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

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        <div xml:id="echoid-div320" type="section" level="1" n="149">
          <p style="it">
            <s xml:id="echoid-s3924" xml:space="preserve">
              <pb o="106" file="118" n="118" rhead=""/>
            æqualis eſt angulo alterno _
              <emph style="sc">Aef</emph>
            ;_ </s>
            <s xml:id="echoid-s3925" xml:space="preserve">cuius sinus rectus est, ex defin. </s>
            <s xml:id="echoid-s3926" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3927" xml:space="preserve">recta _
              <emph style="sc">F</emph>
            H,_ quæ
              <lb/>
              <note position="left" xlink:label="note-118-01" xlink:href="note-118-01a" xml:space="preserve">29. primi.</note>
            quidem æqualis eſt lateri _
              <emph style="sc">E</emph>
            K._ </s>
            <s xml:id="echoid-s3928" xml:space="preserve">Eodem pacto vtrumuis reliquorum laterum in trian-
              <lb/>
              <note position="left" xlink:label="note-118-02" xlink:href="note-118-02a" xml:space="preserve">34 primi.</note>
            gulo rectangulo eſt sinus complementi anguli acuti sibi adiacentis, nempe sinus com-
              <lb/>
            plementi illius arcus, cuius alterum latus est sinus rectus. </s>
            <s xml:id="echoid-s3929" xml:space="preserve">Vt in eodem triangulo re-
              <lb/>
              <note position="left" xlink:label="note-118-03" xlink:href="note-118-03a" xml:space="preserve">Si in trian-
                <lb/>
              gulo rectã-
                <lb/>
              gulo latus
                <lb/>
              recto angu
                <lb/>
              lo oppoſi-
                <lb/>
              tũ ſit ſinus
                <lb/>
              totus, erit
                <lb/>
              vttumui re
                <lb/>
              liquorum
                <lb/>
              alterum la
                <lb/>
              tus ſinus re
                <lb/>
              ctus eſt.</note>
            etangulo _
              <emph style="sc">E</emph>
              <emph style="sc">Kf</emph>
            ,_ latus _
              <emph style="sc">F</emph>
            K,_ eſt sinus complementi anguli _
              <emph style="sc">EF</emph>
            K,_ siue arcus _
              <emph style="sc">F</emph>
            A,_ cuius
              <lb/>
            sinui recto _
              <emph style="sc">F</emph>
            H,_ alterũ latus _
              <emph style="sc">E</emph>
            K,_ æquale eſt. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">Item latus _
              <emph style="sc">E</emph>
            K,_ æquale estipsi _
              <emph style="sc">F</emph>
            H,_ si-
              <lb/>
            nui complementi anguli _
              <emph style="sc">FE</emph>
            K,_ siue arcus _
              <emph style="sc">FB</emph>
            ,_ cuius alterum latus _
              <emph style="sc">F</emph>
            K,_ sinus rectus
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s3931" xml:space="preserve">Sed iam lemma, cuius ſupra fecimus mentionem, demon ſtremus.</s>
            <s xml:id="echoid-s3932" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div334" type="section" level="1" n="150">
          <head xml:id="echoid-head176" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s3933" xml:space="preserve">SI in circulo recta linea è centro ducta aliam rectam non per cen
              <lb/>
            trum ductam bifariam ſecet, ſecabit eadem & </s>
            <s xml:id="echoid-s3934" xml:space="preserve">arcum, cui illa recta
              <lb/>
              <note position="left" xlink:label="note-118-04" xlink:href="note-118-04a" xml:space="preserve">Recta linea
                <lb/>
              è cẽtro du-
                <lb/>
              cta ſecans
                <lb/>
              aliam rectã
                <lb/>
              bifariã ſe-
                <lb/>
              cat quoque
                <lb/>
              arcum, cui
                <lb/>
              illa, ſubten
                <lb/>
              ditur, bifa-
                <lb/>
              tiam: Et cõ
                <lb/>
              tra.</note>
            ſubtenditur, bifariam: </s>
            <s xml:id="echoid-s3935" xml:space="preserve">Et ſi arcum ſe cet bifariam, ſecabit quoque re-
              <lb/>
            ctam ei ſubtenſam bifariam.</s>
            <s xml:id="echoid-s3936" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3937" xml:space="preserve">SECET in eadem figura recta EA, rectam FG, bifariam in H,
              <lb/>
              <figure xlink:label="fig-118-01" xlink:href="fig-118-01a" number="116">
                <image file="118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/118-01"/>
              </figure>
            Dico eandem ſecare quo
              <lb/>
            que arcum FG, bifariã
              <lb/>
            in A, & </s>
            <s xml:id="echoid-s3938" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">Ducta
              <lb/>
            enim recta EG; </s>
            <s xml:id="echoid-s3940" xml:space="preserve">quoniã
              <lb/>
            duo latera EF, EH, triã
              <lb/>
            guli EFH, æqualia ſunt
              <lb/>
            duobus lateribus EG,
              <lb/>
            EH, trianguli EGH,
              <lb/>
            vtrumq; </s>
            <s xml:id="echoid-s3941" xml:space="preserve">vtrique; </s>
            <s xml:id="echoid-s3942" xml:space="preserve">baſisq́,
              <lb/>
            HF, baſi HG, ponitur
              <lb/>
            æqualis; </s>
            <s xml:id="echoid-s3943" xml:space="preserve">erit angulus
              <lb/>
              <note position="left" xlink:label="note-118-05" xlink:href="note-118-05a" xml:space="preserve">2. primi.</note>
            FEH, angulo GEH,
              <lb/>
              <note position="left" xlink:label="note-118-06" xlink:href="note-118-06a" xml:space="preserve">25. tertij.</note>
            æqualis. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">Igitur arcus
              <lb/>
            AF, arcui AG, æqualis
              <lb/>
            erit. </s>
            <s xml:id="echoid-s3945" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s3946" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3947" xml:space="preserve">VERVM ſecet iã
              <lb/>
            recta EA, arcum FG,
              <lb/>
            bifariam in A. </s>
            <s xml:id="echoid-s3948" xml:space="preserve">Dico eandem ſecare quoque rectam FG, bifariam in H.
              <lb/>
            </s>
            <s xml:id="echoid-s3949" xml:space="preserve">Quoniam enim arcus AF, AG, æquales ſunt, erunt quoq; </s>
            <s xml:id="echoid-s3950" xml:space="preserve">anguli FEH,
              <lb/>
              <note position="left" xlink:label="note-118-07" xlink:href="note-118-07a" xml:space="preserve">27. tertij.</note>
            GEH, æquales. </s>
            <s xml:id="echoid-s3951" xml:space="preserve">Igitur cum & </s>
            <s xml:id="echoid-s3952" xml:space="preserve">duo latera EF, EH, trianguli EFH,
              <lb/>
            duobus lateribus EG, EH, trianguli EGH, æqualia ſint; </s>
            <s xml:id="echoid-s3953" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s3954" xml:space="preserve">ba-
              <lb/>
            ſes HF, HG, æquales. </s>
            <s xml:id="echoid-s3955" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s3956" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">4. primi.</note>
          <p style="it">
            <s xml:id="echoid-s3957" xml:space="preserve">EX boc ſequitur, rectam EA, quæ arcum FG, bifariam ſecat in A,
              <lb/>
            ſecare quoque rectam FG, bifariam in H; </s>
            <s xml:id="echoid-s3958" xml:space="preserve">vt ſupra poſuimus.</s>
            <s xml:id="echoid-s3959" xml:space="preserve"/>
          </p>
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