Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/158.jpg" pagenum="71"/>
              culus AC: centrum autem F propinquius eſſe puncto B,
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              quàm centrum S, conſtat ex præcedenti: quare centrum
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              G, totius cylindri LM inter puncta F, S cadet. </s>
              <s>Dico
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              GF ad FS eſſe vt exceſſus, quo recta DE ſuperat tertiam
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              partem minoris extremæ maiori poſita ipſa DE in propor
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              tione continua ipſius DH ad DE vnà cum ſubſeſquial­
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              tera ipſius BD, ad axim BE, ita GF ad FS. </s>
              <s>Quoniam
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              enim portio ABC ad cylindrum LM eſt vt prædictus ex­
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              ceſſus vnà cum ſubſeſquialtera ipſius BD ad axim BE:
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              & vt portio ABC ad LM cylindrum, ita eſt GF ad FS,
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              ob centra grauitatis F, G; erit vt prædictus exceſſus vna
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              cum ſubſeſquialtera ipſius BD ad axim BE, ita GF ad
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              FS. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXIX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis portionis ſphæræ abſciſſæ duobus pla­
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              nis parallelis centrum intercipientibus, & à cen­
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              tro æqualiter diſtantibus, centrum grauitatis eſt
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              in medio axis, vel idem, quod centrum ſphæræ. </s>
            </p>
            <p type="main">
              <s>Sit portio ABCD, ſphæræ, cuius centrum G, abſciſsa
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              duobus planis parallelis
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              centrum G intercipien­
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              tibus, & æquè ab eo di­
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              ſtantibus: ſectiones
                <expan abbr="erũt">erunt</expan>
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              circuli minores, quorum
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              diametri ſint AD, BC
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              centra autem F,E, qui­
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              bus axis portionis termi
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              nabitur, eritque ad pla­
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              na vtriuſque circuli per
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                <figure id="id.043.01.158.1.jpg" xlink:href="043/01/158/1.jpg" number="119"/>
                <lb/>
              pendicularis tranſiens per centrum G: & quia illa plana </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>