Casati, Paolo, Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

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              <s>
                <pb xlink:href="018/01/230.jpg" pagenum="216"/>
              tam. </s>
              <s>Sic autem inueſtigo ſuperficiem VY,
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              quæ ſit media proportionalis inter differen­
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              tias illius & ſuperficiei vaſorum, hoc eſt in­
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              ter OM & CD. </s>
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            <p type="margin">
              <s>
                <margin.target id="note100"/>
                <emph type="italics"/>
              C
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              Ex datis
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              duabus ſu­
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              perficiebus
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              auferre ean­
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              dem ſuperfi­
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              ciem, quæ re
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              linquat re­
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              sidua in Ra­
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              tione dupli­
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              cata data­
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              rum.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Ratio ſuperficierum vaſorum ſit data 8
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              ad 4; Ratio duplicata eſt 8. ad 2. Pono ſu­
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              perficiem ſolidi VY Algebricè 1℞. </s>
              <s>Quare ſu­
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              perficies aquæ OM eſt 8——1℞, & ſuperfi­
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              cies CD eſt 4——1℞: quæ ſunt inter ſe in du­
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              plicatâ Ratione ſuperficiei vaſorum: igitur
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              8——1℞ ad 4——1℞. </s>
              <s>eſt vt 8 ad 2 ergo per
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              19. 7. 16——2℞ æquatur 32——8℞. </s>
              <s>Et fa­
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              ctâ Antitheſi æquatio demum eſt inter 16 &
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              6℞. </s>
              <s>In ſtitutâ it aque diuiſione 1℞ eſt 2 2/3 ſuper­
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              ficies VY; quæ ablata ex 8 ſuperficie vaſis
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              maioris relinquit ſuperficiem OM 5 1/3, &
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              ablata ex ſuperficie vaſis minoris, hoc eſt ex
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              4, relinquit ſuperficiem CD 1 1/3: eſt autem
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              2 2/3 medio loco proportionalis inter 5 1/3 & 1 1/3,
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              quæ præterea ſuperficies 5 1/3, & 1/3 ſunt in Ra­
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              tione duplicatâ Rationis 8 ad 4, hoc eſt in
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              Ratione 8 ad 2. Iam verò ſi baſes aquarum
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              OM ad CD ſint vt 8 ad 2, altitudines ve­
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              rò KN & GA reciprocè vt ſuperficies va­
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              ſorum, hoc eſt KN 4, & GA 8, erit aquą
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              OMRS 32, & aqua CDFE 16, planè iņ
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              Ratione, quam habent ſuperficies vaſorum,
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              in quibus ipſæ aquæ exiſtunt. </s>
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          </chap>
        </body>
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