Weidler, Johann Friedrich, Jo. Friderici Weidleri Tractatus de machinis hydraulicis toto terrarum orbe maximis Marlyensi et Londinensi et aliis rarioribus similibus in quo mensurae prope ipsas machinas notatae describuntur, et de viribus earum luculenter disseritur

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        <div xml:id="echoid-div87" type="section" level="1" n="63">
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              <pb o="24" file="0140" n="145" rhead="GEOMETRIA SVBTERRANEA."/>
            tempore coeperit, quo diſeiplinae liberales, inprimis mathematicae,
              <lb/>
            in Europa fere ubiuis neſciebantur, conſequenseſt, artem fodi-
              <lb/>
            nas accuratius metiendi, non niſi ſero admodum ad illos labores,
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            periculoſiſſimos promouendos ſecurioreſque reddendos, acceſſiſſe.</s>
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        <div xml:id="echoid-div88" type="section" level="1" n="64">
          <head xml:id="echoid-head81" xml:space="preserve">SCHOLION V.</head>
          <p style="it">
            <s xml:id="echoid-s2567" xml:space="preserve">44. </s>
            <s xml:id="echoid-s2568" xml:space="preserve">Sed ex diuerticulo in uiam redeamus. </s>
            <s xml:id="echoid-s2569" xml:space="preserve">Traditis uocabulorum
              <lb/>
            technicorum, et organorum deſcriptionibus, tempus uideba-
              <lb/>
            tur, etiam fundamenta iacere ſcientiae, geometr arum methodo com-
              <lb/>
            ponendae. </s>
            <s xml:id="echoid-s2570" xml:space="preserve">Verum cum eadem et perpauca, et ex geometria et tri-
              <lb/>
            gonometria iam perſpicue cognita, et ſuis locis in matheſeos uniuerſae
              <lb/>
            inſtitutionibus, ex quibus nonnunquam paragraphi uncis concluſi,
              <lb/>
            breuitatis ſtudio commemorantur, ſatis explicata ſint, puto eorum
              <lb/>
            repetitione me hic ſuperſedere poſſe, ſatis habens, ſi fontes illorum
              <lb/>
            principiorum quouis loco in ipſa tractatione indicentur. </s>
            <s xml:id="echoid-s2571" xml:space="preserve">Interea
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            generatim moneo, pleraque, quae in ſequentibus dicentur, ad trian-
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            gulum rectangulum, et eius latera, nec non ad dimenſionem angu-
              <lb/>
            lorum, inuentionem ſinuum eorundem, repraeſentationem linea-
              <lb/>
            rum, beneficio ſcalarum geometricarum, et ſimilia uulgaria tum
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            theoremata, tum problemata, pertinere.</s>
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        <div xml:id="echoid-div89" type="section" level="1" n="65">
          <head xml:id="echoid-head82" xml:space="preserve">THEOREMA.</head>
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            <s xml:id="echoid-s2573" xml:space="preserve">45. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">Filum in libella pondere attractum, monſtrat
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">Figur. 8.</note>
            gradus anguli acuti C, qui eſt in triangulo
              <lb/>
            rectangulo ad baſin.</s>
            <s xml:id="echoid-s2575" xml:space="preserve"/>
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            <s xml:id="echoid-s2576" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s2577" xml:space="preserve">Nam filum a i ſemper indicat
              <lb/>
            trianguli perpendiculum, (§. </s>
            <s xml:id="echoid-s2578" xml:space="preserve">34. </s>
            <s xml:id="echoid-s2579" xml:space="preserve">35. </s>
            <s xml:id="echoid-s2580" xml:space="preserve">Geometr.)
              <lb/>
            </s>
            <s xml:id="echoid-s2581" xml:space="preserve">et arcus i n metitur angulum acutum, qui eſt in tri-
              <lb/>
            anguli rectanguli uertice, ergo arcus complementi,
              <lb/>
            ſiue reſiduus in quadrante e i, angulum comple-
              <lb/>
            menti ad baſin C metitur, (§. </s>
            <s xml:id="echoid-s2582" xml:space="preserve">64. </s>
            <s xml:id="echoid-s2583" xml:space="preserve">Geom.) </s>
            <s xml:id="echoid-s2584" xml:space="preserve"/>
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