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

Table of figures

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        <div xml:id="echoid-div1296" type="section" level="1" n="602">
          <head xml:id="echoid-head637" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s16152" xml:space="preserve">QVOD ſi anguli B, E, vel C, F, non forent æquales, ſed ſolum æquales duobus
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            rectis, adhuc theorematis veritas vetineretur: </s>
            <s xml:id="echoid-s16153" xml:space="preserve">propterea quod anguli B, E, ſemper
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            æquales ſinus rectos habent, ſiue ipſi inter ſe æquales ſint, ſiue æquales duobus re-
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            ctis. </s>
            <s xml:id="echoid-s16154" xml:space="preserve">quod etiam de angulis C, F, dicendum eſt. </s>
            <s xml:id="echoid-s16155" xml:space="preserve">Id quod perſpicue conſtare poteſt ex
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            ijs, quæ in tractatione ſinuum tradidimus.</s>
            <s xml:id="echoid-s16156" xml:space="preserve"/>
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        <div xml:id="echoid-div1297" type="section" level="1" n="603">
          <head xml:id="echoid-head638" xml:space="preserve">THEOR. 58. PROPOS. 60.</head>
          <p>
            <s xml:id="echoid-s16157" xml:space="preserve">SI ab angulo ſphærici trianguli ad baſim arcus
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            maximi circuli demittatur diuidens angulum bi-
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            fariam: </s>
            <s xml:id="echoid-s16158" xml:space="preserve">habebunt ſinus ſegmentorum baſis ean-
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            dem proportionem, quam ſinus reliquorum duo-
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            rum arcuum. </s>
            <s xml:id="echoid-s16159" xml:space="preserve">Et ſi ſinus ſegmentorum baſis ean-
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            dem proportionem habeant, quam ſinus reliquo-
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            rum duorum arcuum: </s>
            <s xml:id="echoid-s16160" xml:space="preserve">diuidet arcus demiſſus an-
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            gulum bifariam.</s>
            <s xml:id="echoid-s16161" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16162" xml:space="preserve">IN triangulo ſphærico ABC, ſecet arcus AD, angulum A, bifariam. </s>
            <s xml:id="echoid-s16163" xml:space="preserve">Di-
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            co ita eſſe ſinum arcus AB, ad ſinum arcus AC, vt eſt, ſinus arcus BD, ad ſi-
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            num arcus DC. </s>
            <s xml:id="echoid-s16164" xml:space="preserve">Quia enim triangula ABD, ACD, angulos ad A, habent
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              <note position="left" xlink:label="note-468-01" xlink:href="note-468-01a" xml:space="preserve">59. huius.
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              & eius ſcho
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              hum.</note>
            æquales, & </s>
            <s xml:id="echoid-s16165" xml:space="preserve">angulos ad D, æquales duobus rectis; </s>
            <s xml:id="echoid-s16166" xml:space="preserve">erit, vt ſinus arcus AB, ad
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            ſinum arcus BD, ita ſinus arcus AC, ad ſinum arcus CD:
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            </s>
            <s xml:id="echoid-s16167" xml:space="preserve">Et permutando, vt ſinus arcus AB, ad ſinum arcus AC,
              <lb/>
              <figure xlink:label="fig-468-01" xlink:href="fig-468-01a" number="336">
                <image file="468-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/468-01"/>
              </figure>
            ita ſinus arcus BD, ad ſinum arcus DC. </s>
            <s xml:id="echoid-s16168" xml:space="preserve">quod eſt pro-
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            poſitum.</s>
            <s xml:id="echoid-s16169" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16170" xml:space="preserve">SED iam ſit, vt ſinus arcus AB, ad ſinum arcus AC,
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            ita ſinus arcus BD, ad ſinum arcus DC. </s>
            <s xml:id="echoid-s16171" xml:space="preserve">Dico angulum
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            A, ſectum eſſe bifariam. </s>
            <s xml:id="echoid-s16172" xml:space="preserve">Erit enim permutando quoque,
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            vt ſinus arcus AB, ad ſinum arcus BD, ita ſinus arcus AC,
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            ad ſinũ arcus CD. </s>
            <s xml:id="echoid-s16173" xml:space="preserve">Habent igitur triangula ABD, ACD,
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            angulos ad D, ęquales duobus rectis, & </s>
            <s xml:id="echoid-s16174" xml:space="preserve">ſinus arcuum circa
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            angulos B, C, proportionales, homologiq́; </s>
            <s xml:id="echoid-s16175" xml:space="preserve">ſunt finus arcuũ angulis ad D, op-
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            poſitorũ. </s>
            <s xml:id="echoid-s16176" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s16177" xml:space="preserve">anguli ad A, vel æquales erunt inter ſe, vel duobus rectis æ-
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              <note position="left" xlink:label="note-468-02" xlink:href="note-468-02a" xml:space="preserve">59. huius.
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              & eius ſeho
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              lium.</note>
            quales: </s>
            <s xml:id="echoid-s16178" xml:space="preserve">Non poſſunt autẽ duobus rectis eſſe æquales, quod angulus A, ſit duo-
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            bus rectis minor. </s>
            <s xml:id="echoid-s16179" xml:space="preserve">Igitur æquales inter ſe erunt. </s>
            <s xml:id="echoid-s16180" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s16181" xml:space="preserve">Si igitur
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            ab angulo ſphærici trianguli ad baſim, &</s>
            <s xml:id="echoid-s16182" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16183" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s16184" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1300" type="section" level="1" n="604">
          <head xml:id="echoid-head639" xml:space="preserve">THEOR. 59. PROPOS. 61.</head>
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            <s xml:id="echoid-s16185" xml:space="preserve">SI ab angulo ſphærici triáguli ad baſim, </s>
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