Clavius, Christoph, Geometria practica

Table of handwritten notes

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[Handwritten note 66]
Page: 193
[Handwritten note 67]
Page: 193
[Handwritten note 64]
Page: 193
[Handwritten note 66]
Page: 193
[Handwritten note 67]
Page: 193
[Handwritten note 68]
Page: 229
[Handwritten note 69]
Page: 229
[Handwritten note 70]
Page: 235
[Handwritten note 71]
Page: 237
[Handwritten note 72]
Page: 237
[Handwritten note 71]
Page: 237
[Handwritten note 72]
Page: 237
[Handwritten note 73]
Page: 383
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        <div xml:id="echoid-div526" type="section" level="1" n="189">
          <p>
            <s xml:id="echoid-s8701" xml:space="preserve">
              <pb o="197" file="227" n="227" rhead="LIBER QVARTVS."/>
            & </s>
            <s xml:id="echoid-s8702" xml:space="preserve">conuertendo, 88. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">Ergo etiam quadratum circumferentiæ 1. </s>
            <s xml:id="echoid-s8705" xml:space="preserve">ad aream cir-
              <lb/>
            culi minorem proportionem habebit, quam 88. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8707" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">Ve-
              <lb/>
            ra igitur etiam eſt poſterior pars propoſitio nis.</s>
            <s xml:id="echoid-s8709" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8710" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8711" xml:space="preserve">
              <emph style="sc">His</emph>
            ita demonſtratis, ſequunturiam quatuor regulæ, per quas aream cir-
              <lb/>
            culi propoſiti ſiue maiorem, ſiue minorem vera, vel ex ſola diametro, vel ex ſo-
              <lb/>
            la circumferentia cognita conijcere licebit.</s>
            <s xml:id="echoid-s8712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div530" type="section" level="1" n="190">
          <head xml:id="echoid-head198" xml:space="preserve">I.</head>
          <head xml:id="echoid-head199" xml:space="preserve">EX diametro aream circuli vera maiorem inueſtigare.</head>
          <p>
            <s xml:id="echoid-s8713" xml:space="preserve">Fiat vt 14. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s8715" xml:space="preserve">ita quadratum datæ diametri ad aliud. </s>
            <s xml:id="echoid-s8716" xml:space="preserve">Product{us} enim numer{us}
              <lb/>
            dabit aream circuli veramaiorem. </s>
            <s xml:id="echoid-s8717" xml:space="preserve"> Cum enim maior ſit proportio quadrati
              <note symbol="a" position="right" xlink:label="note-227-01" xlink:href="note-227-01a" xml:space="preserve">2. Num. 3.</note>
            metri ad aream circuli, quam 14. </s>
            <s xml:id="echoid-s8718" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s8719" xml:space="preserve">Sit autem quadratum diametri datæ ad a-
              <lb/>
            ream inuentam, vt 14. </s>
            <s xml:id="echoid-s8720" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s8721" xml:space="preserve">erit quo que maior proportio quadrati diametri da-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-227-02" xlink:href="note-227-02a" xml:space="preserve">10. quinti.</note>
            tæ ad veram aream circuli, quam ad aream inuentam. </s>
            <s xml:id="echoid-s8722" xml:space="preserve"> Ac proinde vera circuli area erit minor, quaminuenta: </s>
            <s xml:id="echoid-s8723" xml:space="preserve">hoc eſt, area inuenta maior erit, quam vera.</s>
            <s xml:id="echoid-s8724" xml:space="preserve"/>
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        <div xml:id="echoid-div532" type="section" level="1" n="191">
          <head xml:id="echoid-head200" xml:space="preserve">II.</head>
          <head xml:id="echoid-head201" xml:space="preserve">EX diametro aream circuli vera minorem inueſtigare.</head>
          <p>
            <s xml:id="echoid-s8725" xml:space="preserve">Fiat vt 284. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">ita quadratum datæ diametri ad aliud.</s>
            <s xml:id="echoid-s8728" xml:space="preserve">’ Numer{us} enim procrea-
              <lb/>
            t{us} aream circuli vera minorem offeret. </s>
            <s xml:id="echoid-s8729" xml:space="preserve"> Cum enim minor ſit proportio
              <note symbol="c" position="right" xlink:label="note-227-03" xlink:href="note-227-03a" xml:space="preserve">2. Num. 3.</note>
            diametri datæ ad aream circuli, quam 284. </s>
            <s xml:id="echoid-s8730" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">ſit autem quadratum diametri
              <lb/>
            datæ ad aream inuentam, vt 284. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s8733" xml:space="preserve">erit quo que minor proportio quadrati
              <lb/>
              <note symbol="d" position="right" xlink:label="note-227-04" xlink:href="note-227-04a" xml:space="preserve">10. quinti.</note>
            diametri datæ ad veram aream circuli, quam ad areã inuentam: </s>
            <s xml:id="echoid-s8734" xml:space="preserve"> Atque idcirco vera area circuli maior erit, quaminuenta, hoc eſt, inuenta area erit minor, quam
              <lb/>
            vera.</s>
            <s xml:id="echoid-s8735" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div534" type="section" level="1" n="192">
          <head xml:id="echoid-head202" xml:space="preserve">III.</head>
          <head xml:id="echoid-head203" xml:space="preserve">EX circumferentia aream circuli vera maiorem colligere.</head>
          <p>
            <s xml:id="echoid-s8736" xml:space="preserve">Fiat vt 892. </s>
            <s xml:id="echoid-s8737" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8738" xml:space="preserve">ita quadratum datæ circumferentiæ ad aliud. </s>
            <s xml:id="echoid-s8739" xml:space="preserve">Procreat{us} nam-
              <lb/>
            que numer{us} aream circuli vera maiorem indicabit. </s>
            <s xml:id="echoid-s8740" xml:space="preserve"> Cum enim maior ſit
              <note symbol="e" position="right" xlink:label="note-227-05" xlink:href="note-227-05a" xml:space="preserve">3. Num. 3.</note>
            tio quadrati circumferentiæ ad aream circuli, quam 892. </s>
            <s xml:id="echoid-s8741" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8742" xml:space="preserve">Sit autem quadra-
              <lb/>
            tnm datæ circumferentię ad aream inuentam vt 892. </s>
            <s xml:id="echoid-s8743" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8744" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s8745" xml:space="preserve">maior pro-
              <lb/>
            portio quadrati datæ circumferentiæ ad veram aream circuli, quam ad aream in-
              <lb/>
            uentam: </s>
            <s xml:id="echoid-s8746" xml:space="preserve"> ideo que vera circuli area minor erit, quam inuenta; </s>
            <s xml:id="echoid-s8747" xml:space="preserve">hoc eſt,
              <note symbol="f" position="right" xlink:label="note-227-06" xlink:href="note-227-06a" xml:space="preserve">10. quinti.</note>
            area maior erit, quam vera.</s>
            <s xml:id="echoid-s8748" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div536" type="section" level="1" n="193">
          <head xml:id="echoid-head204" xml:space="preserve">IV.</head>
          <head xml:id="echoid-head205" xml:space="preserve">EX circumferentia aream circuli vera minorem concludere.</head>
          <p>
            <s xml:id="echoid-s8749" xml:space="preserve">Fiat vt 88. </s>
            <s xml:id="echoid-s8750" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8751" xml:space="preserve">ita quadratum circumferentiæ datæ ad aliud. </s>
            <s xml:id="echoid-s8752" xml:space="preserve">Numer{us} </s>
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