Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
101 43
102
103
104
105
106
107
108
109
110
< >
page |< < (8) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div208" type="section" level="1" n="69">
          <p>
            <s xml:id="echoid-s3250" xml:space="preserve">
              <pb o="8" file="0127" n="127" rhead="DE CENTRO GRAVIT. SOLID."/>
            æquidiſtant autem c g o, m n p. </s>
            <s xml:id="echoid-s3251" xml:space="preserve">ergo parallelogrãma ſunt
              <lb/>
            o n, g m, & </s>
            <s xml:id="echoid-s3252" xml:space="preserve">linea m n æqualis c g; </s>
            <s xml:id="echoid-s3253" xml:space="preserve">& </s>
            <s xml:id="echoid-s3254" xml:space="preserve">n p ipſi g o. </s>
            <s xml:id="echoid-s3255" xml:space="preserve">aptatis igi-
              <lb/>
            tur
              <emph style="sc">K</emph>
            l m, a b c triãgulis, quæ æqualia & </s>
            <s xml:id="echoid-s3256" xml:space="preserve">ſimilia sũt; </s>
            <s xml:id="echoid-s3257" xml:space="preserve">linea m p
              <lb/>
            in c o, & </s>
            <s xml:id="echoid-s3258" xml:space="preserve">punctum n in g cadet. </s>
            <s xml:id="echoid-s3259" xml:space="preserve">Quòd cũ g ſit centrum gra-
              <lb/>
            uitatis trianguli a b c, & </s>
            <s xml:id="echoid-s3260" xml:space="preserve">n trianguli
              <emph style="sc">K</emph>
            l m grauitatis cen-
              <lb/>
            trum erit id, quod demonſtrandum relinquebatur. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Simili
              <lb/>
            ratione idem contingere demonſtrabimus in aliis priſma-
              <lb/>
            tibus, ſiue quadrilatera, ſiue plurilatera habeant plana,
              <lb/>
            quæ opponuntur.</s>
            <s xml:id="echoid-s3262" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div211" type="section" level="1" n="70">
          <head xml:id="echoid-head77" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s3263" xml:space="preserve">Exiam demonſtratis perſpicue apparet, cuius
              <lb/>
            Iibet priſmatis axem, parallelogrammorum lat eri
              <lb/>
            bus, quæ ab oppoſitis planis ducũtur æquidiſtare.</s>
            <s xml:id="echoid-s3264" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div212" type="section" level="1" n="71">
          <head xml:id="echoid-head78" xml:space="preserve">THEOREMA VI. PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s3265" xml:space="preserve">Cuiuslibet priſmatis centrum grauitatis eſt in
              <lb/>
            plano, quod oppoſitis planis æquidiſtans, reli-
              <lb/>
            quorum planorum latera bifariam diuidit.</s>
            <s xml:id="echoid-s3266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3267" xml:space="preserve">Sit priſma, in quo plana, quæ opponuntur ſint trian-
              <lb/>
            gula a c e, b d f: </s>
            <s xml:id="echoid-s3268" xml:space="preserve">& </s>
            <s xml:id="echoid-s3269" xml:space="preserve">parallelogrammorum latera a b, c d,
              <lb/>
            e f bifariam diuidãtur in punctis g h _K_: </s>
            <s xml:id="echoid-s3270" xml:space="preserve">per diuiſiones au-
              <lb/>
            tem planum ducatur; </s>
            <s xml:id="echoid-s3271" xml:space="preserve">cuius ſectio figura g h _K_. </s>
            <s xml:id="echoid-s3272" xml:space="preserve">eritlinea
              <lb/>
              <note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">33. primi</note>
            g h æquidiſtans lineis a c, b d & </s>
            <s xml:id="echoid-s3273" xml:space="preserve">h k ipſis c e, d f. </s>
            <s xml:id="echoid-s3274" xml:space="preserve">quare ex
              <lb/>
            decimaquinta undecimi elementorum, planum illud pla
              <lb/>
            nis a c e, b d f æquidiſtabit, & </s>
            <s xml:id="echoid-s3275" xml:space="preserve">ſaciet ſectionem figu-
              <lb/>
              <note position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">5. huius</note>
            ram ipſis æqualem, & </s>
            <s xml:id="echoid-s3276" xml:space="preserve">ſimilem, ut proxime demonſtra-
              <lb/>
            uimus. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">Dico centrum grauitatis priſmatis eſſe in plano
              <lb/>
            g h
              <emph style="sc">K</emph>
            . </s>
            <s xml:id="echoid-s3278" xml:space="preserve">Si enim fieri poteſt, ſit eius centrum l: </s>
            <s xml:id="echoid-s3279" xml:space="preserve">& </s>
            <s xml:id="echoid-s3280" xml:space="preserve">ducatur
              <lb/>
            l m uſque ad planum g h
              <emph style="sc">K</emph>
            , quæ ipſi a b æquidiſtet.</s>
            <s xml:id="echoid-s3281" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum