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-div135" type="section" level="1" n="99">
          <p>
            <s xml:id="echoid-s3185" xml:space="preserve">
              <pb o="67" file="0183" n="188" rhead="GEOMETRIA SVBTERRANEA."/>
            cularis deſcenſus, ab eodem initio uerſus eundem puteum,
              <lb/>
            eſt 4. </s>
            <s xml:id="echoid-s3186" xml:space="preserve">Uln. </s>
            <s xml:id="echoid-s3187" xml:space="preserve">ſumma 1 2 {3/4} dabit totam profunditatem a puteo
              <lb/>
            ad imi loci lineam horizontalem. </s>
            <s xml:id="echoid-s3188" xml:space="preserve">quando autem aſcendit
              <lb/>
            mons, et aſcendit quoque ſpecus usque ad aliquem ter-
              <lb/>
            minum, differentia perpendiculorum, dabit altitudinem
              <lb/>
            optatam.</s>
            <s xml:id="echoid-s3189" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div136" type="section" level="1" n="100">
          <head xml:id="echoid-head119" xml:space="preserve">SCHOLION.</head>
          <p style="it">
            <s xml:id="echoid-s3190" xml:space="preserve">74. </s>
            <s xml:id="echoid-s3191" xml:space="preserve">Voigtelius p. </s>
            <s xml:id="echoid-s3192" xml:space="preserve">98. </s>
            <s xml:id="echoid-s3193" xml:space="preserve">uhi de computandis baſibus et perpendiculis,
              <lb/>
            quac bypotenuſis et angulis datis competunt, egit, etiam regu-
              <lb/>
            lam commendat, pro examine calculi inſtituti, talem: </s>
            <s xml:id="echoid-s3194" xml:space="preserve">ſumatur ſigil-
              <lb/>
            latim ſumma baſium, perpendiculorum et bypotenuſarum, ex ſum-
              <lb/>
            mis prioribus fiant quadrata, eademque addantur, et ex aggregato
              <lb/>
            radix quaeratur, ſi haec aequalis eſt ſummae bypotenuſarum, putat
              <lb/>
            recte ſe habere factae menſionis reſolutionem, et ſundamentum huius
              <lb/>
            praecepti in theoremate pythagorico quaerit. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">Enimuero pytbagorae
              <lb/>
            inuentum, quod ad unum tantum triangulum rectangulum pertinet,
              <lb/>
            ad plura et diſſimilia irrito labore trabi, ſequens analytica demon-
              <lb/>
              <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">Figur. 21.
                <lb/>
              Tab. 3.</note>
            ſtratic euincet. </s>
            <s xml:id="echoid-s3196" xml:space="preserve">Sint triangulorum perpendicula a et c, baſes b et d,
              <lb/>
            bypotenuſae x et y, erit</s>
          </p>
          <p>
            <s xml:id="echoid-s3197" xml:space="preserve">ן a + c = a
              <emph style="super">2</emph>
            + 2 a c + c
              <emph style="super">2</emph>
            , et</s>
          </p>
          <p>
            <s xml:id="echoid-s3198" xml:space="preserve">ן b + d = b
              <emph style="super">2</emph>
            + 2 b d + d
              <emph style="super">2</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s3199" xml:space="preserve">ן x + y = x
              <emph style="super">2</emph>
            + 2 x y + yy (§. </s>
            <s xml:id="echoid-s3200" xml:space="preserve">34. </s>
            <s xml:id="echoid-s3201" xml:space="preserve">Analyſ. </s>
            <s xml:id="echoid-s3202" xml:space="preserve">finit.)</s>
            <s xml:id="echoid-s3203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3204" xml:space="preserve">et per theor. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">pyth.</s>
            <s xml:id="echoid-s3206" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3207" xml:space="preserve">a
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            = x
              <emph style="super">2</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s3208" xml:space="preserve">et c
              <emph style="super">2</emph>
            + d
              <emph style="super">2</emph>
            = y y</s>
          </p>
          <p>
            <s xml:id="echoid-s3209" xml:space="preserve">extractaque radice</s>
          </p>
          <p>
            <s xml:id="echoid-s3210" xml:space="preserve">V a
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            = x</s>
          </p>
          <p>
            <s xml:id="echoid-s3211" xml:space="preserve">V c
              <emph style="super">2</emph>
            + d
              <emph style="super">2</emph>
            = y</s>
          </p>
          <p>
            <s xml:id="echoid-s3212" xml:space="preserve">et ſecundum bypotheſin praecepti voigteliani foret</s>
          </p>
          <p>
            <s xml:id="echoid-s3213" xml:space="preserve">a
              <emph style="super">2</emph>
            + 2 a c + c
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            + 2 b d + d
              <emph style="super">2</emph>
            = x
              <emph style="super">2</emph>
            + 2xy + yy</s>
          </p>
          <p>
            <s xml:id="echoid-s3214" xml:space="preserve">ſubſtituto ualore x x et y y</s>
          </p>
          <p>
            <s xml:id="echoid-s3215" xml:space="preserve">a
              <emph style="super">2</emph>
            + 2 a c + c
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            + 2bd + d
              <emph style="super">2</emph>
            = a
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            + 2xy + c
              <emph style="super">2</emph>
            + d
              <emph style="super">2</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s3216" xml:space="preserve">et aequalibus ablatis,</s>
          </p>
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