Archimedes, Archimedis De insidentibvs aqvae

Table of contents

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[21.] TERTIVS.
Page: 23 (4)
[22.] QVARTVS.
Page: 24
[23.] QVINTVS.
Page: 25 (5)
[24.] SEXTVS.
Page: 27 (6)
[25.] SEPTIMVS.
Page: 29 (7)
[26.] OCTAVVS.
Page: 30
[27.] NONVS.
Page: 33 (9)
[28.] DECIMVS.
Page: 36
[29.] Archimedis de inſidentibus in bumido li-ber ſecundus explicit, ad laudem Dei.
Page: 47 (16)
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              <pb o="7" file="0029" n="29" rhead="LIBER II."/>
            quidem inter humidum aſſumpta ex ſolido apol ſurſum ferretur ſecun-
              <lb/>
            dum eam quæ per t, perpendicularem. </s>
            <s xml:id="echoid-s409" xml:space="preserve">Quæ autem extra humidum de-
              <lb/>
            orſum ferret in humidum ſecundum eam, quæ per g, perpendicularem.
              <lb/>
            </s>
            <s xml:id="echoid-s410" xml:space="preserve">Reuoluetur ergo ſolidum apol. </s>
            <s xml:id="echoid-s411" xml:space="preserve">& </s>
            <s xml:id="echoid-s412" xml:space="preserve">baſis ipſius non tanget ſuperficiem
              <lb/>
            bumidi ſecundum vnum ſignum. </s>
            <s xml:id="echoid-s413" xml:space="preserve">Si autem quæ p, i, non ſecuerit lineam
              <lb/>
            K, ***, ſicut in ſolida ſigura deſcriptum eſt. </s>
            <s xml:id="echoid-s414" xml:space="preserve">Manifestum quod ſignum t,
              <lb/>
            quod eſt centrum grauitatis demerſę portionis cadet inter p, & </s>
            <s xml:id="echoid-s415" xml:space="preserve">i, & </s>
            <s xml:id="echoid-s416" xml:space="preserve">re-
              <lb/>
            liqua ſimiliter demonſtrabuntur.</s>
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          <head xml:id="echoid-head35" xml:space="preserve">SEPTIMVS.</head>
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            <s xml:id="echoid-s418" xml:space="preserve">Recta portio rectanguli conoy dalis quando humido le-
              <lb/>
            uior fuerit, & </s>
            <s xml:id="echoid-s419" xml:space="preserve">axem habuerit maiorem quidem quàm æmyo
              <lb/>
            lium eiusq́ uſque ad axem minorem, aut ut proportionem
              <lb/>
            habeat ad eam, quæ uſque ad axem quàm quindecim ad quat
              <lb/>
            tuor dimiſſa in humidum, ita ut baſis ipſius tota ſit in humi-
              <lb/>
            do, nunquam ſtabit ita ut baſis ipſius tangat ſuperficiem hu-
              <lb/>
            midi, ſed ut tota ſit in humido, necſecundum vnum ſignum
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            tangens ſuperficiem.</s>
            <s xml:id="echoid-s420" xml:space="preserve"/>
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            <s xml:id="echoid-s421" xml:space="preserve">_S_It portio qualis dicta eſt, & </s>
            <s xml:id="echoid-s422" xml:space="preserve">_dimißa in humidum, ſicut dictum eſt cõ
              <lb/>
            ſiſt at ita ut baſis ipſius tangat ſuperficiem humidi, demonstrandum
              <lb/>
            quòd non manet, ſed reuoluetur ita, ut baſis ipſius tangat ſuperficiẽ
              <lb/>
            humidi non ſecundum vnum ſignum : </s>
            <s xml:id="echoid-s423" xml:space="preserve">ſecta enim ipſa plano, recta ad ſu
              <lb/>
            perficiem humidi : </s>
            <s xml:id="echoid-s424" xml:space="preserve">Sectio ſit quæ apol rectanguli coni ſectio. </s>
            <s xml:id="echoid-s425" xml:space="preserve">Sit autem
              <lb/>
            & </s>
            <s xml:id="echoid-s426" xml:space="preserve">ſuperficiei humida ſectio quæ s, a, axis autem portionis, & </s>
            <s xml:id="echoid-s427" xml:space="preserve">dyameter
              <lb/>
            quę p, f, ſit i. </s>
            <s xml:id="echoid-s428" xml:space="preserve">Rurſum autem ſecetur quæ p, f, ſecundum r, quidem ita
              <lb/>
            ut quæ r, p, ſit dupla ipſius r, f, ſecundum ***. </s>
            <s xml:id="echoid-s429" xml:space="preserve">autem ita ut quæ p, ***, ad
              <lb/>
            r, ***, proportionem habeat quam quindecim ad quattuor. </s>
            <s xml:id="echoid-s430" xml:space="preserve">& </s>
            <s xml:id="echoid-s431" xml:space="preserve">quæ ***.
              <lb/>
            </s>
            <s xml:id="echoid-s432" xml:space="preserve">
              <figure xlink:label="fig-0029-01" xlink:href="fig-0029-01a" number="24">
                <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-01"/>
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