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

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        <div xml:id="echoid-div320" type="section" level="1" n="149">
          <pb o="102" file="114" n="114" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s3720" xml:space="preserve">_EXPONATVR_ circulus _ABCD,_ cuius centrum _E,_ per quod ducantur duæ
              <lb/>
            diametri _AC, BD,_ ſeſe ad rectos angulos ſecantes & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">totum circulum in quatuor
              <lb/>
            quadrantes equales diuidentes, vtpote qui angulis rectis æqualibus in centro ſub
              <lb/>
              <note position="left" xlink:label="note-114-01" xlink:href="note-114-01a" xml:space="preserve">26. tettij.</note>
            tenduntur: </s>
            <s xml:id="echoid-s3722" xml:space="preserve">ſumanturque arcus æquales _AF, AG:_ </s>
            <s xml:id="echoid-s3723" xml:space="preserve">Item _BF, BI;_ </s>
            <s xml:id="echoid-s3724" xml:space="preserve">& </s>
            <s xml:id="echoid-s3725" xml:space="preserve">rectæ ducantur
              <lb/>
            _FG, FI,_ ſecantes diametros in _H,_ & </s>
            <s xml:id="echoid-s3726" xml:space="preserve">_K._ </s>
            <s xml:id="echoid-s3727" xml:space="preserve">Arcusigitur _FB,_ dicitur complementum
              <lb/>
              <note position="left" xlink:label="note-114-02" xlink:href="note-114-02a" xml:space="preserve">Exẽpla deſi
                <lb/>
              nitionum.</note>
            arcus _FA;_ </s>
            <s xml:id="echoid-s3728" xml:space="preserve">quia quadrans _AB,_ arcum _FA,_ ſuperat arcu _FB._ </s>
            <s xml:id="echoid-s3729" xml:space="preserve">Eadem ratione arcus
              <lb/>
            _FA,_ complementum nominatur arcus _FB._ </s>
            <s xml:id="echoid-s3730" xml:space="preserve">Item arcus _BI,_ complementum appellatur
              <lb/>
            arcus _AI;_ </s>
            <s xml:id="echoid-s3731" xml:space="preserve">quiaarcu _BI,_ ſuperatur quadrans _AB,_ ab arcu _AI._</s>
            <s xml:id="echoid-s3732" xml:space="preserve"/>
          </p>
          <figure number="114">
            <image file="114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/114-01"/>
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          <p style="it">
            <s xml:id="echoid-s3733" xml:space="preserve">_RECTA_ deinde _FG,_
              <lb/>
            chorda dicitur arcus _FAG;_
              <lb/>
            </s>
            <s xml:id="echoid-s3734" xml:space="preserve">& </s>
            <s xml:id="echoid-s3735" xml:space="preserve">recta _FI,_ chorda arcus
              <lb/>
            _FBI._ </s>
            <s xml:id="echoid-s3736" xml:space="preserve">Et quia diameter _AC,_
              <lb/>
            ſecãs arcũ _FAG,_ bifariã ſecat
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s3737" xml:space="preserve">rectã _FG,_ bifariã, vt ex
              <lb/>
            coroll, 1. </s>
            <s xml:id="echoid-s3738" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s3739" xml:space="preserve">_IO._ </s>
            <s xml:id="echoid-s3740" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3742" xml:space="preserve">
              <lb/>
            Euil. </s>
            <s xml:id="echoid-s3743" xml:space="preserve">cõſtat, (quod tamen in
              <lb/>
            lẽmate ſequẽti breuius oſtẽde
              <lb/>
            mus.) </s>
            <s xml:id="echoid-s3744" xml:space="preserve">erit recta _FH,_ ſinus re-
              <lb/>
            ctus arcus _FA,_ iuxtapriorẽ de
              <lb/>
            fin. </s>
            <s xml:id="echoid-s3745" xml:space="preserve">ſinus recti: </s>
            <s xml:id="echoid-s3746" xml:space="preserve">quia eſt dimi-
              <lb/>
            diũ chordæ _FG,_ ſubtendentis
              <lb/>
            arcũ _FAG,_ duplum arcus _FA,_
              <lb/>
            cuius _FH,_ dicitur ſinus. </s>
            <s xml:id="echoid-s3747" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s3748" xml:space="preserve">
              <lb/>
            ſi quemlibet arcũ, eiusq́; </s>
            <s xml:id="echoid-s3749" xml:space="preserve">chor
              <lb/>
            dam bifariã ſecemus, dimidiũ
              <lb/>
            chordæ dicetur ſinus rectus
              <lb/>
            dimidiati arcus. </s>
            <s xml:id="echoid-s3750" xml:space="preserve">Hinc factum
              <lb/>
