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

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        <div xml:id="echoid-div219" type="section" level="1" n="105">
          <p style="it">
            <s xml:id="echoid-s2356" xml:space="preserve">
              <pb o="60" file="072" n="72" rhead=""/>
            meter circuli _ABC;_ </s>
            <s xml:id="echoid-s2357" xml:space="preserve">& </s>
            <s xml:id="echoid-s2358" xml:space="preserve">ſuper ipſam rectum circuli ſegmentum _A G D,_ conſtitutum,
              <lb/>
            quod quidem inæqualiter ſecatur in _
              <emph style="sc">G</emph>
            ,_ (Nam quia, ex defin. </s>
            <s xml:id="echoid-s2359" xml:space="preserve">poli, rectæ ſubtenſæ
              <lb/>
            _F A, F D,_ æquales ſunt, erunt quoque arcus _F A, F D,_ æquales; </s>
            <s xml:id="echoid-s2360" xml:space="preserve">ac proinde arcus
              <lb/>
              <note position="left" xlink:label="note-072-01" xlink:href="note-072-01a" xml:space="preserve">28. tertij.</note>
            _A D,_ ſectus erit bifariam in _F,_ at que ob id in _G,_ non bifariam ) maiorq́; </s>
            <s xml:id="echoid-s2361" xml:space="preserve">pars eſt _G A._
              <lb/>
            </s>
            <s xml:id="echoid-s2362" xml:space="preserve">
              <note position="left" xlink:label="note-072-02" xlink:href="note-072-02a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s2363" xml:space="preserve">minor _G D._ </s>
            <s xml:id="echoid-s2364" xml:space="preserve">Igitur rectarum ductarum ex _G,_ ad circunferentiam circuli _A B C,_
              <lb/>
            maxima eſt _G A,_ & </s>
            <s xml:id="echoid-s2365" xml:space="preserve">minima _G D: </s>
            <s xml:id="echoid-s2366" xml:space="preserve">G B,_ verò maior quàm _GC;_ </s>
            <s xml:id="echoid-s2367" xml:space="preserve">& </s>
            <s xml:id="echoid-s2368" xml:space="preserve">_G B,_ _G E,_ æqua-
              <lb/>
            les. </s>
            <s xml:id="echoid-s2369" xml:space="preserve">Quare cum arcus, quibus ſúbtenduntur, ponantur ſemicirculo minores, erit
              <lb/>
              <note position="left" xlink:label="note-072-03" xlink:href="note-072-03a" xml:space="preserve">Schol. 28.
                <lb/>
              terti.j</note>
            & </s>
            <s xml:id="echoid-s2370" xml:space="preserve">arcus _G A,_ maximus, & </s>
            <s xml:id="echoid-s2371" xml:space="preserve">_G D,_ minimus: </s>
            <s xml:id="echoid-s2372" xml:space="preserve">_
              <emph style="sc">G</emph>
            B,_ verò maior, quàm _
              <emph style="sc">G</emph>
            C;_ </s>
            <s xml:id="echoid-s2373" xml:space="preserve">Arcus de-
              <lb/>
            nique _
              <emph style="sc">G</emph>
            B,
              <emph style="sc">G</emph>
            E,_ æquales.</s>
            <s xml:id="echoid-s2374" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">28. tertij.</note>
        </div>
        <div xml:id="echoid-div222" type="section" level="1" n="106">
          <head xml:id="echoid-head118" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s2375" xml:space="preserve">SI in ſphæræ ſuperficie extra circuli cuiuſque peripheriam pun-
              <lb/>
              <note position="left" xlink:label="note-072-05" xlink:href="note-072-05a" xml:space="preserve">32.</note>
            ctum ſignetur præter eius polum, ab eo autem ad circuli circunfe-
              <lb/>
            rentiam plurimi arcus circulorum maximorum ducantur ſemicir-
              <lb/>
            culo minores, ſecantesq́; </s>
            <s xml:id="echoid-s2376" xml:space="preserve">circunferentiam circuli; </s>
            <s xml:id="echoid-s2377" xml:space="preserve">maximus eſt, qui
              <lb/>
            per circuli polum ducitur; </s>
            <s xml:id="echoid-s2378" xml:space="preserve">Reliquorum verò maximo propinquior,
              <lb/>
            remotiore ſemper maior eſt: </s>
            <s xml:id="echoid-s2379" xml:space="preserve">Minimus autem eſt ille, qui inter pun-
              <lb/>
            ctum, & </s>
            <s xml:id="echoid-s2380" xml:space="preserve">circuli circunferentiam extra circulum interijcitur; </s>
            <s xml:id="echoid-s2381" xml:space="preserve">Reli-
              <lb/>
            quorum verò minimo propinquior, remotiore ſemper minor eſt:
              <lb/>
            </s>
            <s xml:id="echoid-s2382" xml:space="preserve">Duo verò arcus ab eodem maximo, vel minimo æqualiter remoti in-
              <lb/>
            ter ſe æquales ſunt.</s>
            <s xml:id="echoid-s2383" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2384" xml:space="preserve">_IN_ ſphara circulus ſit _A B C D E,_ cuius polus _F;_ </s>
            <s xml:id="echoid-s2385" xml:space="preserve">ſigneturq́; </s>
            <s xml:id="echoid-s2386" xml:space="preserve">in ſphæræ ſuperficie
              <lb/>
            extra peripheriam circuli, punctum quodvis _
              <emph style="sc">G</emph>
            ,_ præter alterum polum circuli
              <lb/>
              <figure xlink:label="fig-072-01" xlink:href="fig-072-01a" number="82">
                <image file="072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/072-01"/>
              </figure>
            _
