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

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            <p type="main">
              <s>
                <pb xlink:href="018/01/076.jpg" pagenum="68"/>
              480, aſſumatur BC 1 ℞: tum fiat vt particu­
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              læ OA ad particulas AS, ita ped. 1 ℞ + 480
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              ad aliud, & proueniet quartus terminus CD
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              æqualis ipſi CB 1 ℞: atque adeò factâ Anti­
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              theſi, & inſtitutâ diuiſione habetur quanti­
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              tas ipſius CD. </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="note33"/>
                <emph type="italics"/>
              XXXIII
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              Idem aliter
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              ſine Trigo­
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              nometria.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Quid? </s>
              <s>quod ſinè Algebrâ res tam facilis
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                <arrow.to.target n="note34"/>
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              eſt, vt penè non audeam dicere, ne vulgata
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              vilecat. </s>
              <s>Fiat vt OI, differentia inter OA &
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              AS, ad ipſam AS, ita nota altitudo AB ad
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              aliud, & proueniet CD quæſita terræ ſemi­
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              diameter. </s>
              <s>Eſt nimirum AB differentia inter
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              AC & CD, & vt tota AC ad totam AO, ita
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              ablata CB ad ablatam AI; igitur & reliqua
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              AB ad reliquam IO vt tota AC ad totam
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              AO: ergo permutando, & diuidendo, vt
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              AB ad BC, hoc eſt CD, ita OI ad IA, hoc
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              eſt AS. </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="note34"/>
                <emph type="italics"/>
              XXXIV
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              Idem ſine
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              Trigonome­
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              tria & ſine
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              Algebra.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Et hæc quidem dicta ſint, ſi fortè angu­
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                <arrow.to.target n="note35"/>
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              lum CAD præcognoſcere non libeat. </s>
              <s>Cæ­
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              terùm illo cognito rem aggredi licet ſine
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              Algebrâ ope ſoliûs Trigonometriæ, quæ
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              multiplicem ſubminiſtrare poterit metho­
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              dum. </s>
              <s>Et primò datâ altitudine AB, & an­
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              gulo ad A obſeruato ex. </s>
              <s>gr.gr.89.m.36.ſec.
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              33., notus eſt angulus ad centrum C gr.o.
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              m. 23. ſec. 27, ac proinde eius ſubtenſa iņ
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              partibus Radij innoteſcit. </s>
              <s>Igitur ductâ BD, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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