Clavius, Christoph, Geometria practica

Table of handwritten notes

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[Handwritten note 66]
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[Handwritten note 67]
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[Handwritten note 64]
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[Handwritten note 66]
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[Handwritten note 67]
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[Handwritten note 68]
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[Handwritten note 69]
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[Handwritten note 70]
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[Handwritten note 71]
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[Handwritten note 72]
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[Handwritten note 71]
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[Handwritten note 72]
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[Handwritten note 73]
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        <div xml:id="echoid-div522" type="section" level="1" n="188">
          <pb o="196" file="226" n="226" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s8585" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            ſi fiat, vt 71. </s>
            <s xml:id="echoid-s8586" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8587" xml:space="preserve">ita diameter 1. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">ad aliud, reperietur perregulam
              <lb/>
            2. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8590" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8591" xml:space="preserve">circumſerentia circuli 3 {10/71}. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">vel {223/71}. </s>
            <s xml:id="echoid-s8593" xml:space="preserve">minor, quam vera. </s>
            <s xml:id="echoid-s8594" xml:space="preserve">Igitur, vt
              <lb/>
            Num. </s>
            <s xml:id="echoid-s8595" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8596" xml:space="preserve">dictum eſt ex eius ſemiſſe {223/142}. </s>
            <s xml:id="echoid-s8597" xml:space="preserve">in {1/2}. </s>
            <s xml:id="echoid-s8598" xml:space="preserve">ſemidiametrum producetur area
              <lb/>
            circuli {223/284}. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">maior tamen, quam vera: </s>
            <s xml:id="echoid-s8600" xml:space="preserve"> Ac proinde quadratum diametri 1.</s>
            <s xml:id="echoid-s8601" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-226-01" xlink:href="note-226-01a" xml:space="preserve">8. quinti.</note>
            quod eſt 1. </s>
            <s xml:id="echoid-s8602" xml:space="preserve">ad veram circuli aream, quę maior eſt, quam {223/284}. </s>
            <s xml:id="echoid-s8603" xml:space="preserve">minorem habebit
              <lb/>
            proportionem, quam ad {223/284}. </s>
            <s xml:id="echoid-s8604" xml:space="preserve">Cum ergo ſit 1. </s>
            <s xml:id="echoid-s8605" xml:space="preserve">ad {223/284}. </s>
            <s xml:id="echoid-s8606" xml:space="preserve">vt 284. </s>
            <s xml:id="echoid-s8607" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8608" xml:space="preserve">(Nam quia
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s8609" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8610" xml:space="preserve">Minutiarum, eadem eſt proportio Numeratoris 223. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">ad denomi-
              <lb/>
            natorem 284. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">quę minutię {223/284}. </s>
            <s xml:id="echoid-s8613" xml:space="preserve">ad ſuum integrum 1. </s>
            <s xml:id="echoid-s8614" xml:space="preserve">erit conuertendo, vt 284.
