Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000916">
                <pb pagenum="44" xlink:href="023/01/095.jpg"/>
              relinquetur pe ipſi n
                <foreign lang="grc">χ</foreign>
              æqualis. </s>
              <s id="s.000917">cum autem be ſit dupla
                <lb/>
              ed, & op dupla pn, hoc eſt ipſius e
                <foreign lang="grc">χ,</foreign>
              & reliquum, uideli­
                <lb/>
                <arrow.to.target n="marg109"/>
                <lb/>
              cet bo unà cum pe ipſius reliqui
                <foreign lang="grc">χ</foreign>
              d duplum erit. </s>
              <s id="s.000918">eſtque
                <lb/>
              bo dupla
                <foreign lang="grc">ρ</foreign>
              d. </s>
              <s id="s.000919">ergo pe, hoc eſt n
                <foreign lang="grc">χ</foreign>
              ipſius
                <foreign lang="grc">χρ</foreign>
              dupla. </s>
              <s id="s.000920">ſed dn
                <lb/>
              dupla eſt n
                <foreign lang="grc">ρ.</foreign>
              reliqua igitur d
                <foreign lang="grc">χ</foreign>
              dupla reliquæ
                <foreign lang="grc">χ</foreign>
              n. </s>
              <s id="s.000921">ſunt au­
                <lb/>
              tem d
                <foreign lang="grc">χ,</foreign>
              pn inter ſe æquales:
                <expan abbr="itemq;">itemque</expan>
              æquales
                <foreign lang="grc">χ</foreign>
              n, pe. </s>
              <s id="s.000922">qua­
                <lb/>
              re conſtat np ipſius pe duplam eſſe. </s>
              <s id="s.000923">& idcirco pe ipſi en
                <lb/>
              æqualem. </s>
              <s id="s.000924">Rurſus cum ſit
                <foreign lang="grc">μν</foreign>
              dupla o
                <foreign lang="grc">ν,</foreign>
              &
                <foreign lang="grc">μ σ</foreign>
              dupla
                <foreign lang="grc">ς γ;</foreign>
              erit
                <lb/>
              etiam reliqua
                <foreign lang="grc">νσ</foreign>
              reliquæ
                <foreign lang="grc">σ</foreign>
              o dupla. </s>
              <s id="s.000925">Eadem quoque ratione
                <lb/>
                <expan abbr="cõcludetur">concludetur</expan>
                <foreign lang="grc">π υ</foreign>
              dupla
                <foreign lang="grc">υ</foreign>
              m. </s>
              <s id="s.000926">ergo ut
                <foreign lang="grc">νσ</foreign>
              ad
                <foreign lang="grc">σ</foreign>
              o, ita
                <foreign lang="grc">πυ</foreign>
              ad
                <foreign lang="grc">υ</foreign>
              m:
                <lb/>
                <expan abbr="componendoq;">componendoque</expan>
              , & permutando, ut
                <foreign lang="grc">ν</foreign>
              o ad
                <foreign lang="grc">π</foreign>
              m, ita o
                <foreign lang="grc">σ</foreign>
              ad
                <lb/>
              m
                <foreign lang="grc">υ·</foreign>
              & ſunt æquales
                <foreign lang="grc">ν</foreign>
              o,
                <foreign lang="grc">π</foreign>
              m. </s>
              <s id="s.000927">quare & o
                <foreign lang="grc">ς,</foreign>
              m
                <foreign lang="grc">υ</foreign>
              æquales. </s>
              <s id="s.000928">præ
                <lb/>
              terea
                <foreign lang="grc">σπ</foreign>
              dupla eſt
                <foreign lang="grc">πτ,</foreign>
              &
                <foreign lang="grc">νπ</foreign>
              ipſius
                <foreign lang="grc">π</foreign>
              m. </s>
              <s id="s.000929">reliqua igitur
                <foreign lang="grc">σν</foreign>
              re
                <lb/>
              liquæ m
                <foreign lang="grc">τ</foreign>
              dupla. </s>
              <s id="s.000930">atque erat
                <foreign lang="grc">νσ</foreign>
              dupla
                <foreign lang="grc">σ</foreign>
