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-div96" type="section" level="1" n="69">
          <p>
            <s xml:id="echoid-s2685" xml:space="preserve">
              <pb o="28" file="0144" n="149" rhead="GEOMETRIA SVBTERRANEA."/>
            altera decimales digiti minutias, quas ſcrupulos uocaui-
              <lb/>
            mus, denotat. </s>
            <s xml:id="echoid-s2686" xml:space="preserve">Quando tres numeri in area habentur,
              <lb/>
            primus ſiniſter octauas partes ulnae, ſequens et medius di-
              <lb/>
            gitos, tertius ſcrupulos digiti refert. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Quarta denique et
              <lb/>
            quinta nota ſiniſtra, integras ulnas indicat.</s>
            <s xml:id="echoid-s2688" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2689" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2690" xml:space="preserve">Quando uero hypotenuſa data non accurate
              <lb/>
            in numeris frontis reperitur, tum, pro proxime minore
              <lb/>
            numero et angulo, quaeritur cathetus uel baſis, et pro re-
              <lb/>
            ſidua parte uel appendice, ſeruato eodem angulo, inueſti-
              <lb/>
            gatur particula catheto uel baſi addenda. </s>
            <s xml:id="echoid-s2691" xml:space="preserve">cum enim idem
              <lb/>
            angulus ad baſin C retinetur, oriuntur duo triangula fh C,
              <lb/>
              <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">Figur. 12.</note>
            et ABC ſimilia, utpote aequiangula, in quibus latera
              <lb/>
            aequalibus angulis oppoſita ſunt proportionalia, (§. </s>
            <s xml:id="echoid-s2692" xml:space="preserve">68.
              <lb/>
            </s>
            <s xml:id="echoid-s2693" xml:space="preserve">Geom.) </s>
            <s xml:id="echoid-s2694" xml:space="preserve">unde analogia, ualet Cf: </s>
            <s xml:id="echoid-s2695" xml:space="preserve">fH = AC: </s>
            <s xml:id="echoid-s2696" xml:space="preserve">AB, uel
              <lb/>
            Cf † AC: </s>
            <s xml:id="echoid-s2697" xml:space="preserve">fH † AB = Cf: </s>
            <s xml:id="echoid-s2698" xml:space="preserve">fh = AC: </s>
            <s xml:id="echoid-s2699" xml:space="preserve">AB. </s>
            <s xml:id="echoid-s2700" xml:space="preserve">
              <lb/>
            (§. </s>
            <s xml:id="echoid-s2701" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">Analyſ. </s>
            <s xml:id="echoid-s2703" xml:space="preserve">ſinitor et §. </s>
            <s xml:id="echoid-s2704" xml:space="preserve">56. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Arithm.) </s>
            <s xml:id="echoid-s2706" xml:space="preserve">nam a: </s>
            <s xml:id="echoid-s2707" xml:space="preserve">ea = b: </s>
            <s xml:id="echoid-s2708" xml:space="preserve">
              <lb/>
            eb et a † b: </s>
            <s xml:id="echoid-s2709" xml:space="preserve">ea † eb = a: </s>
            <s xml:id="echoid-s2710" xml:space="preserve">ea = b: </s>
            <s xml:id="echoid-s2711" xml:space="preserve">eb.</s>
            <s xml:id="echoid-s2712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2713" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2714" xml:space="preserve">Si etiam hypotenuſa praeter ulnas, et octauas
              <lb/>
            eius partes, digitos aliquos complectitur, ope regulae au-
              <lb/>
            reae iisdem perpendiculi uel baſeos particulae aptantur,
              <lb/>
            dum pars octaua angulo dato reſpondens in digitos decem
              <lb/>
            reſoluta ponitur.</s>
            <s xml:id="echoid-s2715" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div98" type="section" level="1" n="70">
          <head xml:id="echoid-head87" xml:space="preserve">EXEMPLVM I.</head>
          <p>
            <s xml:id="echoid-s2716" xml:space="preserve">Quaeritur perpendiculum pro angulo 12 {1/2} gr. </s>
            <s xml:id="echoid-s2717" xml:space="preserve">et hypote-
              <lb/>
            nuſa 6 Uln. </s>
            <s xml:id="echoid-s2718" xml:space="preserve">prior numerus in ſiniſtra columna, alter in fronte
              <lb/>
            deprehenditur, et in communi area eſt cathetus 1238 h. </s>
            <s xml:id="echoid-s2719" xml:space="preserve">e.
              <lb/>
            </s>
            <s xml:id="echoid-s2720" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">Uln. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">2 octau. </s>
            <s xml:id="echoid-s2723" xml:space="preserve">3 {8/10} dig.</s>
            <s xml:id="echoid-s2724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2725" xml:space="preserve">iterum qu. </s>
            <s xml:id="echoid-s2726" xml:space="preserve">baſis pro angulo 17. </s>
            <s xml:id="echoid-s2727" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">et hypotenuſa 5 Uln.
              <lb/>
            </s>
            <s xml:id="echoid-s2729" xml:space="preserve">prior numerus in columna dextra, alter in fronte </s>
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