Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div472" type="section" level="1" n="175">
          <p>
            <s xml:id="echoid-s7545" xml:space="preserve">
              <pb o="179" file="209" n="209" rhead="LIBER QVARTVS."/>
            tum venire poſsimus in cognitionem alterius figurę ſimilis illi, ſimiliterque po-
              <lb/>
            ſitę latus homologum etiam notum habentis: </s>
            <s xml:id="echoid-s7546" xml:space="preserve">quæ ſic ſe habet.</s>
            <s xml:id="echoid-s7547" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7548" xml:space="preserve">Quadrat{us} numer{us} denominatoris proportionis, quam lat{us} figuræ ignotæ ad lat{us}
              <lb/>
              <note position="right" xlink:label="note-209-01" xlink:href="note-209-01a" xml:space="preserve">Quaratione
                <lb/>
              ex area cu-
                <lb/>
              iusl@bet figuræ
                <lb/>
              eruatur areæ
                <lb/>
              alteriu figuræ
                <lb/>
              ſimilis.</note>
            figuræ cognitæ hab{et}, (qui denominator habebitur, ſi lat{us} figuræ ignotæ per lat{us} figuræ
              <lb/>
            cognitæ diuidatur) ſi ducatur in aream cognitam, produc{et}ur area alteri{us} figuræ quæſi-
              <lb/>
            tæ. </s>
            <s xml:id="echoid-s7549" xml:space="preserve">Debent autem figuræ eſſe ſimil{es}, ſimiliter que poſitæ, & </s>
            <s xml:id="echoid-s7550" xml:space="preserve">earum latera homologa ſumi
              <lb/>
            vt dictum est.</s>
            <s xml:id="echoid-s7551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7552" xml:space="preserve">Nam denominator proportionis lateris figurę quæſitę ad latus figuræ datę
              <lb/>
            in ſe multiplicatus gignit denominatorem proportionis duplicatę eorum late-
              <lb/>
              <note symbol="a" position="right" xlink:label="note-209-02" xlink:href="note-209-02a" xml:space="preserve">18. vel 20.
                <lb/>
              ſexti.</note>
            rum, vt ad defin. </s>
            <s xml:id="echoid-s7553" xml:space="preserve">10. </s>
            <s xml:id="echoid-s7554" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7555" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7556" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s7557" xml:space="preserve">ſcripſimus. </s>
            <s xml:id="echoid-s7558" xml:space="preserve"> Cum ergo figurę ſimiles ſimili- terque poſitę habeant etiam proportionem duplicatam laterum homologo-
              <lb/>
            rum; </s>
            <s xml:id="echoid-s7559" xml:space="preserve">fit vt denominator proportionis duplicatę laterum prædictorum multi-
              <lb/>
            plicans aream cognitam producat aream quęſitam, hoc eſt, numerum, qui ad
              <lb/>
            aream cognitam proportionem habeat duplicatam proportionis datorum la-
              <lb/>
            terum, denominatam ſcilicet à denominatore, qui ex denominatore proportio-
              <lb/>
            nis eorum laterum in ſe multip licato producitur. </s>
            <s xml:id="echoid-s7560" xml:space="preserve">Verbi gratia, Trianguli ABC,
              <lb/>
            cuius latus A B, 10. </s>
            <s xml:id="echoid-s7561" xml:space="preserve">AC, 17. </s>
            <s xml:id="echoid-s7562" xml:space="preserve">& </s>
            <s xml:id="echoid-s7563" xml:space="preserve">B C, 21. </s>
            <s xml:id="echoid-s7564" xml:space="preserve">area eſt 84. </s>
            <s xml:id="echoid-s7565" xml:space="preserve">Si ergo ſit aliud triangulum
              <lb/>
            huic ſimile habens latus ipſi A B, homologum 70. </s>
            <s xml:id="echoid-s7566" xml:space="preserve">ipſi verò A C, homologum
              <lb/>
              <figure xlink:label="fig-209-01" xlink:href="fig-209-01a" number="132">
                <image file="209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/209-01"/>
              </figure>
            119. </s>
            <s xml:id="echoid-s7567" xml:space="preserve">& </s>
            <s xml:id="echoid-s7568" xml:space="preserve">ipſi B C, homologum 147. </s>
            <s xml:id="echoid-s7569" xml:space="preserve">diuidaturque latus 70. </s>
            <s xml:id="echoid-s7570" xml:space="preserve">per 10. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">vt denomi-
              <lb/>
            nator 7. </s>
