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

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          <p>
            <s xml:id="echoid-s1249" xml:space="preserve">
              <pb o="34" file="046" n="46" rhead=""/>
            Ex polo igitur E, & </s>
            <s xml:id="echoid-s1250" xml:space="preserve">ad interuallum E B, circulus deſcribatur B F. </s>
            <s xml:id="echoid-s1251" xml:space="preserve">Dico cir-
              <lb/>
            culum maximum A B, tangere quoque circulum B F, in B, & </s>
            <s xml:id="echoid-s1252" xml:space="preserve">circulum B F,
              <lb/>
            æqualem eſſe, ac parallelum circulo A C. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">Quoniam enim recta D E, per po-
              <lb/>
            los circulorũ A C, B F, tranſiens perpendicularis eſt ad ipſos circulos, erunt
              <lb/>
              <figure xlink:label="fig-046-01" xlink:href="fig-046-01a" number="52">
                <image file="046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/046-01"/>
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              <note position="left" xlink:label="note-046-01" xlink:href="note-046-01a" xml:space="preserve">10. i. huius.</note>
            circuli A C, B F, paralleli. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">Rurſus quia cir
              <lb/>
              <note position="left" xlink:label="note-046-02" xlink:href="note-046-02a" xml:space="preserve">14. vndec.</note>
            culi maximi in ſphęra bifariam ſe ſecant, ſe-
              <lb/>
              <note position="left" xlink:label="note-046-03" xlink:href="note-046-03a" xml:space="preserve">11. 1. huius.</note>
            micirculus erit A C B; </s>
            <s xml:id="echoid-s1255" xml:space="preserve">atque adeo ſemicir-
              <lb/>
            culo D C E, æqualis. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">Dempto ergo commu
              <lb/>
            ni arcu B D, æquales remanebũt arcus D A,
              <lb/>
            E B; </s>
            <s xml:id="echoid-s1257" xml:space="preserve">atque adeo rectæ D A, E B, à polis D,
              <lb/>
              <note position="left" xlink:label="note-046-04" xlink:href="note-046-04a" xml:space="preserve">29. tertij.</note>
            E, ad circunferentias circulorum A C, B F,
              <lb/>
            ductæ æquales. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">Quare æquales ſunt circuli
              <lb/>
              <note position="left" xlink:label="note-046-05" xlink:href="note-046-05a" xml:space="preserve">Schol. 21.
                <lb/>
              1. huius.</note>
            A C, B F. </s>
            <s xml:id="echoid-s1259" xml:space="preserve">Denique quia circuli A B, B F, in
              <lb/>
            eodem puncto B, ſecant maximum circulũ
              <lb/>
            A E B, in quo quidem polos habent, ſe
              <lb/>
            mutuo tangent in B, circuli A B, B F. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Qua-
              <lb/>
              <note position="left" xlink:label="note-046-06" xlink:href="note-046-06a" xml:space="preserve">3. huius.</note>
            re circulus maximus A B, tangens in ſphæra
              <lb/>
            circulum A C, tangit quoque alterum circulum B F, ipſi A C, æqualem, & </s>
            <s xml:id="echoid-s1261" xml:space="preserve">
              <lb/>
            parallelũ. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Ac proinde ſi in ſphæra maximus circulus aliquem circulorum, &</s>
            <s xml:id="echoid-s1263" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s1264" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1265" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div142" type="section" level="1" n="78">
          <head xml:id="echoid-head90" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s1266" xml:space="preserve">HINC perſpicuum eſt, puncta contactuum A, B, per diametrum eſſe oppoſita. </s>
            <s xml:id="echoid-s1267" xml:space="preserve">Oſten-
              <lb/>
            ſum enim eſt, A C B, eſſe ſemicirculum, ac propterea rectam ex A, ad B, ductam eſſe dia-
              <lb/>
            metrum ſphæræ, ſen circuli maximi A C B, &</s>
            <s xml:id="echoid-s1268" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1269" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">8.</note>
        </div>
        <div xml:id="echoid-div143" type="section" level="1" n="79">
          <head xml:id="echoid-head91" xml:space="preserve">THEOREMA 7. PROPOS. 7.</head>
          <p>
            <s xml:id="echoid-s1270" xml:space="preserve">SI ſint in ſphæra duo æquales, & </s>
            <s xml:id="echoid-s1271" xml:space="preserve">paralleli cir-
              <lb/>
            culi, maximus circulus, qui eorum alterum tetige
              <lb/>
            rit, reliquum quoque tanget.</s>
            <s xml:id="echoid-s1272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1273" xml:space="preserve">IN eadem figura ſint duo circuli æquales, & </s>
            <s xml:id="echoid-s1274" xml:space="preserve">paralleli A C, B F, & </s>
            <s xml:id="echoid-s1275" xml:space="preserve">maxi-
              <lb/>
            mus A B, tangat A C. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Dico eundem A B, tangere quoque B F. </s>
            <s xml:id="echoid-s1277" xml:space="preserve">Sienim A B,
              <lb/>
            non tangat ipſum B F, tanget vtique alterum ipſi A C, æqualem, & </s>
            <s xml:id="echoid-s1278" xml:space="preserve">paralle-
              <lb/>
              <note position="left" xlink:label="note-046-08" xlink:href="note-046-08a" xml:space="preserve">6. huius.</note>
            lum. </s>
            <s xml:id="echoid-s1279" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s1280" xml:space="preserve">B F, eidem A C, æqualis ponatur, & </s>
            <s xml:id="echoid-s1281" xml:space="preserve">parellelus, erunt tres
              <lb/>
            circuli in ſphæra, nempe A C, B F, & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">ille alius, quem A B, tangit, inter ſe
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s1283" xml:space="preserve">paralleli. </s>
            <s xml:id="echoid-s1284" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s1285" xml:space="preserve">Non enim plures circuli æquales
              <lb/>
              <note position="left" xlink:label="note-046-09" xlink:href="note-046-09a" xml:space="preserve">Schol. 2.
                <lb/>
              huius.</note>
            ſunt, & </s>
            <s xml:id="echoid-s1286" xml:space="preserve">paralleli in ſphæra, quàm duo. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">Tanget igitur circulus A B, circulũ
              <lb/>
            B F. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">Quamobrẽ, ſi ſint in ſphæra duo æquales, & </s>
            <s xml:id="echoid-s1289" xml:space="preserve">paralleli circuli, &</s>
            <s xml:id="echoid-s1290" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1291" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s1292" xml:space="preserve"/>
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        <div xml:id="echoid-div145" type="section" level="1" n="80">
          <head xml:id="echoid-head92" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1293" xml:space="preserve">_IN_ alia verſione demonſtratur & </s>
            <s xml:id="echoid-s1294" xml:space="preserve">ſequens theorema.</s>
            <s xml:id="echoid-s1295" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1296" xml:space="preserve">CIRCVLI in ſphæra paralleli, quos maximus aliquis circu-
              <lb/>
              <note position="left" xlink:label="note-046-10" xlink:href="note-046-10a" xml:space="preserve">9.</note>
            lus tangit, æquales inter ſe ſunt.</s>
            <s xml:id="echoid-s1297" xml:space="preserve"/>
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