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

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        <div xml:id="echoid-div103" type="section" level="1" n="59">
          <pb o="25" file="037" n="37" rhead=""/>
          <p>
            <s xml:id="echoid-s923" xml:space="preserve">IN ſphæra data ſumptis vtcunq́ue duobus punctis A, B, deſcribatur ex
              <lb/>
            A, polo, & </s>
            <s xml:id="echoid-s924" xml:space="preserve">interuallo A B, circulus B D, cuius diametro æqualis recta deſcri
              <lb/>
              <note position="right" xlink:label="note-037-01" xlink:href="note-037-01a" xml:space="preserve">18. huius.</note>
            batur F G: </s>
            <s xml:id="echoid-s925" xml:space="preserve">& </s>
            <s xml:id="echoid-s926" xml:space="preserve">fiat ſupra F G, triangulum E F G, habens vtruque reliquorum
              <lb/>
              <figure xlink:label="fig-037-01" xlink:href="fig-037-01a" number="35">
                <image file="037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/037-01"/>
              </figure>
              <note position="right" xlink:label="note-037-02" xlink:href="note-037-02a" xml:space="preserve">Schol 22.
                <lb/>
              primi.</note>
            laterum E F, E G, rectæ ducte
              <lb/>
              <note position="right" xlink:label="note-037-03" xlink:href="note-037-03a" xml:space="preserve">primi.</note>
            A B, æquale. </s>
            <s xml:id="echoid-s927" xml:space="preserve">Deinde ex F, G,
              <lb/>
            ad E F, E G, perpendiculares
              <lb/>
            educantur F H, G H, coeun-
              <lb/>
            tes in H;</s>
            <s xml:id="echoid-s928" xml:space="preserve">iungaturq́; </s>
            <s xml:id="echoid-s929" xml:space="preserve">recta E H.
              <lb/>
            </s>
            <s xml:id="echoid-s930" xml:space="preserve">Dico E H, æqualem eſſe dia-
              <lb/>
            metro datæ ſphæræ. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Ducta em̃
              <lb/>
            ſphæræ diametro A C, traijcia
              <lb/>
            tur per rectas A B, A C, pla-
              <lb/>
            num ſaciens in ſphæra circulũ
              <lb/>
              <note position="right" xlink:label="note-037-04" xlink:href="note-037-04a" xml:space="preserve">1. huius.</note>
            A B C D, qui maximus erit,
              <lb/>
              <note position="right" xlink:label="note-037-05" xlink:href="note-037-05a" xml:space="preserve">6. huius.</note>
            cum per diametrum ſphæræ,
              <lb/>
            atque adeo per centrum eiuſ-
              <lb/>
            dem ducatur. </s>
            <s xml:id="echoid-s932" xml:space="preserve">Quare idẽ per A, polũ circuli B D, ductus circulum B D, bifa-
              <lb/>
              <note position="right" xlink:label="note-037-06" xlink:href="note-037-06a" xml:space="preserve">15. huius.</note>
            riam ſecabit; </s>
            <s xml:id="echoid-s933" xml:space="preserve">ac propterea communis ſectio B D, diameter erit circuli B D.
