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

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        <div xml:id="echoid-div216" type="section" level="1" n="104">
          <p style="it">
            <s xml:id="echoid-s2302" xml:space="preserve">
              <pb o="59" file="071" n="71" rhead=""/>
            maiorem eſſe, quàm _F B,_ &</s>
            <s xml:id="echoid-s2303" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">Maxima ergo omnium eſt recta _F D._ </s>
            <s xml:id="echoid-s2305" xml:space="preserve">Præterea in om-
              <lb/>
            nibus figuris erunt duo quadrata ex _G C,_ _
              <emph style="sc">G</emph>
            F,_ maiora duobus quadratis ex _
              <emph style="sc">GB</emph>
            ,_
              <lb/>
            _
              <emph style="sc">G</emph>
            F:_ </s>
            <s xml:id="echoid-s2306" xml:space="preserve">quibus cum æqualia ſint quadrata ex _F C,
              <emph style="sc">Fb</emph>
            ;_ </s>
            <s xml:id="echoid-s2307" xml:space="preserve">erit quoque quadratum ex _F C,_
              <lb/>
              <note position="right" xlink:label="note-071-01" xlink:href="note-071-01a" xml:space="preserve">47. primi.</note>
            maius quadrato ex _FB;_ </s>
            <s xml:id="echoid-s2308" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s2309" xml:space="preserve">recta _F C,_ maior erit, quàm _F B._ </s>
            <s xml:id="echoid-s2310" xml:space="preserve">Non ali-
              <lb/>
            ter oſtendemus, rectam _F C,_ quæ propinquior eſt maximæ _F D,_ maiorem eſſe quacun-
              <lb/>
            quealia remotiore, &</s>
            <s xml:id="echoid-s2311" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2312" xml:space="preserve">Adhuc in omnibus figuris erunt duo quadrata ex _G I,
              <emph style="sc">G</emph>
            F,_
              <lb/>
            minora duobus quadratis ex _
              <emph style="sc">G</emph>
            H,
              <emph style="sc">G</emph>
            F:_ </s>
            <s xml:id="echoid-s2313" xml:space="preserve">quibus cum æqualia ſint quadrata ex _F I,_
              <lb/>
              <note position="right" xlink:label="note-071-02" xlink:href="note-071-02a" xml:space="preserve">47. primi.</note>
            _FH;_ </s>
            <s xml:id="echoid-s2314" xml:space="preserve">erit quoque quadratum ex _F I,_ minus quadrato ex _FH;_ </s>
            <s xml:id="echoid-s2315" xml:space="preserve">proptereaq́ & </s>
            <s xml:id="echoid-s2316" xml:space="preserve">recta
              <lb/>
            _F I,_ minor, quàm _F H,_ erit. </s>
            <s xml:id="echoid-s2317" xml:space="preserve">Eodemq́; </s>
            <s xml:id="echoid-s2318" xml:space="preserve">modo demonſtrabimus, rectam _F I,_ quæ pro-
              <lb/>
            pinquior eſt minimæ _F A,_ minorem eſſe quacunque alia remotiore, &</s>
            <s xml:id="echoid-s2319" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2320" xml:space="preserve">Poſtremo
              <lb/>
            erunt duo quadrata ex _
              <emph style="sc">G</emph>
            C,
              <emph style="sc">G</emph>
            F,_ æqualia duobus quadratis ex _
              <emph style="sc">G</emph>
            E,
              <emph style="sc">G</emph>
            F:_ </s>
            <s xml:id="echoid-s2321" xml:space="preserve">quibus
              <lb/>
            cum æqualia ſint quadrata ex _F C, F E,_ æqualia quoque erunt quadrata ex _F C,_
              <lb/>
              <note position="right" xlink:label="note-071-03" xlink:href="note-071-03a" xml:space="preserve">47. primi.</note>
            _FE;_ </s>
            <s xml:id="echoid-s2322" xml:space="preserve">atque adeò & </s>
            <s xml:id="echoid-s2323" xml:space="preserve">rectæ _F C, F E,_ æquales erunt. </s>
            <s xml:id="echoid-s2324" xml:space="preserve">Conſtat ergo id, quod proponitur.
