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

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        <div xml:id="echoid-div99" type="section" level="1" n="57">
          <p>
            <s xml:id="echoid-s876" xml:space="preserve">
              <pb o="24" file="036" n="36" rhead=""/>
            munis fectio circulorum diameter erit circuli maximi A C B; </s>
            <s xml:id="echoid-s877" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s878" xml:space="preserve">
              <lb/>
            ſphæræ. </s>
            <s xml:id="echoid-s879" xml:space="preserve">Quoniamverò circulus maximus A C B, circulum A B, per polos ſe-
              <lb/>
            cans ſecat bifariam, erit quoq; </s>
            <s xml:id="echoid-s880" xml:space="preserve">A B, communis ſectio diameter circuli A B,
              <lb/>
              <note position="left" xlink:label="note-036-01" xlink:href="note-036-01a" xml:space="preserve">15. huius.</note>
            ac proinde cum & </s>
            <s xml:id="echoid-s881" xml:space="preserve">ſphæræ diameter ſit, circulus maximus erit A B. </s>
            <s xml:id="echoid-s882" xml:space="preserve">Si in ſphæ
              <lb/>
            ra ergo ſit circulus, à cuius polo, &</s>
            <s xml:id="echoid-s883" xml:space="preserve">c. </s>
            <s xml:id="echoid-s884" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s885" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div101" type="section" level="1" n="58">
          <head xml:id="echoid-head69" xml:space="preserve">PROBL. 2. PROP. 18.</head>
          <note position="left" xml:space="preserve">28.</note>
          <p>
            <s xml:id="echoid-s886" xml:space="preserve">LINEAM rectam deſcribere æqualem dia-
              <lb/>
            metro circuli cuiuſlibetin ſphæra dati.</s>
            <s xml:id="echoid-s887" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s888" xml:space="preserve">IN ſphæra ſit datus circulus quilibet A B C D, cuius diametro rectam
              <lb/>
            æqualem oporteat deſcribere. </s>
            <s xml:id="echoid-s889" xml:space="preserve">Sumptis tribus punctis in circunferentia circu
              <lb/>
            li vtcunq; </s>
            <s xml:id="echoid-s890" xml:space="preserve">A, B, D, & </s>
            <s xml:id="echoid-s891" xml:space="preserve">iunctis rectis A B, A D, B D, conſtituatur triangulo
              <lb/>
            A B D, triangulum æquale E F G, ita vt latus E F, lateri A B, & </s>
            <s xml:id="echoid-s892" xml:space="preserve">E G, ipfi
              <lb/>
              <figure xlink:label="fig-036-01" xlink:href="fig-036-01a" number="34">
                <image file="036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/036-01"/>
              </figure>
              <note position="left" xlink:label="note-036-03" xlink:href="note-036-03a" xml:space="preserve">Schol 22.
                <lb/>
              primi.</note>
            A D, & </s>
            <s xml:id="echoid-s893" xml:space="preserve">F G, ipſi B D, æqua-
              <lb/>
            le ſit. </s>
            <s xml:id="echoid-s894" xml:space="preserve">Deinde ex G, F, ducan-
              <lb/>
            tur ad rectas E F, E G, perpen
              <lb/>
            diculares F H, G H, coeuntes
              <lb/>
            in H, connectaturq́; </s>
            <s xml:id="echoid-s895" xml:space="preserve">recta E H.
              <lb/>
            </s>
            <s xml:id="echoid-s896" xml:space="preserve">Dico E H, æqualem eſſe diame
              <lb/>
            tro circuli A B C D. </s>
            <s xml:id="echoid-s897" xml:space="preserve">Ducta enim
              <lb/>
            diam etro A C, iungatur recta
              <lb/>
            D C. </s>
            <s xml:id="echoid-s898" xml:space="preserve">Quoniam vero quatuor
              <lb/>
            anguli quadrilateri E F H G,
              <lb/>
            quatuor rectis æquales ſunt,
              <lb/>
              <note position="left" xlink:label="note-036-04" xlink:href="note-036-04a" xml:space="preserve">Schol. 32.
