Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div540" type="section" level="1" n="194">
          <pb o="201" file="231" n="231" rhead="LIBER QVARTVS."/>
        </div>
        <div xml:id="echoid-div545" type="section" level="1" n="195">
          <head xml:id="echoid-head208" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s8921" xml:space="preserve">DATA circuli area, circumferentiam, ac diametrum cognoſcere.</s>
            <s xml:id="echoid-s8922" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8923" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 7. </s>
            <s xml:id="echoid-s8924" xml:space="preserve">ad 88. </s>
            <s xml:id="echoid-s8925" xml:space="preserve">ita data area ad aliud. </s>
            <s xml:id="echoid-s8926" xml:space="preserve">Productus enim numerus erit qua-
              <lb/>
            dratum circumferentiæ vero maius, vt ex 4. </s>
            <s xml:id="echoid-s8927" xml:space="preserve">reg. </s>
            <s xml:id="echoid-s8928" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8929" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8930" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s8931" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8932" xml:space="preserve">liquet. </s>
            <s xml:id="echoid-s8933" xml:space="preserve">Radix
              <lb/>
            ergo quadrata numeri producti dabit circumferentiam vera maiorem. </s>
            <s xml:id="echoid-s8934" xml:space="preserve">Quod ſi
              <lb/>
            fiat, vt 71. </s>
            <s xml:id="echoid-s8935" xml:space="preserve">ad 892. </s>
            <s xml:id="echoid-s8936" xml:space="preserve">ita data area ad aliud, gignetur quadratum circumferentiæ ve-
              <lb/>
            to minus, vt conſtat ex 3. </s>
            <s xml:id="echoid-s8937" xml:space="preserve">reg. </s>
            <s xml:id="echoid-s8938" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8939" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8940" xml:space="preserve">capit. </s>
            <s xml:id="echoid-s8941" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8942" xml:space="preserve">Ac proinde eius radix quadrata
              <lb/>
            circumferentiam vera minorem indicabit.</s>
            <s xml:id="echoid-s8943" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8944" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            rurſus, vt 223. </s>
            <s xml:id="echoid-s8945" xml:space="preserve">ad 284. </s>
            <s xml:id="echoid-s8946" xml:space="preserve">ita area propoſita ad aliud. </s>
            <s xml:id="echoid-s8947" xml:space="preserve">Procreatus nam-
              <lb/>
            que numerus erit quadratum diametri verò maius, vt ex 2. </s>
            <s xml:id="echoid-s8948" xml:space="preserve">reg. </s>
            <s xml:id="echoid-s8949" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8950" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8951" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s8952" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s8953" xml:space="preserve">perſpicuum eſt. </s>
            <s xml:id="echoid-s8954" xml:space="preserve">Radix ergo quadrata numeri producti diametrum exhibebit
              <lb/>
            vera maiorem. </s>
            <s xml:id="echoid-s8955" xml:space="preserve">Quod ſi fiat, vt 11. </s>
            <s xml:id="echoid-s8956" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s8957" xml:space="preserve">ita area data ad aliud, reperietur qua-
              <lb/>
            dratum diametri verò minus, vt ex reg. </s>
            <s xml:id="echoid-s8958" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8959" xml:space="preserve">Num 4. </s>
            <s xml:id="echoid-s8960" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s8961" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8962" xml:space="preserve">colligitur. </s>
            <s xml:id="echoid-s8963" xml:space="preserve">Ac proinde
              <lb/>
            tadix eius quadrata diametrum offeret vera minorem.</s>
            <s xml:id="echoid-s8964" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div546" type="section" level="1" n="196">
          <head xml:id="echoid-head209" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s8965" xml:space="preserve">DATO arcu cuiuſuis circuli, diametrum circuli in numeris inueſti-
              <lb/>
            gare.</s>
            <s xml:id="echoid-s8966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8967" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datus arcus A B C. </s>
            <s xml:id="echoid-s8968" xml:space="preserve">Ducta chorda A C, ſectaque bifariam in F, ducatur
              <lb/>
              <note symbol="a" position="right" xlink:label="note-231-01" xlink:href="note-231-01a" xml:space="preserve">coroll. 1.
                <lb/>
              tertij.</note>
            per F, perpendicularis FB, quæ per centrum circuli tranſibit, ideo querectan- gulum ſub C F, A F, hoc eſt, quadratum ex A F, æquale eritre-
              <lb/>
              <figure xlink:label="fig-231-01" xlink:href="fig-231-01a" number="146">
                <image file="231-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/231-01"/>
              </figure>
            ctangulo ſub B F, & </s>
            <s xml:id="echoid-s8969" xml:space="preserve">reliqua portione diametri. </s>
            <s xml:id="echoid-s8970" xml:space="preserve">Si igitur A F,
              <lb/>
              <note symbol="b" position="right" xlink:label="note-231-02" xlink:href="note-231-02a" xml:space="preserve">35. tertij.</note>
            FB, per aliquam menſuram fiant notæ, & </s>
            <s xml:id="echoid-s8971" xml:space="preserve">quadratus numerus
              <lb/>
            rectæ A F, diuidatur per F B, prodibit reliqua portio diametri
              <lb/>
            F D, quæ addita perpendiculari FB, conficiet totam diametrum
              <lb/>
            BD, notam in eadem menſura, in qua A F, FB, cognitæ ſunt.</s>
            <s xml:id="echoid-s8972" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8973" xml:space="preserve">
              <emph style="sc">Geometrice</emph>
            eadem portio FD, reperietur, ſi duabus
              <lb/>
            F B, A F, inueniatur tertia proportionalis F D: </s>
            <s xml:id="echoid-s8974" xml:space="preserve">propterea quod ex ſcholio pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8975" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8976" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8977" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8978" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s8979" xml:space="preserve">AF, media proportionalis eſt inter diametri ſegmenta.</s>
            <s xml:id="echoid-s8980" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div548" type="section" level="1" n="197">
          <head xml:id="echoid-head210" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s8981" xml:space="preserve">DATIS diametris duorum circulorum, vel circumferentiis: </s>
            <s xml:id="echoid-s8982" xml:space="preserve">Aut duo-
              <lb/>
            bus lateribus homologis duarum figurarum ſimilium, ſimilium, ſimiliterq; </s>
            <s xml:id="echoid-s8983" xml:space="preserve">po-
              <lb/>
            ſitarum: </s>
            <s xml:id="echoid-s8984" xml:space="preserve">quam proportionem proportionem circuli, vel figuræ inter ſe habeant, co-
              <lb/>
            gnoſcere.</s>
            <s xml:id="echoid-s8985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8986" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            circuli, & </s>
            <s xml:id="echoid-s8987" xml:space="preserve">figuræ ſimiles ſimiliterque poſitæ, habent duplica-
              <lb/>
            tam proportionem diametrorum, vel circumferentiarum, & </s>
            <s xml:id="echoid-s8988" xml:space="preserve">laterum homolo-
              <lb/>
            gorum: </s>
            <s xml:id="echoid-s8989" xml:space="preserve">ſi maior diameter, vel circumferentia per minorem, & </s>
            <s xml:id="echoid-s8990" xml:space="preserve">maius latus ho-
              <lb/>
            mologum per minus diuidatur, prodibit denominator proportionis, quam ma-
              <lb/>
            ior diameter, circumferentiaue ad minorem, vel maius latus homologum ad mi-
              <lb/>
            nus habet. </s>
            <s xml:id="echoid-s8991" xml:space="preserve">Siigitur hic denominator in ſe ducatur, producetur </s>
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