DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N161E9" type="main">
              <s id="N16257">
                <pb xlink:href="077/01/163.jpg" pagenum="159"/>
                <emph type="italics"/>
              ſeſquitertias eſſe triangulorum, erit igitur magnitudinis ex vtriſ〈que〉 por-
                <emph.end type="italics"/>
                <arrow.to.target n="marg284"/>
                <lb/>
                <emph type="italics"/>
              tionibus A
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              B BLC compoſitæ centrum grauitatis punctum
                <expan abbr="q.">〈que〉</expan>
              magni­
                <lb/>
              tudinis verò ex vtriſ〈que〉 triangulis AKB BLC compoſitæ punctum
                <lb/>
              T. Rurſus ita〈que〉 quoniam trianguli ABC centrum grauitatis eſt
                <expan abbr="punctū">punctum</expan>
                <lb/>
              E, magnitudinis verò ex vtriſ〈que〉 A
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              B BLC portionibus punctum
                <lb/>
                <expan abbr="q.">〈que〉</expan>
              manifestum eſt totius portionis A
                <emph.end type="italics"/>
              B
                <emph type="italics"/>
              C centrum grauitatis eſſe in linea
                <lb/>
              QE ita diuiſa
                <emph.end type="italics"/>
              in O puncto,
                <emph type="italics"/>
              vt quam proportionem habet trian­
                <lb/>
              gulum ABC ad vtraſ〈que〉 portiones A
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              B BLC, eandem habeat por
                <emph.end type="italics"/>
                <arrow.to.target n="marg285"/>
                <lb/>
                <emph type="italics"/>
              tio ipſius terminum habens punctum Q,
                <emph.end type="italics"/>
              hoc eſt OQ
                <emph type="italics"/>
              ad portionem
                <lb/>
              minorem
                <emph.end type="italics"/>
              OE.
                <emph type="italics"/>
              pentagoni autem AKBLC,
                <emph.end type="italics"/>
              hoc eſt magnitudinis
                <lb/>
              ex triangulo ABC, trianguliſquè AKB BLC compoſitæ
                <lb/>
                <emph type="italics"/>
              centrum grauitatis eſt in linea ET ſic diuiſa
                <emph.end type="italics"/>
              in S,
                <emph type="italics"/>
              vt quam habet
                <lb/>
              proportionem triangulum ABC ad triangula AKB BLC, eande ha­
                <lb/>
              beat portio ipſius ad T terminata,
                <emph.end type="italics"/>
              hoc eſt ST
                <emph type="italics"/>
              ad reliquam
                <emph.end type="italics"/>
              SE.
                <lb/>
                <emph type="italics"/>
              Quoniam igitur maiorem habet proportionem triangulum ABC ad
                <expan abbr="triã">triam</expan>
                <emph.end type="italics"/>
                <arrow.to.target n="marg286"/>
                <lb/>
                <emph type="italics"/>
              gula KAB LBC, quam ad portiones
                <emph.end type="italics"/>
              AKB BLC; minora enim
                <lb/>
              ſunt triangula portionibus. </s>
              <s id="N162EB">habebit TS ad SE
                <expan abbr="miorẽ">miorem</expan>
              pro­
                <lb/>
              portio nem, quam QO ad OE ac propterea erit
                <expan abbr="punctũ">punctum</expan>
              S
                <lb/>
              propinquiusipſi E, quàm O. Nam ſi punctum S primùm
                <lb/>
              eſſet in eodem puncto O, tunc TO ad OE, non quidem
                <lb/>
              maiorem, ſed minorem haberet proportionem, quàm
                <arrow.to.target n="marg287"/>
                <lb/>
              ad OE, cùm ſit TO minor QO. ſimiliter ob eadem cau
                <lb/>
              ſam ſi punctum S eſſet inter OT, minorem
                <arrow.to.target n="marg288"/>
              pro­
                <lb/>
              portionem TS ad SE, quàm QS ad SE, quare & ad huc
                <lb/>
              maiorem haberet proportionem QO ad OE, quàm TS
                <lb/>
              ad SE. neceſſe eſt igitur punctum S eſſe inter puncta OE.
                <lb/>
              Itaquè cùm punctum O ſit
                <expan abbr="centrũ">centrum</expan>
              grauitatis portionis ABC,
                <lb/>
              punctum verò S centrum ſit grauitatis rectilineæ figuræ
                <lb/>
              AK BLC;
                <emph type="italics"/>
              constat portionis ABC centrum grauitatis propinquius
                <lb/>
              eſſe vertici B, quàm centrum rectilineæ figuræ inſcriptæ. </s>
              <s id="N1631D">Et in om­
                <lb/>
              nibus rectilineis figuris in portionibus planè inſcriptis eadem eſt ratio.
                <emph.end type="italics"/>
                <lb/>
              quod demonſtrare oportebat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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