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

Table of Notes

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        <div xml:id="echoid-div58" type="section" level="1" n="37">
          <head xml:id="echoid-head48" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s480" xml:space="preserve">SI in ſphæra ſit circulus, & </s>
            <s xml:id="echoid-s481" xml:space="preserve">ab altero polorum eius per centrum
              <lb/>
              <note position="right" xlink:label="note-027-01" xlink:href="note-027-01a" xml:space="preserve">14.</note>
            ſphæræ recta linea ducatur, erit hæc ad planum circuli perpendi-
              <lb/>
            cularis, & </s>
            <s xml:id="echoid-s482" xml:space="preserve">producta cadet in centrum ipſius, & </s>
            <s xml:id="echoid-s483" xml:space="preserve">in reliquum polum.</s>
            <s xml:id="echoid-s484" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s485" xml:space="preserve">_IN_ ſphæra _A B C D,_ cuius centrum _E,_ ſit circulus _B G D H,_ a cuius polo _A,_
              <lb/>
            per _E,_ centrum ſphæræ ducatur recta _A E,_ occurrens plano circuli in _F,_ & </s>
            <s xml:id="echoid-s486" xml:space="preserve">ſuperſi
              <lb/>
            ciei ſphæræ in _C. </s>
            <s xml:id="echoid-s487" xml:space="preserve">D_ico _A E,_ perpendicularem eſſe ad planum circuli, tranſireq́ per
              <lb/>
            eius centrum, & </s>
            <s xml:id="echoid-s488" xml:space="preserve">reliquum polum, hoc eſt, _F,_ eſſe eius centrum; </s>
            <s xml:id="echoid-s489" xml:space="preserve">& </s>
            <s xml:id="echoid-s490" xml:space="preserve">_C,_ reliquum
              <lb/>
              <figure xlink:label="fig-027-01" xlink:href="fig-027-01a" number="20">
                <image file="027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/027-01"/>
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            polum. </s>
            <s xml:id="echoid-s491" xml:space="preserve">_D_uctis enim per _F,_ duabus xectis vtcun-
              <lb/>
            que _B D, G H,_ iungantur extrema cum punctis
              <lb/>
            _A,_ & </s>
            <s xml:id="echoid-s492" xml:space="preserve">_E,_ vt in figura; </s>
            <s xml:id="echoid-s493" xml:space="preserve">eruntq́; </s>
            <s xml:id="echoid-s494" xml:space="preserve">_A B, A H, A D,_
              <lb/>
            _A G,_ ex definitione poli, inter ſe æquales; </s>
            <s xml:id="echoid-s495" xml:space="preserve">nec
              <lb/>
            non & </s>
            <s xml:id="echoid-s496" xml:space="preserve">_E B, E H, E D, E G,_ ſemidiametri ſphæ-
              <lb/>
            ræinter ſe æquales. </s>
            <s xml:id="echoid-s497" xml:space="preserve">Quoniamigitur duo trian-
              <lb/>
            gula _A B E, A D E,_ duo latera _A B, A E,_ duo-
              <lb/>
            bus lateribus _A D, A E,_ & </s>
            <s xml:id="echoid-s498" xml:space="preserve">baſim _E B,_ baſi _E D,_
              <lb/>
            habent æqualem; </s>
            <s xml:id="echoid-s499" xml:space="preserve">erunt anguli _B A E, D A E._
              <lb/>
            </s>
            <s xml:id="echoid-s500" xml:space="preserve">
              <note position="right" xlink:label="note-027-02" xlink:href="note-027-02a" xml:space="preserve">8. primi.</note>
            æquales. </s>
            <s xml:id="echoid-s501" xml:space="preserve">_I_taque duo triangula _A B F, A D F,_
              <lb/>
            duo latera _A B, A F,_ duobus lateribus _A D, A F,_
              <lb/>
            æqualia habent, anguloſq́ ſub ipſis contentos
              <lb/>
            _B A F, D A F,_ æquales, vt proxime oſtenſum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s502" xml:space="preserve">Quare anguli _A F B, A F D,_ æquales erunt, at-
              <lb/>
