Valerio, Luca, De centro gravitatis solidorvm libri tres

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/019.jpg" pagenum="11"/>
              æqualis angulo DHL, & vt KG, ad GA, ita LH, ad
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              HD: ſed vt GA, ad AC, ita eſt HD ad DF: & vt
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              AC ad AB, ita DF ad DE, ex æquali igitur erit vt
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              KG ad AB, ita LH ad DE: ſed vt AB ad BG, ita
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              eſt DE ad EH, propter ſimilitudinem triangulorum
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              ABG, DEH: & vt BG ad GO ita eſt EH ad HP,
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              propter triangulorum centra O, P; ex æquali igitur erit
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              vt KG ad GO, ita LH ad HP: & permutando vt
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              OG ad PH, ideſt vt BG ad EH, ideſt vt AB ad ED,
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              ita KG ad LH, & reliqua OK ad reliquam PL. </s>
            </p>
            <p type="main">
              <s>Sed ſint puncta ſimiliter poſita M, N, quæ cadant ex­
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              tra lineas BG, EH, iunctæque OM, PN. </s>
              <s>Dico iti­
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              dem eſse vt AB ad ED, ita OM ad PN. </s>
              <s>Iungantur
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              enim rectæ MB, NE, quæ cum quibus lateribus homo­
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              logis angulos æquales faciunt, ea ſint AB, DE, quod
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              propter iſoſcelia triangula ſit dictum in ſimiliter poſitis
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              triangulis. </s>
              <s>igitur etiam angulus BAM, æqualis erit an­
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              gulo EDN; ſimilia igitur triangula ABM, DEN: &
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              vt MB ad BA, ita erit NE ad ED: ſed vt AB ad
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              BG, ita eſt DE ad EH, propter ſimilitudinem trian­
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              gulorum, & vt BG ad BO, ita eſt EH ad EP, ob
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              triangulorum ſimilium centra O, P: ex æquali igitur
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              erit vt MB, ad BO, ita NE ad EP. </s>
              <s>Rurſus quo­
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              niam angulus ABM, æqualis eſt angulo DEN, quorum
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              angulus ABG, æqualis eſt angulo DEH: erit reliquus
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              angulus OBM, æqualis reliquo angulo PEN: ſed vt MB
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              ad BO, ita erat NE ad EP; triangulum igitur OBM
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              triangulo PEN, ſimile erit, & vt BO ad EP, hoc eſt
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              BG ad EH, hoc eſt AB ad DE, ita OM ad PN.
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              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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