Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div286" type="section" level="1" n="132">
          <p style="it">
            <s xml:id="echoid-s3548" xml:space="preserve">
              <pb o="92" file="104" n="104" rhead=""/>
            Recta igitur ducta _ED,_ minor erit, quàm recta _EG;_ </s>
            <s xml:id="echoid-s3549" xml:space="preserve">ac proinde cum circulus _GE,_
              <lb/>
              <note position="left" xlink:label="note-104-01" xlink:href="note-104-01a" xml:space="preserve">ſchol. 21. 2.
                <lb/>
              huius.</note>
            minor ſit circulo _DE,_ mator erit circunferentia _
              <emph style="sc">Eg</emph>
            ,_ quàm circunferentia _DE._
              <lb/>
            </s>
            <s xml:id="echoid-s3550" xml:space="preserve">Sienim recta rectæ _ED,_ æqualis aufert ex circulo _GE,_ maiorem arcum, quàm
              <lb/>
              <note position="left" xlink:label="note-104-02" xlink:href="note-104-02a" xml:space="preserve">lemma 6.
                <lb/>
              huius.</note>
            recta _DE,_ ex circulo _DE;_ </s>
            <s xml:id="echoid-s3551" xml:space="preserve">multo magis recta _
              <emph style="sc">Eg</emph>
            ,_ quæ maior eſt, quàm recta
              <lb/>
            _ED,_ vt oſtendimus, maiorem arcum auferet, &</s>
            <s xml:id="echoid-s3552" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">Quare minor erit propor-
              <lb/>
            tio arcus _
              <emph style="sc">B</emph>
            C,_ ad arcum _GE,_ quàm ad arcum _DE._ </s>
            <s xml:id="echoid-s3554" xml:space="preserve">Quoniam vero eſt, vt arcus _BC,_
              <lb/>
              <note position="left" xlink:label="note-104-03" xlink:href="note-104-03a" xml:space="preserve">8.quinti.</note>
              <figure xlink:label="fig-104-01" xlink:href="fig-104-01a" number="108">
                <image file="104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/104-01"/>
              </figure>
            ad totam circunferentiam cir-
              <lb/>
            culi _BC,_ ita arcus _
              <emph style="sc">G</emph>
            E,_ ad to-
              <lb/>
            tam circũferentiã circuli _GE,_
              <lb/>
            propter ſimilitudinem arcuum
              <lb/>
            _BC, GE;_ </s>
            <s xml:id="echoid-s3555" xml:space="preserve">(In hoc enim conſiſtit
              <lb/>
            ſimilitudo arcuum, vt ad ſuo-
              <lb/>
            rum circulorum circunferen-
              <lb/>
            tias integras eandem habeant
              <lb/>
            proportionem, vt in ſcholio pro
              <lb/>
            poſ 33. </s>
            <s xml:id="echoid-s3556" xml:space="preserve">li. </s>
            <s xml:id="echoid-s3557" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3558" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">tradidimus)
              <lb/>
            atque adeo permutando, vt ar-
              <lb/>
            cus _BC,_ ad arcũ _
              <emph style="sc">G</emph>
            E,_ itateta
              <lb/>
            circunferentia circuli _BC,_ ad
              <lb/>
            totam circunferentiam circuli
              <lb/>
            _
              <emph style="sc">G</emph>
            E;_ </s>
            <s xml:id="echoid-s3560" xml:space="preserve">erit quoque minor propor
              <lb/>
            tio circunferentiæ circuli _BC,_
              <lb/>
            ad circunferentiã circuli _
              <emph style="sc">G</emph>
            E,_
              <lb/>
            quàm arcus _
              <emph style="sc">B</emph>
            C,_ ad arcum
              <lb/>
            _DE:_ </s>
            <s xml:id="echoid-s3561" xml:space="preserve">Vt autem circunferentia
              <lb/>
            circuli _
              <emph style="sc">B</emph>
            C,_ ad circunferentiam circuli _GE,_ ita eſt diameter _BI,_ (quæ ſphæræ etiam
              <lb/>
            diameter eſt.) </s>
            <s xml:id="echoid-s3562" xml:space="preserve">ad diametrum _GH,_ vt Pappus demonſtrauit, & </s>
