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

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            <s xml:id="echoid-s8651" xml:space="preserve">
              <pb o="297" file="309" n="309" rhead=""/>
            quæ angulum continent, interiectus: </s>
            <s xml:id="echoid-s8652" xml:space="preserve">ita vt quot graduum fuerit ille arcus, totidem
              <lb/>
              <note position="right" xlink:label="note-309-01" xlink:href="note-309-01a" xml:space="preserve">Angulus r@
                <lb/>
              ctilineus eſt
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              tot partiũ,
                <lb/>
              quot gra-
                <lb/>
              duũ eſt ar-
                <lb/>
              cus circuli,
                <lb/>
              cui in cen-
                <lb/>
              tro inſiſtit.</note>
            partium ſit & </s>
            <s xml:id="echoid-s8653" xml:space="preserve">angulus, qualium quatuor recti ſunt 360. </s>
            <s xml:id="echoid-s8654" xml:space="preserve">aut vnus rectus 90. </s>
            <s xml:id="echoid-s8655" xml:space="preserve">Ex
              <lb/>
            quo fit, indifferenter ſinum anguli rectilinei pro ſinù arcus accipi poſſe, & </s>
            <s xml:id="echoid-s8656" xml:space="preserve">contra;
              <lb/>
            </s>
            <s xml:id="echoid-s8657" xml:space="preserve">quod etiam de tangente, & </s>
            <s xml:id="echoid-s8658" xml:space="preserve">ſecante intelligatur: </s>
            <s xml:id="echoid-s8659" xml:space="preserve">quandoquidem arcus, & </s>
            <s xml:id="echoid-s8660" xml:space="preserve">angulus il-
              <lb/>
            li in centro inſiſtens eundem habent partium numerum, licet diuerſi generis, cum par
              <lb/>
            tes arcus ſint arcus, partes vero anguli ſint anguli: </s>
            <s xml:id="echoid-s8661" xml:space="preserve">quamuis & </s>
            <s xml:id="echoid-s8662" xml:space="preserve">partes anguli dici
              <lb/>
            poſsint arcus, ita vt angulus dicatur habere tot gradus, quot in arcu, cui inſiſtit,
              <lb/>
            comprehenduntur.</s>
            <s xml:id="echoid-s8663" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8664" xml:space="preserve">QVANDOCVNQVE ergo arcus angulum rectilineum metiens eſt quadrãs,
              <lb/>
            id eſt, quarta pars totius circunferentiæ, angulus ei inſiſtens in centro rectus erit,
              <lb/>
            nempe quarta pars quatuor rectorum, quibus ſpatium, quod circumſtat centrum
              <lb/>
              <note position="right" xlink:label="note-309-02" xlink:href="note-309-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              15. primi.</note>
            circuli æqualiter omnes partes circunferentiæ reſpiciens, æquale eſt; </s>
            <s xml:id="echoid-s8665" xml:space="preserve">quando autem
              <lb/>
            arcus idem eſt quadrante minor, angulus quoq; </s>
            <s xml:id="echoid-s8666" xml:space="preserve">minor erit recto, nempe acutus: </s>
            <s xml:id="echoid-s8667" xml:space="preserve">quan
              <lb/>
            do deniq; </s>
            <s xml:id="echoid-s8668" xml:space="preserve">arcus eſt maior quadrante, angulus etiam recto maior erit, nimirum obtu-
              <lb/>
            ſus. </s>
            <s xml:id="echoid-s8669" xml:space="preserve">
              <emph style="sc">E</emph>
            t contra, quando angulus eſt rectus, erit arcus illum metiens quadrans: </s>
            <s xml:id="echoid-s8670" xml:space="preserve">quan-
              <lb/>
            do acutus, quadrante minor: </s>
            <s xml:id="echoid-s8671" xml:space="preserve">quando deniq; </s>
            <s xml:id="echoid-s8672" xml:space="preserve">obtuſus, maior quadrante. </s>
            <s xml:id="echoid-s8673" xml:space="preserve">Quæ omnia
              <lb/>
            ex lemmate ſequenti erunt perſpicua.</s>
            <s xml:id="echoid-s8674" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div772" type="section" level="1" n="451">