            <s xml:id="echoid-s7572" xml:space="preserve">proportionis lateris 70. </s>
            <s xml:id="echoid-s7573" xml:space="preserve">ad latus 10. </s>
            <s xml:id="echoid-s7574" xml:space="preserve">procreetur, & </s>
            <s xml:id="echoid-s7575" xml:space="preserve">quadratus nume-
              <lb/>
            rus huius denominatoris; </s>
            <s xml:id="echoid-s7576" xml:space="preserve">nimirum 49. </s>
            <s xml:id="echoid-s7577" xml:space="preserve">ducatur in 84. </s>
            <s xml:id="echoid-s7578" xml:space="preserve">areã trianguli A B C, pro-
              <lb/>
            ducetur area 4116. </s>
            <s xml:id="echoid-s7579" xml:space="preserve">poſterioris trianguli. </s>
            <s xml:id="echoid-s7580" xml:space="preserve">Rurſus quia area trianguli æquila-
              <lb/>
            teri, cuius ſingula latera ſint, 1. </s>
            <s xml:id="echoid-s7581" xml:space="preserve">area eſt {13/30}. </s>
            <s xml:id="echoid-s7582" xml:space="preserve">fermè, vt ſupra patuit, ſi de-
              <lb/>
            tur aliud triangulumæquilaterum, cuius ſingula latera ſint 70. </s>
            <s xml:id="echoid-s7583" xml:space="preserve">inueniemus eius
              <lb/>
            aream hoc modo. </s>
            <s xml:id="echoid-s7584" xml:space="preserve">Denominator proportionis laterum eſt ipſummet latus 70.
              <lb/>
            </s>
            <s xml:id="echoid-s7585" xml:space="preserve">quod 70. </s>
            <s xml:id="echoid-s7586" xml:space="preserve">diuiſa per 1. </s>
            <s xml:id="echoid-s7587" xml:space="preserve">faciant 70. </s>
            <s xml:id="echoid-s7588" xml:space="preserve">Ducemus ergo 4900. </s>
            <s xml:id="echoid-s7589" xml:space="preserve">quadratum lateris 70. </s>
            <s xml:id="echoid-s7590" xml:space="preserve">
              <lb/>
            in {13/30}. </s>
            <s xml:id="echoid-s7591" xml:space="preserve">aream cognitam. </s>
            <s xml:id="echoid-s7592" xml:space="preserve">Productus enim numerus 2123 {1/3}. </s>
            <s xml:id="echoid-s7593" xml:space="preserve">erit area poſt erioris
              <lb/>
            trianguli.</s>
            <s xml:id="echoid-s7594" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7595" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            regula ita quoque proponi poterit. </s>
            <s xml:id="echoid-s7597" xml:space="preserve">Fiat vt quadrat{us} nu-
              <lb/>
            mer{us} lateris figuræ cognitæ ad quadratum numerum lateris figuræ quæſitæ, ita a
              <lb/>
              <note position="right" xlink:label="note-209-03" xlink:href="note-209-03a" xml:space="preserve">Regula ſupra-
                <lb/>
              dicta aliter
                <lb/>
              propoſita.</note>
            rea figuræ cognitæ ad aliud. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">Product{us} enim numer{us} erit area figuræ quæſitæ.
              <lb/>
            </s>
            <s xml:id="echoid-s7599" xml:space="preserve">Propterea quod eadem eſt proportio quadrati lateris cognitæ figuræ ad qua-
              <lb/>
            dratum lateris figuræ quæſitę, quæ figurę notæ ad figuram quæſitam: </s>
            <s xml:id="echoid-s7600" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-209-04" xlink:href="note-209-04a" xml:space="preserve">19. vel 20.
                <lb/>
              ſexti.</note>
            pe cum vtraque proportio ſit duplicata proportionis laterum homologo-
              <lb/>
            rum. </s>
            <s xml:id="echoid-s7601" xml:space="preserve">Et quoniam quadratum lateris 1. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">eſt 1. </s>
            <s xml:id="echoid-s7603" xml:space="preserve">fit, vt quotieſcunque latus figu-
              <lb/>
            ræ aream cognitam habentis fuerit 1. </s>
            <s xml:id="echoid-s7604" xml:space="preserve">ſatis ſit, quadratum numerum lateris fi-
              <lb/>
            guræ quæſitæ multiplicare in datam aream, vt quęſita area producatur: </s>
            <s xml:id="echoid-s7605" xml:space="preserve">Adeo
              <lb/>
            vt operæ pretium ſit areas inueſtigare plurimarum figurarum regularium, qua-
              <lb/>
            rum latera ſint 1. </s>
            <s xml:id="echoid-s7606" xml:space="preserve">Ex his enim ſine magno labore areæ aliarum </s>
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