            <s xml:id="echoid-s3563" xml:space="preserve">nos in libello Archi-
              <lb/>
            medis de dimenſione circuli oſtendimus. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">Igitur minor quoque erit proportio diame-
              <lb/>
            tri ſphæræ _
              <emph style="sc">B</emph>
            I,_ ad _
              <emph style="sc">G</emph>
            H,_ diametrum paralleli _
              <emph style="sc">G</emph>
            E,_ quàm arcus _
              <emph style="sc">B</emph>
            C,_ ad circunferen-
              <lb/>
            tiam _DE._ </s>
            <s xml:id="echoid-s3565" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s3566" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div289" type="section" level="1" n="133">
          <head xml:id="echoid-head147" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s3567" xml:space="preserve">HINC ſit, ijſdem poſitis, maiorem eſſe rationem circunferentiæ BC, maximi parallelo-
              <lb/>
            rum interceptæ inter maximum circulum AB, primo poſitum, & </s>
            <s xml:id="echoid-s3568" xml:space="preserve">maximum circulum AC,
              <lb/>
            per polos parallelorum tranſeuntem, ad circunferentiam DE, obliqui circuli inter coſdem
              <lb/>
            circulos interceptam, quàm ſinus totius ad ſinum circunferentiæ AE, maximi circuli per
              <lb/>
            polos parallelorum tranſeuntis; </s>
            <s xml:id="echoid-s3569" xml:space="preserve">minorem vero, quàm ſinus totius ad ſinum circunferenciæ
              <lb/>
            AD, maximi circuli primò poſiti inter polos parall elorum, & </s>
            <s xml:id="echoid-s3570" xml:space="preserve">obliquum circulum inter-
              <lb/>
            ceptæ. </s>
            <s xml:id="echoid-s3571" xml:space="preserve">Quoniam enim hoc Theoremate oſtenſum eſt, maiorem eſſe rationem arcus BC, ad
              <lb/>
            arcum DE, quàm diametri ſphæræ ad diametrum paralleli GE: </s>
            <s xml:id="echoid-s3572" xml:space="preserve">vt autem diameter BI,
              <lb/>
            ſphæræ ad GH, diametrum circuli GE, ita eſt BK, ſemidiameter, hoc eſt, ſinus rotus, ad
              <lb/>
              <note position="left" xlink:label="note-104-04" xlink:href="note-104-04a" xml:space="preserve">15. quinti.</note>
            GN, ſemidiametrum, hoc eſt, ad ſinum arcus AE. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">(Cum enim arcus AG, AE, æquales ſint,
              <lb/>
              <note position="left" xlink:label="note-104-05" xlink:href="note-104-05a" xml:space="preserve">10.2.huius.</note>
            ſitque GN, ſinus arcus AG; </s>
            <s xml:id="echoid-s3574" xml:space="preserve">erit quoque GN, ſinus arcus AE.) </s>
            <s xml:id="echoid-s3575" xml:space="preserve">Maiorigitur erit quoque
              <lb/>
            tatio arcus BC, ad arcum DE, quàm ſinus totius BK, ad GN, ſinum arcus AE.</s>
            <s xml:id="echoid-s3576" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3577" xml:space="preserve">RVRSVS, quoniã oſtenſum eſt, minorem eſſe rationem ascus BC, ad arcum DE, quàm
              <lb/>
              <note position="left" xlink:label="note-104-06" xlink:href="note-104-06a" xml:space="preserve">11. huius.</note>
            diametri ſphæræ ad diametrum paralleli DF: </s>
            <s xml:id="echoid-s3578" xml:space="preserve">Vt autem diameter ſphæræ BI, ad DF, diame
              <lb/>
            trum paralleli DF, ita eſt BK, ſinus totus ad DO, ſinum artus AD. </s>
            <s xml:id="echoid-s3579" xml:space="preserve">Minor igitur quoque
              <lb/>
              <note position="left" xlink:label="note-104-07" xlink:href="note-104-07a" xml:space="preserve">15. quinti.</note>
            eſt proportio arcus BC, ad arcum DE, q̃ ſinus totius ad ſinũ arcus AD. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3582" xml:space="preserve">CÆTERVM quid ſit ſinus, ex ſequenti tractatione intelligetur.</s>
            <s xml:id="echoid-s3583" xml:space="preserve"/>
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