              <lb/>
            </s>
            <s xml:id="echoid-s8615" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8616" xml:space="preserve">ita 1. </s>
            <s xml:id="echoid-s8617" xml:space="preserve">ad {223/284}.) </s>
            <s xml:id="echoid-s8618" xml:space="preserve">habebit quoque quadratum diametri 1. </s>
            <s xml:id="echoid-s8619" xml:space="preserve">ad aream veram
              <lb/>
            circuli minorem proportionem, quam 284. </s>
            <s xml:id="echoid-s8620" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8621" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s8622" xml:space="preserve">Con-
              <lb/>
            ſtat ergo ſecunda etiam pars propoſitionis.</s>
            <s xml:id="echoid-s8623" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div526" type="section" level="1" n="189">
          <head xml:id="echoid-head197" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s8624" xml:space="preserve">PROPORTIO quadrati à circumferentia circuli cuiuſuis deſcripti
              <lb/>
            ad circuli aream maior eſt, quam 892. </s>
            <s xml:id="echoid-s8625" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8626" xml:space="preserve">minor autem, quam
              <lb/>
            88. </s>
            <s xml:id="echoid-s8627" xml:space="preserve">ad 7.</s>
            <s xml:id="echoid-s8628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8629" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            enim circumferentia cuiuſuis circuli ad circumferentiam
              <note symbol="b" position="left" xlink:label="note-226-02" xlink:href="note-226-02a" xml:space="preserve">1. hui{us}
                <lb/>
              Num. 3.</note>
            terius circuli eſt, vt diameter ad diametrum: </s>
            <s xml:id="echoid-s8630" xml:space="preserve"> erit quoque quadratum circum- ferentiæ ad quadratum circumferentię, vt quadratum diametri, ad quadratum
              <lb/>
              <note symbol="c" position="left" xlink:label="note-226-03" xlink:href="note-226-03a" xml:space="preserve">22. ſexti.</note>
            diametri. </s>
            <s xml:id="echoid-s8631" xml:space="preserve"> Sed vt quadratrum diametri ad quadratum diametri, ita eſt
              <note symbol="d" position="left" xlink:label="note-226-04" xlink:href="note-226-04a" xml:space="preserve">2. duodec.</note>
            ad circulum. </s>
            <s xml:id="echoid-s8632" xml:space="preserve">Igitur erit quadratum quo que circumferentię ad quadratum cir-
              <lb/>
            cumferentię; </s>
            <s xml:id="echoid-s8633" xml:space="preserve">vt circulus ad circulum: </s>
            <s xml:id="echoid-s8634" xml:space="preserve">Et permutando quadratum circumfe-
              <lb/>
            rentię, ad ſuum circulũ, vt quadratum alterius circumferentię ad ſuum circu-
              <lb/>
            lum. </s>
            <s xml:id="echoid-s8635" xml:space="preserve">Poſita autem circumferentia alicuius circuli 1. </s>
            <s xml:id="echoid-s8636" xml:space="preserve">proportio quadrati circum-
              <lb/>
            ferentię illius circuli ad circulum maior eſt, quam 892. </s>
            <s xml:id="echoid-s8637" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8638" xml:space="preserve">minor verò, quàm
              <lb/>
            88. </s>
            <s xml:id="echoid-s8639" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8640" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s8641" xml:space="preserve">proportio quadrati circumferentię cuiuslibet alterius circuli
              <lb/>
            ad ipſum circulum maior erit, quam 892. </s>
            <s xml:id="echoid-s8642" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8643" xml:space="preserve">minor autem, quam 88. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">ad 7.</s>
            <s xml:id="echoid-s8645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8646" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            autem proportio quadrati ex circumferentia 1. </s>
            <s xml:id="echoid-s8647" xml:space="preserve">deſcripti, ad ſuum
              <lb/>
            circulum maior ſit, quam 892. </s>
            <s xml:id="echoid-s8648" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8649" xml:space="preserve">minor verò, quam 88. </s>
            <s xml:id="echoid-s8650" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8651" xml:space="preserve">ſic demonſtra-
              <lb/>
            bimus. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">Quoniã ſi fiat, vt 223. </s>
            <s xml:id="echoid-s8653" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8654" xml:space="preserve">ita data circumferentia 1. </s>