              <note position="right" xlink:label="note-027-03" xlink:href="note-027-03a" xml:space="preserve">4. primi.</note>
            que adeo recti. </s>
            <s xml:id="echoid-s503" xml:space="preserve">_E_odem modo demonſtrabimus re-
              <lb/>
            ctos eſſe angulos _A F H, A F G,._ </s>
            <s xml:id="echoid-s504" xml:space="preserve">_R_ecta igitur _A F,_ duabus rectis _B D, G H,_ inſiſtit
              <lb/>
            ad angulos rectos. </s>
            <s xml:id="echoid-s505" xml:space="preserve">Quare perpendicularis erit ad planum circuli _B G D H,_ per re-
              <lb/>
              <note position="right" xlink:label="note-027-04" xlink:href="note-027-04a" xml:space="preserve">4. vndec.</note>
            ctas _B D, G H,_ ductum. </s>
            <s xml:id="echoid-s506" xml:space="preserve">_I_taque producta cadet & </s>
            <s xml:id="echoid-s507" xml:space="preserve">in centrum circuli, & </s>
            <s xml:id="echoid-s508" xml:space="preserve">in reli-
              <lb/>
              <note position="right" xlink:label="note-027-05" xlink:href="note-027-05a" xml:space="preserve">9. huius.</note>
            quum polum: </s>
            <s xml:id="echoid-s509" xml:space="preserve">ac proinde _F,_ centrum erit circuli, & </s>
            <s xml:id="echoid-s510" xml:space="preserve">_C,_ reliquus polus. </s>
            <s xml:id="echoid-s511" xml:space="preserve">Quod eſt
              <lb/>
            propoſitum. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Si in ſphæra igitur ſit circulus, &</s>
            <s xml:id="echoid-s513" xml:space="preserve">c. </s>
            <s xml:id="echoid-s514" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s515" xml:space="preserve"/>
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        <div xml:id="echoid-div61" type="section" level="1" n="38">
          <head xml:id="echoid-head49" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s516" xml:space="preserve">HINC fit, circulum maximum, qui per alterum polorum cuiuſlibet circuli in ſphæ-
              <lb/>
            ra tranſit, tranſire quoq; </s>
            <s xml:id="echoid-s517" xml:space="preserve">per polum reliquum. </s>
            <s xml:id="echoid-s518" xml:space="preserve">Nam ſi ex vno polo per centrum ſphæræ dia
              <lb/>
            meter ducatur circuli maximi, qui per illum polum tranſit, cadet hæc in alterum polum,
              <lb/>
            vt demonſtratum eſt. </s>
            <s xml:id="echoid-s519" xml:space="preserve">Idem ergo circulus maximus per reliquum polum tranſibit.</s>
            <s xml:id="echoid-s520" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s521" xml:space="preserve">Et quia diameter circuli maximi eſt quoq; </s>
            <s xml:id="echoid-s522" xml:space="preserve">diameter ſphæræ, manifeſtum eſt, duos po-
              <lb/>
            los circuli cuiuſlibet in ſphæra per diametrum eſſe oppoſitos: </s>
            <s xml:id="echoid-s523" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s524" xml:space="preserve">adeò inter ipſos inter-
              <lb/>
            poſitum eſſe ſemicircuium maximi circuli.</s>
            <s xml:id="echoid-s525" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head50" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s526" xml:space="preserve">SI in ſphæra ſit circulus, & </s>
            <s xml:id="echoid-s527" xml:space="preserve">à centro ſphæræ per centrum circu-
              <lb/>
              <note position="right" xlink:label="note-027-06" xlink:href="note-027-06a" xml:space="preserve">15.</note>
            lirecta linea ducatur, cadet hæc in vtrumque polum circuli.</s>
            <s xml:id="echoid-s528" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s529" xml:space="preserve">_IN_ eadem figura ducatur per _E,_ centrum ſphæræ, & </s>
            <s xml:id="echoid-s530" xml:space="preserve">_F,_ centrum circuli _B G D </s>
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