              <lb/>
            </s>
            <s xml:id="echoid-s934" xml:space="preserve">Iunctis autem rectis A D, D C, erunt duo latera A B, B D, duobus lateribus
              <lb/>
            E F, F G, æqualia, nec non & </s>
            <s xml:id="echoid-s935" xml:space="preserve">baſes A D, E G, æquales. </s>
            <s xml:id="echoid-s936" xml:space="preserve">Eſt enium F G, diame-
              <lb/>
            tro B D, æqualis, ex conſtructione: </s>
            <s xml:id="echoid-s937" xml:space="preserve">& </s>
            <s xml:id="echoid-s938" xml:space="preserve">vtraque E F, E G, rectæ A B, vel A D. </s>
            <s xml:id="echoid-s939" xml:space="preserve">
              <lb/>
            Igitur & </s>
            <s xml:id="echoid-s940" xml:space="preserve">anguli A B D, E F G, æquales erunt. </s>
            <s xml:id="echoid-s941" xml:space="preserve">Eſt autem angulo A B D, an-
              <lb/>
              <note position="right" xlink:label="note-037-07" xlink:href="note-037-07a" xml:space="preserve">8. primi.</note>
            gulus A C D, æqualis: </s>
            <s xml:id="echoid-s942" xml:space="preserve">& </s>
            <s xml:id="echoid-s943" xml:space="preserve">angulo E F G, angulus E H G, vt in præcedenti
              <lb/>
              <note position="right" xlink:label="note-037-08" xlink:href="note-037-08a" xml:space="preserve">27. tertij.</note>
            propoſ. </s>
            <s xml:id="echoid-s944" xml:space="preserve">demonſtratum eſt. </s>
            <s xml:id="echoid-s945" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s946" xml:space="preserve">anguli A C D, E H G, æquales erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s947" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s948" xml:space="preserve">recti A D C, E G H, æquales, & </s>
            <s xml:id="echoid-s949" xml:space="preserve">latus A D, lateri E G, quod
              <lb/>
            vni æqualium angulorum obijcitur, æquale. </s>
            <s xml:id="echoid-s950" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s951" xml:space="preserve">recta E H, rectæ A C,
              <lb/>
              <note position="right" xlink:label="note-037-09" xlink:href="note-037-09a" xml:space="preserve">26. primi.</note>
            æqualis erit. </s>
            <s xml:id="echoid-s952" xml:space="preserve">Lineam igitur rectam E H, deſcripſimus æqualẽ diametro A C,
              <lb/>
            datæ ſphæræ. </s>
            <s xml:id="echoid-s953" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s954" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div105" type="section" level="1" n="60">
          <head xml:id="echoid-head71" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s955" xml:space="preserve">_ADDITVR_in alia verſione ſequens hoc Theorema.</s>
            <s xml:id="echoid-s956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s957" xml:space="preserve">LINEA recta à polo cuiuſuis circuli in ſphæra ad ſuperficiem
              <lb/>
              <note position="right" xlink:label="note-037-10" xlink:href="note-037-10a" xml:space="preserve">30.</note>
            ſphæræ ducta, quæ ſit æqualis lineæ rectæ ab eodem polo ad circun-
              <lb/>
            ferentiam circuli ductæ, in circuli circunferentiam cadit.</s>
            <s xml:id="echoid-s958" xml:space="preserve"/>
          </p>
          <figure number="36">
            <image file="037-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/037-02"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s959" xml:space="preserve">_IN_ſphæra ex _A,_ polo circuli _B C,_ recta du-
              <lb/>
            cta ſit vtcumque _A D,_ ad eius circunferentiã,
              <lb/>
            quæ minor erit diametro ſphæræ, atque adeo dia
              <lb/>
            metro circuli maximi in ſphæra, cum diameter
              <lb/>
            ſphæræ ſit omnium rectarum in ſphæra ductarũ
              <lb/>
            maxima Ducatur iam ex eodem polo A. </s>
            <s xml:id="echoid-s960" xml:space="preserve">ad ſu-
              <lb/>
            perficiem ſphæræ recta _A E,_ quæ ipſi _A D,_ æqua-
              <lb/>
            lis ſit. </s>
            <s xml:id="echoid-s961" xml:space="preserve">Dico rectam A E, caderein circunferen-
              <lb/>
            tiam circuli _B C._ </s>
            <s xml:id="echoid-s962" xml:space="preserve">Si enim ſi eri poteſt, non cadat
              <lb/>
            in eius circunferentiam. </s>
            <s xml:id="echoid-s963" xml:space="preserve">Et per rectam _A E,_ & </s>
            <s xml:id="echoid-s964" xml:space="preserve">
              <lb/>
            centrum ſphæræ ducatur planũ faciens in ſphæ-
              <lb/>
              <note position="right" xlink:label="note-037-11" xlink:href="note-037-11a" xml:space="preserve">1. huius.</note>
            </s>
          </p>
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