            <s xml:id="echoid-s8655" xml:space="preserve">ad aliud, diameter
              <lb/>
            procreatur {71/223}. </s>
            <s xml:id="echoid-s8656" xml:space="preserve">maior, quam vera, vt ex 3. </s>
            <s xml:id="echoid-s8657" xml:space="preserve">regula Num. </s>
            <s xml:id="echoid-s8658" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8659" xml:space="preserve">conſtat. </s>
            <s xml:id="echoid-s8660" xml:space="preserve">fit vt {1/2}. </s>
            <s xml:id="echoid-s8661" xml:space="preserve">ſe-
              <lb/>
            miſsis circumferentię ducta in {71/446}. </s>
            <s xml:id="echoid-s8662" xml:space="preserve">ſemiſſem diametri inuentę producat aream
              <lb/>
            circuli {71/892}. </s>
            <s xml:id="echoid-s8663" xml:space="preserve">vera maiorem, vt Num. </s>
            <s xml:id="echoid-s8664" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8665" xml:space="preserve">dictum eſt. </s>
            <s xml:id="echoid-s8666" xml:space="preserve"> Igitur quadratum
              <note symbol="e" position="left" xlink:label="note-226-05" xlink:href="note-226-05a" xml:space="preserve">8. quinti.</note>
            rentię 1. </s>
            <s xml:id="echoid-s8667" xml:space="preserve">quod eſt 1. </s>
            <s xml:id="echoid-s8668" xml:space="preserve">ad veram aream circuli, quę minor eſt, quam {71/892}. </s>
            <s xml:id="echoid-s8669" xml:space="preserve">maiorem
              <lb/>
            proportionem habebit, quam ad {71/892}. </s>
            <s xml:id="echoid-s8670" xml:space="preserve">Vt autem 1. </s>
            <s xml:id="echoid-s8671" xml:space="preserve">ad {71/892}. </s>
            <s xml:id="echoid-s8672" xml:space="preserve">ita eſt, ex propoſ. </s>
            <s xml:id="echoid-s8673" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s8674" xml:space="preserve">minutiarum, & </s>
            <s xml:id="echoid-s8675" xml:space="preserve">conuertendo, 892. </s>
            <s xml:id="echoid-s8676" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8677" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s8678" xml:space="preserve">quadratum circumferentiæ
              <lb/>
            1. </s>
            <s xml:id="echoid-s8679" xml:space="preserve">ad veram circuli aream maiorem proportionem habebit, quam 892. </s>
            <s xml:id="echoid-s8680" xml:space="preserve">ad 71
              <lb/>
            quod eſt propoſitum. </s>
            <s xml:id="echoid-s8681" xml:space="preserve">Vera ergo eſt prior propoſitio nis pars.</s>
            <s xml:id="echoid-s8682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8683" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            , quia ſi fiat, vt 22. </s>
            <s xml:id="echoid-s8684" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8685" xml:space="preserve">ita data circumferentia 1. </s>
            <s xml:id="echoid-s8686" xml:space="preserve">ad aliud, diame-
              <lb/>
            ter producitur {7/22}. </s>
            <s xml:id="echoid-s8687" xml:space="preserve">minor quam vera: </s>
            <s xml:id="echoid-s8688" xml:space="preserve">fit vt {1/2}. </s>
            <s xml:id="echoid-s8689" xml:space="preserve">ſemiſsis circumferentię ducta in
              <lb/>
            {7/44}. </s>
            <s xml:id="echoid-s8690" xml:space="preserve">ſemiſſem diametri inuentæ producat aream circuli {7/88}. </s>
            <s xml:id="echoid-s8691" xml:space="preserve">vera minorem, vt ex
              <lb/>
            iis, conſtat, quæ Num. </s>
            <s xml:id="echoid-s8692" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8693" xml:space="preserve">diximus. </s>
            <s xml:id="echoid-s8694" xml:space="preserve"> Igitur quadratum circumferentię 1. </s>
            <s xml:id="echoid-s8695" xml:space="preserve">quod
              <note symbol="f" position="left" xlink:label="note-226-06" xlink:href="note-226-06a" xml:space="preserve">8. quinti.</note>
            1. </s>
            <s xml:id="echoid-s8696" xml:space="preserve">ad aream veram circuli, quæ maior eſt, quam {7/88}. </s>
            <s xml:id="echoid-s8697" xml:space="preserve">minorem habebit proportio-
              <lb/>
            nem, quam ad {7/88}. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">Vtautem 1. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">ad {7/88}. </s>
            <s xml:id="echoid-s8700" xml:space="preserve">ita eſt, ex propoſitione 2. </s>
            <s xml:id="echoid-s8701" xml:space="preserve"/>
          </p>
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