              o. </s>
              <s id="s.000931">ergo m
                <foreign lang="grc">τ, σ</foreign>
              o æ­
                <lb/>
              quales ſunt: & ita æquales m
                <foreign lang="grc">υ,</foreign>
              n
                <foreign lang="grc">φ.</foreign>
              at o
                <foreign lang="grc">ς,</foreign>
              eſt æqualis
                <lb/>
              m
                <foreign lang="grc">υ.</foreign>
              Sequitur igitur, ut omnes o
                <foreign lang="grc">ς,</foreign>
              m
                <foreign lang="grc">τ,</foreign>
              m
                <foreign lang="grc">υ,</foreign>
              n
                <foreign lang="grc">φ</foreign>
              in­
                <lb/>
              ter ſe ſint æquales. </s>
              <s id="s.000932">Sed ut
                <foreign lang="grc">ρπ</foreign>
              ad
                <foreign lang="grc">πτ,</foreign>
              hoc eſt ut 3 ad 2, ita nd
                <lb/>
              ad d
                <foreign lang="grc">χ·</foreign>
                <expan abbr="permutãdoq;">permutandoque</expan>
              ut
                <foreign lang="grc">ρπ</foreign>
              ad nd, ita
                <foreign lang="grc">πτ</foreign>
              ad d
                <foreign lang="grc">χ.</foreign>
              &
                <expan abbr="ſũt">ſunt</expan>
              æqua
                <lb/>
              les
                <foreign lang="grc">ρπ,</foreign>
              nd. </s>
              <s id="s.000933">ergo d
                <foreign lang="grc">χ,</foreign>
              hoc eſt np, &
                <foreign lang="grc">πτ</foreign>
              æquales. </s>
              <s id="s.000934">Sed etiam æ­
                <lb/>
              quales n
                <foreign lang="grc">π, π</foreign>
              m. </s>
              <s id="s.000935">reliqua igitur
                <foreign lang="grc">π</foreign>
              p reliquæ m
                <foreign lang="grc">τ,</foreign>
              hoc eſt ipſi
                <lb/>
              n
                <foreign lang="grc">φ</foreign>
              æqualis erit. </s>
              <s id="s.000936">quare dempta p
                <foreign lang="grc">π</foreign>
              ex pe, &
                <foreign lang="grc">φ</foreign>
              n dempta ex
                <lb/>
              ne, relinquitur pe æqualis e
                <foreign lang="grc">φ.</foreign>
              Itaque
                <foreign lang="grc">π, φ</foreign>
              centra
                <expan abbr="figurarũ">figurarum</expan>
                <lb/>
              ſecundo loco deſcriptarum a primis centris pn æquali in­
                <lb/>
              teruallo recedunt. </s>
              <s id="s.000937">quòd ſi rurſus aliæ figuræ deſcribantur,
                <lb/>
              eodem modo demonſtrabimus earum centra æqualiter ab
                <lb/>
              his recedere, & ad portionis conoidis centrum propius ad
                <lb/>
              moueri. </s>
              <s id="s.000938">Ex quibus conſtat lineam
                <foreign lang="grc">πφ</foreign>
              à centro grauitatis
                <lb/>
              portionis diuidi in partes æquales. </s>
              <s id="s.000939">Si enim fieri poteſt, non
                <lb/>
              ſit centrum in puncto e, quod eſt lineæ
                <foreign lang="grc">πφ</foreign>
              medium: ſed in
                <lb/>
                <foreign lang="grc">ψ·</foreign>
              & ipſi
                <foreign lang="grc">πψ</foreign>
              æqualis fiat
                <foreign lang="grc">φω.</foreign>
              Cum igitur in portione ſolida
                <lb/>
              quædam figura inſcribi posſit, ita ut linea, quæ inter cen­
                <lb/>
              trum grauitatis portionis, & inſcriptæ figuræ interiicitur,
                <lb/>
              qualibet linea propoſita ſit minor, quod proxime demon­
                <lb/>
              ſtrauimus: perueniet tandem
                <foreign lang="grc">φ</foreign>
              centrum inſcriptæ figuræ </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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