Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
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          <pb o="32" file="0175" n="175" rhead="DE CENTRO GRAVIT. SOLID."/>
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            <s xml:id="echoid-s4367" xml:space="preserve">SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
              <lb/>
            cuius maior baſis a b, minor c d. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">& </s>
            <s xml:id="echoid-s4369" xml:space="preserve">ſecetur altero plano
              <lb/>
            baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
              <lb/>
            baſes a b, c d. </s>
            <s xml:id="echoid-s4370" xml:space="preserve">conſtituatur autẽ pyramis, uel conus, uel co-
              <lb/>
            ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
              <lb/>
            ſti, & </s>
            <s xml:id="echoid-s4371" xml:space="preserve">altitudo æqualis. </s>
            <s xml:id="echoid-s4372" xml:space="preserve">Di-
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              <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a" number="129">
                <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-01"/>
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            co fruſtum a d ad pyrami-
              <lb/>
            dem, uel conum, uel coni
              <lb/>
            portionem a g b eandem
              <lb/>
            proportionẽ habere, quã
              <lb/>
            utræque baſes, a b, c d unà
              <lb/>
            cum e f ad baſim a b. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">eſt
              <lb/>
            enim fruſtum a d æquale
              <lb/>
            pyramidi, uel cono, uel co-
              <lb/>
            ni portioni, cuius baſis ex
              <lb/>
            tribus baſibus a b, e f, c d
              <lb/>
            conſtat; </s>
            <s xml:id="echoid-s4374" xml:space="preserve">& </s>
            <s xml:id="echoid-s4375" xml:space="preserve">altitudo ipſius
              <lb/>
            altitudini eſt æqualis: </s>
            <s xml:id="echoid-s4376" xml:space="preserve">quod mox oſtendemus. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Sed pyrami
              <lb/>
            des, coni, uel coni portiões,
              <lb/>
              <figure xlink:label="fig-0175-02" xlink:href="fig-0175-02a" number="130">
                <image file="0175-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-02"/>
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            quæ ſunt æquali altitudine,
              <lb/>
            eãdem inter ſe, quam baſes,
              <lb/>
            proportionem habent, ſicu-
              <lb/>
            ti demonſtratum eſt, partim
              <lb/>
            ab Euclide in duodecimo li-
              <lb/>
              <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">6. 11. duo
                <lb/>
              decimi</note>
            bro elementorum, partim à
              <lb/>
            nobis in cõmentariis in un-
              <lb/>
            decimam propoſitionẽ Ar-
              <lb/>
            chimedis de conoidibus, & </s>
            <s xml:id="echoid-s4378" xml:space="preserve">
              <lb/>
            ſphæroidibus. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">quare pyra-
              <lb/>
            mis, uel conus, uel coni por-
              <lb/>
            tio, cuius baſis eſt tribus illis
              <lb/>
            baſibus æqualis ad a g b eam
              <lb/>
            habet proportionem, quam
              <lb/>
            baſes a b, e f, c d ad ab bafim. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">Fruſtum igitur a d ad a g </s>
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