              <lb/>
            </s>
            <s xml:id="echoid-s2325" xml:space="preserve">Cæterum vt ex demonſtratione patet, eam rectam dicimus propinquiorem maximæ
              <lb/>
            _F D,_ quæ cadit in puctum vicinius pucto _D:_ </s>
            <s xml:id="echoid-s2326" xml:space="preserve">Illam verò propinquiorem minimæ _F A,_
              <lb/>
            quæ cadit in puctum propinquius puncto _A._</s>
            <s xml:id="echoid-s2327" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div219" type="section" level="1" n="105">
          <head xml:id="echoid-head117" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s2328" xml:space="preserve">SI in ſphæræ ſuperficie intra circuli cuiuſque peripheriam pun-
              <lb/>
              <note position="right" xlink:label="note-071-04" xlink:href="note-071-04a" xml:space="preserve">31.</note>
            ctum ſignetur præter eius polum, ab eo autem ad circuli circunfe-
              <lb/>
            rétiam plurimi arcus circulorum maximorum ducantur ſemicircu
              <lb/>
            lo minores; </s>
            <s xml:id="echoid-s2329" xml:space="preserve">maximus eſt, qui per circuli polum ducitur; </s>
            <s xml:id="echoid-s2330" xml:space="preserve">minimus
              <lb/>
            autem, qui ei adiacet: </s>
            <s xml:id="echoid-s2331" xml:space="preserve">Reliquorum verò propinquior maximo, re-
              <lb/>
            motiore ſemper maior eſt: </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Duo verò arcus ab eodem maximo, vel
              <lb/>
            minimo æqualiter remoti inter ſe æquales ſunt.</s>
            <s xml:id="echoid-s2333" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2334" xml:space="preserve">_SIT_ in ſphæra circulus _A B C D E,_ cuius polus F, ſigneturq́; </s>
            <s xml:id="echoid-s2335" xml:space="preserve">in ſphæræ ſuperfi-
              <lb/>
            tie intra peripheriam circuli præter polum _F,_ punctum quodlibet _G,_ à quo plurimi
              <lb/>
              <figure xlink:label="fig-071-01" xlink:href="fig-071-01a" number="81">
                <image file="071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/071-01"/>
              </figure>
            arcus maximorum circulorum ad circunferen-
              <lb/>
            tiam circuli _A B C D E,_ ducantur, quorum _G A,_
              <lb/>
            in vtramque partem eductus tranſeat per polum
              <lb/>
            F; </s>
            <s xml:id="echoid-s2336" xml:space="preserve">arcus verò _G B,_ propinquior ſit ipſi _G A,_ quàm
              <lb/>
            _GC;_ </s>
            <s xml:id="echoid-s2337" xml:space="preserve">duo denique _G B, G E,_ æqualiter diſtent ab
              <lb/>
            eodem _G A,_ vel à _GD;_ </s>
            <s xml:id="echoid-s2338" xml:space="preserve">ſintque omnes hi arcus ſe-
              <lb/>
            micirculo minores: </s>
            <s xml:id="echoid-s2339" xml:space="preserve">quod tum demam erit, cum
              <lb/>
            ſe mutuo non interſecabunt in alio puncto, quàm
              <lb/>
            in _G._ </s>
            <s xml:id="echoid-s2340" xml:space="preserve">Cum enim circuli maximi ſe mutuo diui-
              <lb/>
              <note position="right" xlink:label="note-071-05" xlink:href="note-071-05a" xml:space="preserve">11. 1. huius.</note>
            dant bifariam, erunt arcus _G A, G E,_ ſemicircu-
              <lb/>
            lo minores, cum nondum ſe interſecent. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">Eademq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2342" xml:space="preserve">ratione erunt alij arcus ex _G,_ exeuntes minores
              <lb/>
            ſemicirculo, ſi ſe mutuo non interſecent. </s>
            <s xml:id="echoid-s2343" xml:space="preserve">Quòd ſi vnus eorum, vt v. </s>
            <s xml:id="echoid-s2344" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">arcus _G A,_
              <lb/>
            eſſet ſemicirculus, tranſirent omnes alij per punctum A, eſſentq́; </s>
            <s xml:id="echoid-s2346" xml:space="preserve">ſemicirculi quoque: </s>
            <s xml:id="echoid-s2347" xml:space="preserve">
              <lb/>
            Si vero _G A,_ eſſet ſemicirculo maior, ſecarent eum omnes alij, antequam ad circun-
              <lb/>
            ferentiam peruenirent, eſſentq́; </s>
            <s xml:id="echoid-s2348" xml:space="preserve">ſemicirculo maiores, vt patst. </s>
            <s xml:id="echoid-s2349" xml:space="preserve">Vnde nihil colligi
              <lb/>
            poſſet. </s>
            <s xml:id="echoid-s2350" xml:space="preserve">Dico arcum _G A,_ omnium eſſe maximum, & </s>
            <s xml:id="echoid-s2351" xml:space="preserve">_G D,_ minimum: </s>
            <s xml:id="echoid-s2352" xml:space="preserve">_G B,_ verò ma-
              <lb/>
            iorem eſſe arcu _
              <emph style="sc">G</emph>
            C;_ </s>
            <s xml:id="echoid-s2353" xml:space="preserve">duos denique _
              <emph style="sc">G</emph>
            B, G E,_ eſſe æquales. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">Quoniam enim arcus _A D,_
              <lb/>
            ſecat circulum _
              <emph style="sc">Ab</emph>
            C,_ bifariam, & </s>
            <s xml:id="echoid-s2355" xml:space="preserve">ad angulos rectos; </s>
            <s xml:id="echoid-s2356" xml:space="preserve">erit recta ſubtenſa _A D,_ dia-
              <lb/>
              <note position="right" xlink:label="note-071-06" xlink:href="note-071-06a" xml:space="preserve">15. 1. huius.</note>
            </s>
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