          <head xml:id="echoid-head483" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s8675" xml:space="preserve">RECTÆ lineæ angulum rectum comprehendentes abſcindũt
              <lb/>
              <note position="right" xlink:label="note-309-03" xlink:href="note-309-03a" xml:space="preserve">Quomodo
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              ſe habeant
                <lb/>
              anguli recti
                <lb/>
              linei ad ar-
                <lb/>
              cus circulo-
                <lb/>
              rú ex ipſis,
                <lb/>
              vt centris,
                <lb/>
              deſcriptorũ,
                <lb/>
              & contra.</note>
            quadrantem ex circulo, qui ex ipſo angulo, vt centro, ad quodcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s8676" xml:space="preserve">interuallum deſcribitur: </s>
            <s xml:id="echoid-s8677" xml:space="preserve">lineæ vero rectæ angulum acutum conti-
              <lb/>
            nentes auferunt arcum quadrante minorem: </s>
            <s xml:id="echoid-s8678" xml:space="preserve">lineæ deniq; </s>
            <s xml:id="echoid-s8679" xml:space="preserve">rectę con-
              <lb/>
            ſtituentes angulum obtuſum intercipiunt in eodem circulo arcum
              <lb/>
            maiorem quadrante. </s>
            <s xml:id="echoid-s8680" xml:space="preserve">Et contra, rectæ lineæ ex centro circuli egre-
              <lb/>
            dientes, quadrantemq́; </s>
            <s xml:id="echoid-s8681" xml:space="preserve">intercipientes conſtituunt angulum rectum: </s>
            <s xml:id="echoid-s8682" xml:space="preserve">
              <lb/>
            lineæ vero arcum quadrante minorem abſcindentes angulum acu-
              <lb/>
            tum continent: </s>
            <s xml:id="echoid-s8683" xml:space="preserve">rectæ deniq; </s>
            <s xml:id="echoid-s8684" xml:space="preserve">lineæ auſerentes arcum maiorem qua-
              <lb/>
            drante obtuſum angulum comprehendunt.</s>
            <s xml:id="echoid-s8685" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8686" xml:space="preserve">RECTAE lineæ AB, CB, angulum rectum contineant ABC, & </s>
            <s xml:id="echoid-s8687" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-309-01" xlink:href="fig-309-01a" number="158">
                <image file="309-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/309-01"/>
              </figure>
            ex B, circulus deſcribatur ACDE. </s>
            <s xml:id="echoid-s8688" xml:space="preserve">Dico
              <lb/>
            arcum AC, quadrantem eſſe, &</s>
            <s xml:id="echoid-s8689" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8690" xml:space="preserve">Quoniam
              <lb/>
            enim eſt, vt angulus ABC, in centro ad qua-
              <lb/>
              <note position="right" xlink:label="note-309-04" xlink:href="note-309-04a" xml:space="preserve">Coroll. 2.
                <lb/>
              33. ſexti.</note>
            tuor rectos, ita arcus AC, ad totam circun.
              <lb/>
            </s>
            <s xml:id="echoid-s8691" xml:space="preserve">ferentiam; </s>
            <s xml:id="echoid-s8692" xml:space="preserve">eſt autem angulus ABC, cum re-
              <lb/>
            ctus ſit, quarta pars quatuor rectorum: </s>
            <s xml:id="echoid-s8693" xml:space="preserve">erit
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s8694" xml:space="preserve">arcus AC, totius circunferentiæ quar
              <lb/>
            t a pars, id eſt, quadrans. </s>
            <s xml:id="echoid-s8695" xml:space="preserve">Quoniam vero re-
              <lb/>
            cta linea conſtituens cum recta AB, in pun-
              <lb/>
            cto B, angulum acutum cadit in arcum AC,
              <lb/>
            recta vero linea cum eadem AB, conſtituens angulum obtuſum in puncto
              <lb/>
            B, cadit in arcum CD; </s>
            <s xml:id="echoid-s8696" xml:space="preserve">liquido conſtat, rectas lineas angulum acutum </s>
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