Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4528" xml:space="preserve">
              <pb file="0182" n="182" rhead="FED. COMMANDINI"/>
            nis, quouſque in unum punctum r conueniant; </s>
            <s xml:id="echoid-s4529" xml:space="preserve">erit pyra-
              <lb/>
            midis a b c r, & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">pyramidis d e f r grauitatis centrum in li-
              <lb/>
            nea r h. </s>
            <s xml:id="echoid-s4531" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4532" xml:space="preserve">reliquæ magnitudinis, uidelicet fruſti cen-
              <lb/>
            trum in eadem linea neceſſario comperietur. </s>
            <s xml:id="echoid-s4533" xml:space="preserve">Iungantur
              <lb/>
            d b, d c, d h, d m: </s>
            <s xml:id="echoid-s4534" xml:space="preserve">& </s>
            <s xml:id="echoid-s4535" xml:space="preserve">per lineas d b, d c ducto altero plano
              <lb/>
            intelligatur fruſtum in duas pyramides diuiſum: </s>
            <s xml:id="echoid-s4536" xml:space="preserve">in pyra-
              <lb/>
            midem quidem, cuius baſis eſt triangulum a b c, uertex d:
              <lb/>
            </s>
            <s xml:id="echoid-s4537" xml:space="preserve">& </s>
            <s xml:id="echoid-s4538" xml:space="preserve">in eam, cuius idem uertex, & </s>
            <s xml:id="echoid-s4539" xml:space="preserve">baſis trapezium b c f e. </s>
            <s xml:id="echoid-s4540" xml:space="preserve">erit
              <lb/>
            igitur pyramidis a b c d axis d h, & </s>
            <s xml:id="echoid-s4541" xml:space="preserve">pyramidis b c f e d axis
              <lb/>
            d m: </s>
            <s xml:id="echoid-s4542" xml:space="preserve">atque erunt tres axes g h, d h, d m in eodem plano
              <lb/>
            d a K l. </s>
            <s xml:id="echoid-s4543" xml:space="preserve">ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
              <lb/>
            quæ lineam d h in u ſecet: </s>
            <s xml:id="echoid-s4544" xml:space="preserve">per p uero ducatur x y æquidi-
              <lb/>
            ſtans eidem, ſecansque d m in
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="135">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0182-01"/>
              </figure>
            z: </s>
            <s xml:id="echoid-s4545" xml:space="preserve">& </s>
            <s xml:id="echoid-s4546" xml:space="preserve">iungatur z u, quæ ſecet
              <lb/>
            g h in φ. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">tranſibit ea per q: </s>
            <s xml:id="echoid-s4548" xml:space="preserve">& </s>
            <s xml:id="echoid-s4549" xml:space="preserve">
              <lb/>
            erunt φ q unum, atque idem
              <lb/>
            pun ctum; </s>
            <s xml:id="echoid-s4550" xml:space="preserve">ut inferius appare-
              <lb/>
            bit. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">Quoniam igitur linea u o
              <lb/>
            æ quidiſtat ipſi d g, erit d u ad
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">2. ſexti.</note>
            u h, ut g o ad o h. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">Sed g o tri-
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            pla eſt o h. </s>
            <s xml:id="echoid-s4553" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">d u ipſius
              <lb/>
            u h eſt tripla: </s>
            <s xml:id="echoid-s4555" xml:space="preserve">& </s>
            <s xml:id="echoid-s4556" xml:space="preserve">ideo pyrami-
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            dis a b c d centrum grauitatis
              <lb/>
            erit punctum 11. </s>
            <s xml:id="echoid-s4557" xml:space="preserve">Rurſus quo-
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            niam z y ipſi d l æquidiſtat, d z
              <lb/>
            a d z m eſt, utly ad y m: </s>
            <s xml:id="echoid-s4558" xml:space="preserve">eſtque
              <lb/>
            ly ad y m, ut g p ad p n. </s>
            <s xml:id="echoid-s4559" xml:space="preserve">ergo
              <lb/>
            d z ad z m eſt, ut g p ad p n.
              <lb/>
            </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Quòd cum g p ſit tripla p n; </s>
            <s xml:id="echoid-s4561" xml:space="preserve">
              <lb/>
            erit etiam d z ipſius z m tri-
              <lb/>
            pla. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">atque ob eandem cauſ-
              <lb/>
            ſam punctum z eſt centrũ gra-
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            uitatis pyramidis b c f e d. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">iun
              <lb/>
            ctaigitur z u, in ea erit </s>
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