                <lb/>
              primi.</note>
            ſuntq́; </s>
            <s xml:id="echoid-s899" xml:space="preserve">E F H, E G H, recti;
              <lb/>
            </s>
            <s xml:id="echoid-s900" xml:space="preserve">erunt F E G, F H G, duobus re
              <lb/>
            ctis æquales; </s>
            <s xml:id="echoid-s901" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s902" xml:space="preserve">adeo in quadrilatero E F H G, duo quilibet anguli ex ad-
              <lb/>
            uerſo duobus rectis æqua les erunt. </s>
            <s xml:id="echoid-s903" xml:space="preserve">Quare circa ipſum circulus deſcribi po-
              <lb/>
              <note position="left" xlink:label="note-036-05" xlink:href="note-036-05a" xml:space="preserve">Schol. 22.
                <lb/>
              tertij.</note>
            teſt: </s>
            <s xml:id="echoid-s904" xml:space="preserve">quo deſcripto erunt anguli E F G, E H G, eidem ſegmento, cuius chor
              <lb/>
            da E G, inſiſtentes, æquales. </s>
            <s xml:id="echoid-s905" xml:space="preserve">Eſt autem angulus E F G, angulo A B D, æqua-
              <lb/>
              <note position="left" xlink:label="note-036-06" xlink:href="note-036-06a" xml:space="preserve">27. tertij.</note>
            lis; </s>
            <s xml:id="echoid-s906" xml:space="preserve">quod duo latera E F, F G, duobus lateribus A B, B D, æqualia ſint, & </s>
            <s xml:id="echoid-s907" xml:space="preserve">ba-
              <lb/>
              <note position="left" xlink:label="note-036-07" xlink:href="note-036-07a" xml:space="preserve">8. primi.</note>
            ſis E G, baſi A D, ex conſtructione: </s>
            <s xml:id="echoid-s908" xml:space="preserve">& </s>
            <s xml:id="echoid-s909" xml:space="preserve">angulus A B D, angulo A C D, æqua-
              <lb/>
              <note position="left" xlink:label="note-036-08" xlink:href="note-036-08a" xml:space="preserve">27. tertij.</note>
            lis eſt. </s>
            <s xml:id="echoid-s910" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s911" xml:space="preserve">angulus E H G, angulo A C D, æqualis erit. </s>
            <s xml:id="echoid-s912" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s913" xml:space="preserve">re-
              <lb/>
            ctus angulus E G H, angulo A D C, æqualis, quòd hic quoque rectus ſit in ſe-
              <lb/>
              <note position="left" xlink:label="note-036-09" xlink:href="note-036-09a" xml:space="preserve">31. tertij.</note>
            micirculo A D C, exiſtens. </s>
            <s xml:id="echoid-s914" xml:space="preserve">Igitur triangula E H G, A C D, duos angulos
              <lb/>
            duobus angulis æquales habent, necnon & </s>
            <s xml:id="echoid-s915" xml:space="preserve">latus E G, lateri A D, quod æqua-
              <lb/>
              <note position="left" xlink:label="note-036-10" xlink:href="note-036-10a" xml:space="preserve">26. primi.</note>
            lium angulorum vni ſubtenditur, æquale. </s>
            <s xml:id="echoid-s916" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s917" xml:space="preserve">latus E H, lateri A C,
              <lb/>
            æquale erit. </s>
            <s xml:id="echoid-s918" xml:space="preserve">Lineam igitur rectam E H, deſcripſimus æqualem diametro A C,
              <lb/>
            circuli A B C D. </s>
            <s xml:id="echoid-s919" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s920" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div103" type="section" level="1" n="59">
          <head xml:id="echoid-head70" xml:space="preserve">PROBL. 3. PROPOS. 19.</head>
          <note position="left" xml:space="preserve">29.</note>
          <p>
            <s xml:id="echoid-s921" xml:space="preserve">LINEAM rectam deſcribere æqualem dia-
              <lb/>
            metro datæ ſphæræ.</s>
            <s xml:id="echoid-s922" xml:space="preserve"/>
          </p>
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