum abcdef tribus dictis pyramidibus æqua
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                <figure id="id.023.01.072.1.jpg" xlink:href="023/01/072/1.jpg" number="65"/>
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              le erit. </s>
              <s id="s.000685">Itaque ſi intelligatur alia pyra­
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              mis æque alta, quæ baſim habeat ex tri
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              bus baſibus abc, def, ghk conſtan­
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              tem; perſpicuum eſt ipſam eiſdem py­
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              ramidibus, & propterea ipſi fruſto æ­
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              qualem eſſe.</s>
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            <p type="main">
              <s id="s.000686">Rurſus ſit fruſtum pyramidis ag, cu
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              ius maior baſis quadrilaterum abcd,
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              minor efgh: & ſecetur plano baſi­
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              bus æquidiſtante, ita ut fiat ſectio qua­
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              drilaterum Klmn, quod ſit proportio
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              nale inter quadrilatera abcd, efgh. </s>
              <s id="s.000687">Dico pyramidem,
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              cuius baſis ſit æqualis tribus quadrilateris abcd, klmn,
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              efgh, & altitudo æqualis altitudini fruſti, ipſi fruſto ag
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              æqualem eſſe. </s>
              <s id="s.000688">Ducatur enim planum per lineas fb, hd, </s>
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          </chap>
        </body>
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