              <emph style="sc">Ab</emph>
            C D E:_ </s>
            <s xml:id="echoid-s2387" xml:space="preserve">& </s>
            <s xml:id="echoid-s2388" xml:space="preserve">à _
              <emph style="sc">G</emph>
            ,_ plurimi arcus maximorum
              <lb/>
            circulorum ducantur ad circunferentiam circu-
              <lb/>
            li _A B C D E,_ ipſam ſecantes; </s>
            <s xml:id="echoid-s2389" xml:space="preserve">quorum _
              <emph style="sc">G</emph>
            D F A,_
              <lb/>
            per polum _F,_ tranſeat;</s>
            <s xml:id="echoid-s2390" xml:space="preserve">arcus verò _
              <emph style="sc">G</emph>
            H B,_ pro-
              <lb/>
            pinquior ſit ipſi _
              <emph style="sc">G</emph>
            D F A,_ quàm _
              <emph style="sc">G</emph>
            I C:_ </s>
            <s xml:id="echoid-s2391" xml:space="preserve">duo de-
              <lb/>
            nique _
              <emph style="sc">G</emph>
              <emph style="sc">Hb</emph>
            ,
              <emph style="sc">G</emph>
            K E,_ æqualiter diſtent ab eo-
              <lb/>
            dem _
              <emph style="sc">G</emph>
            D F A,_ vel à _
              <emph style="sc">G</emph>
            D,_ ſintque omnes hi ar-
              <lb/>
            cus ſemicirculo minores: </s>
            <s xml:id="echoid-s2392" xml:space="preserve">quod tum demum erit,
              <lb/>
            cum ſe mutuo non interſecabunt in alio puncto,
              <lb/>
            quàm in _
              <emph style="sc">G</emph>
            ,_ veluti in antecedenti theoremate
              <lb/>
            eſt oſtenſum. </s>
            <s xml:id="echoid-s2393" xml:space="preserve">Dico arcum _
              <emph style="sc">G</emph>
            A,_ eſſe omnium
              <lb/>
            maximum; </s>
            <s xml:id="echoid-s2394" xml:space="preserve">& </s>
            <s xml:id="echoid-s2395" xml:space="preserve">_
              <emph style="sc">G</emph>
            B,_ maiorem quàm _
              <emph style="sc">G</emph>
            C:_ </s>
            <s xml:id="echoid-s2396" xml:space="preserve">Mini-
              <lb/>
            mum autem eſſe _
              <emph style="sc">G</emph>
            D;_ </s>
            <s xml:id="echoid-s2397" xml:space="preserve">& </s>
            <s xml:id="echoid-s2398" xml:space="preserve">_
              <emph style="sc">G</emph>
            H,_ minorem quàm _
              <emph style="sc">G</emph>
            I:_ </s>
            <s xml:id="echoid-s2399" xml:space="preserve">Denique duos arcus _
              <emph style="sc">G</emph>
            B,
              <emph style="sc">G</emph>
            E,_
              <lb/>
            Item _
              <emph style="sc">G</emph>
            H,_ _
              <emph style="sc">G</emph>
            K,_ æquales eße. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">Quoniam enim arcus _
              <emph style="sc">G</emph>
            A,_ ſecat circulum _A B C D E,_
              <lb/>
              <note position="left" xlink:label="note-072-06" xlink:href="note-072-06a" xml:space="preserve">35. 1. huius.</note>
            bifariam, & </s>
            <s xml:id="echoid-s2401" xml:space="preserve">ad angulos rectos;</s>
            <s xml:id="echoid-s2402" xml:space="preserve">erit recta ſubten ſa _
              <emph style="sc">A</emph>
            D,_ diameter circuli _A B C D E,_
              <lb/>
            & </s>
            <s xml:id="echoid-s2403" xml:space="preserve">ſuper ipſam rectum circuli ſegmentũ conſtitutum _
              <emph style="sc">Dg</emph>
            ,_ quod initium ſumens à _D,_
              <lb/>
            per _
              <emph style="sc">G</emph>
            ,_ ducitur, donec in alio puncto _A,_ circulum _A B C D E,_ iterum ſecet: </s>
            <s xml:id="echoid-s2404" xml:space="preserve">quod qui-
              <lb/>
            dem non bifariam ſectum eſt in _
              <emph style="sc">G</emph>
            ,_ (quòd _
              <emph style="sc">G</emph>
            ,_ non ponatur polus circuli _A B C D E,_
              <lb/>
            in quo dictum ſegmentum bifariam diuiditur, vtin præcedenti theoremate oſtenſum
              <lb/>
            eſt.) </s>
            <s xml:id="echoid-s2405" xml:space="preserve">maiorque pars eſt à puncto _
              <emph style="sc">G</emph>
            ,_ vſque ad _A,_ cum in ea ſit reliquus polus, (alias ar
              <lb/>
            cus _
              <emph style="sc">G</emph>
            DA,_ per vtrumque polum duceretur.)</s>
            <s xml:id="echoid-s2406" xml:space="preserve">minor vero _
              <emph style="sc">Dg</emph>
            ._ </s>
            <s xml:id="echoid-s2407" xml:space="preserve">Igitur rectarum ex _
              <emph style="sc">G</emph>
            ,_
              <lb/>
              <note position="left" xlink:label="note-072-07" xlink:href="note-072-07a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            ad circunferentiam circuli _A B C D E,_ ductarum, maxima eſt _
              <emph style="sc">G</emph>
            A,_ & </s>
            <s xml:id="echoid-s2408" xml:space="preserve">minima _
              <emph style="sc">G</emph>
            </s>
          </p>
        </div>
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