            eſt, vt Sinus recti à plerisque
              <lb/>
              <note position="left" xlink:label="note-114-03" xlink:href="note-114-03a" xml:space="preserve">Sinus recti
                <lb/>
              curdicãtur
                <lb/>
              ſemiſſes re-
                <lb/>
              ctarum in
                <lb/>
              circulo ſub
                <lb/>
              tenſarum.</note>
            dicantur Semiſſes rectarum
              <lb/>
            in circulo ſubtenſarum. </s>
            <s xml:id="echoid-s3751" xml:space="preserve">Eadem quoque recta _FH,_ erit ſinus rectus eiuſdem arcus
              <lb/>
            _FA,_ ſecundum poſteriorem defin. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">ſinus recti: </s>
            <s xml:id="echoid-s3753" xml:space="preserve">quoniam perpendicularis eſt, ducta ab _F,_
              <lb/>
            extremo dicti arcus ad diametrum _AC,_ ab altero extremo _A,_ eiuſdem arcus ductam;
              <lb/>
            </s>
            <s xml:id="echoid-s3754" xml:space="preserve">propterea quod recta _EA,_ ſecans rectã _FG,_ bifariam, ſecat eandẽ ad angulos rectos.</s>
            <s xml:id="echoid-s3755" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">3. tertij.</note>
          <p style="it">
            <s xml:id="echoid-s3756" xml:space="preserve">_RECTA_ vero _AH,_ ſinus verſus eſt eiuſdem arcus _FA;_ </s>
            <s xml:id="echoid-s3757" xml:space="preserve">cum ſit pars diametri
              <lb/>
            _AC,_ inter _A,_ extremum dicti arcus, & </s>
            <s xml:id="echoid-s3758" xml:space="preserve">ſinum eius rectum _FH,_ intercepta. </s>
            <s xml:id="echoid-s3759" xml:space="preserve">Dicitur
              <lb/>
            autem verſus Inc Sinus, quia verſomodo collocatur, ſi cum ſinu recto conferatur.
              <lb/>
            </s>
            <s xml:id="echoid-s3760" xml:space="preserve">
              <note position="left" xlink:label="note-114-05" xlink:href="note-114-05a" xml:space="preserve">Sinus vet-
                <lb/>
              ſus cur di-
                <lb/>
              catur ſagit
                <lb/>
              ta.</note>
            Hunc nonnulli dicunt ſagittam, quoniam inſtar ſagittæ eſt in arcu _FAG,_ à chorda
              <lb/>
            _FG,_ excuſſæ.</s>
            <s xml:id="echoid-s3761" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3762" xml:space="preserve">_RECTA_ porrò _FK,_ est ſinus complementi arcus _FA;_ </s>
            <s xml:id="echoid-s3763" xml:space="preserve">quia eſt ſinus rectus arcus
              <lb/>
              <note position="left" xlink:label="note-114-06" xlink:href="note-114-06a" xml:space="preserve">Sinꝰ verſus
                <lb/>
              cõplemẽti
                <lb/>
              alicuius ar
                <lb/>
              cus quid.</note>
            FB, qui complementum eſt arcus FA.</s>
            <s xml:id="echoid-s3764" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3765" xml:space="preserve">_RECTA_ autem _KB,_ eſt ſinus verſus complementi arcus _FA,_ hoc eſt, ſinus ber-
              <lb/>
            ſus arcus _FB,_ qui complementum eſt arcus _FA._</s>
            <s xml:id="echoid-s3766" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Sinus rectꝰ
            <lb/>
          primꝰ ac ſe
            <lb/>
          cundus: Itẽ
            <lb/>
          ſinus pri-
            <lb/>
          mus & ſinꝰ
            <lb/>
          ſecundus
            <lb/>
          apud quos
            <lb/>
          dam quid.</note>
          <p style="it">
            <s xml:id="echoid-s3767" xml:space="preserve">_NONNVLLI_ porro Aſtronomi Sinum, quem nos rectum diximus, appellant
              <lb/>
            Sinum rectum primum; </s>
            <s xml:id="echoid-s3768" xml:space="preserve">Sinum vero, quem Sinum complementi diximus, bocant Sinum
              <lb/>
            rectum ſecundum. </s>
            <s xml:id="echoid-s3769" xml:space="preserve">Vt rectam _FH,_ appellant ſinum rectum primum arcus _FA;_ </s>
            <s xml:id="echoid-s3770" xml:space="preserve">re-
              <lb/>
            ctam bero _FK,_ ſinum rectum ſecundum eiuſdem arcus. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">Sunt alij etiam, qui ſinum
              <lb/>
            rectum ſimpliciter appellent ſinum primum, verſum autem dicantſinum ſecundum.</s>
            <s xml:id="echoid-s3772" xml:space="preserve"/>
          </p>
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