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

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          <p style="it">
            <s xml:id="echoid-s3772" xml:space="preserve">
              <pb o="103" file="115" n="115" rhead=""/>
            Quod dixerim, btintelligas auctores, qui varie de ſinubus ſunt locuti Nos communem
              <lb/>
              <note position="right" xlink:label="note-115-01" xlink:href="note-115-01a" xml:space="preserve">Quandofit
                <lb/>
              mentio ali
                <lb/>
              cuius ſinus
                <lb/>
              abſolure,
                <lb/>
              intelligit ſi
                <lb/>
              nus rectus.</note>
            modum loquendi retinuimus. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">Caterum cum ſcriptores de ſinu alique loquuntur, ſem-
              <lb/>
            per intelligunt ſinum rectum: </s>
            <s xml:id="echoid-s3774" xml:space="preserve">niſi illum bocent ſinum complementi, aut verſum.</s>
            <s xml:id="echoid-s3775" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3776" xml:space="preserve">_SEMIDIAMETER_ deinde _AE,_ ſinus eſt tam rectus, quàm verſus quadran-
              <lb/>
            tis _AB:_ </s>
            <s xml:id="echoid-s3777" xml:space="preserve">qui totus dicitur, ſiue maximus, propterea quò d maximus ſit omnium ſinuum
              <lb/>
            tam rectorum, quàm complemẽtorum; </s>
            <s xml:id="echoid-s3778" xml:space="preserve">immo vero & </s>
            <s xml:id="echoid-s3779" xml:space="preserve">maior omnibus ſinubus verſis il-
              <lb/>
              <note position="right" xlink:label="note-115-02" xlink:href="note-115-02a" xml:space="preserve">Sinus totus
                <lb/>
              vel maxi-
                <lb/>
              mus cur ſic
                <lb/>
              dicatur.</note>
            lorum arcuum, qui quadrante minores ſunt: </s>
            <s xml:id="echoid-s3780" xml:space="preserve">Solum minor eſt ſinubus verſis illorum
              <lb/>
            arcuum, qui quadrante ſunt maiores, vt infradicemus, qui quidem rarius in vſum
              <lb/>
            veniunt, quàm alij. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">Vel certe dicitur totus, ſiue maximus, quia in tabula Sinuum, in
              <lb/>
            qua Sinus recti tantummodo ponuntur, omnium Sinuum maximus eſt ille, qui qua-
              <lb/>
            dranti, ſeu gradibus 90. </s>
            <s xml:id="echoid-s3782" xml:space="preserve">reſpondet, vt ex tabula Sinuum, quam infra ponemus, perſpi-
              <lb/>
            cuumerit.</s>
            <s xml:id="echoid-s3783" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3784" xml:space="preserve">_POSTREMO,_ ducta recta _EF,_ erit recta _FH,_ ſinus rectus anguli _FEH;_ </s>
            <s xml:id="echoid-s3785" xml:space="preserve">re-
              <lb/>
            cta autem _FK,_ ſinus complementi eiusdem anguli; </s>
            <s xml:id="echoid-s3786" xml:space="preserve">& </s>
            <s xml:id="echoid-s3787" xml:space="preserve">recta _AH,_ eiusdem anguli ſi-
              <lb/>
              <note position="right" xlink:label="note-115-03" xlink:href="note-115-03a" xml:space="preserve">Duo arcus
                <lb/>
              ſemicircu-
                <lb/>
              lum conſi-
                <lb/>
              cientes eũ-
                <lb/>
              dem habẽt
                <lb/>
              ſinum, quẽ
                <lb/>
              admodum
                <lb/>
              & duo arc
                <lb/>
              circulũ con
                <lb/>
              ficiẽtes, eã-
                <lb/>
              dẽ chordã:
                <lb/>
              ſinꝰ tń ver-
                <lb/>
              ſos habent
                <lb/>
              differentes,
                <lb/>
              conficiẽtes
                <lb/>
              totã diame
                <lb/>
              trum.</note>
            nus verſus: </s>
            <s xml:id="echoid-s3788" xml:space="preserve">quoniam recta _FH,_ eſt ſinus rectus arcus _FA,_ in circulo deſcripto ex an-
              <lb/>
            gulo _FEH,_ interceptus inter rectas _EF, EA,_ angulum dictum conſt: </s>
            <s xml:id="echoid-s3789" xml:space="preserve">tuentes: </s>
            <s xml:id="echoid-s3790" xml:space="preserve">recta
              <lb/>
            autem _FK,_ eſt ſinus complementi eiusdem arcus; </s>
            <s xml:id="echoid-s3791" xml:space="preserve">& </s>
            <s xml:id="echoid-s3792" xml:space="preserve">recta _AH,_ ſinus verſus.</s>
            <s xml:id="echoid-s3793" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3794" xml:space="preserve">_CAETERVM_ duo arcus ſemicirculum conſtituentes eundem prorſus habent ſi-
              <lb/>
            num, tam rectum, quàm complementi; </s>
            <s xml:id="echoid-s3795" xml:space="preserve">quemadmodũ & </s>
            <s xml:id="echoid-s3796" xml:space="preserve">duo arcus circulum conficien-
              <lb/>
            tes vnam eandemq́; </s>
            <s xml:id="echoid-s3797" xml:space="preserve">chordam habent: </s>
            <s xml:id="echoid-s3798" xml:space="preserve">ſinus tamen verſi eorum differunt, conficiuntq́;
              <lb/>
            </s>
            <s xml:id="echoid-s3799" xml:space="preserve">totam circuli diametrum. </s>
            <s xml:id="echoid-s3800" xml:space="preserve">Vt duo arcus _FA, FC,_ conficientes ſemicirculum _ABC,_
              <lb/>
            cundem habent ſinum rectum _FH,_ quemadmodum & </s>
            <s xml:id="echoid-s3801" xml:space="preserve">duo arcus _FAG, FCG,_ eorum
              <lb/>
            dupli, circulum conficientes, eandem habent chordam _
              <emph style="sc">Fg</emph>
            ,_ cuius dimidium eſt ſinus
              <lb/>
            rectus _FH,_ vt vult prior deſinitio ſinus recti; </s>
            <s xml:id="echoid-s3802" xml:space="preserve">qui quidem ſinus rectus _FH,_ linea
              <lb/>
            perpendi cularis eſt, ducta à communi extremo _F,_ vtriuſque arcus _FA, FC,_ ad dia-
              <lb/>
            metrum _AC,_ ab extremis reliquis _A, C,_ eorundem arcuum ductam, vt vult poſte-
              <lb/>
            rior ſinus recti definitio. </s>
            <s xml:id="echoid-s3803" xml:space="preserve">Iidem duo arcus _FA, FC,_ eundem ſinum complementi ha-
              <lb/>
              <note position="right" xlink:label="note-115-04" xlink:href="note-115-04a" xml:space="preserve">Sinꝰ verſus
                <lb/>
              arcus qua-
                <lb/>
              drãte maio
                <lb/>
              ris maior ẽ
                <lb/>
              ſinu toto.</note>
            bent _FK;_ </s>
            <s xml:id="echoid-s3804" xml:space="preserve">propterea quòd arcus _FB,_ cuius ſinus rectus eſt _FK,_ eſt complementum
              <lb/>
            vtriuſque arcus. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">Sinus tamen ve ſi ijdem non ſunt, ſed _AH,_ eſt ſinus verſus arcus
              <lb/>
            _FA;_ </s>
            <s xml:id="echoid-s3806" xml:space="preserve">& </s>
            <s xml:id="echoid-s3807" xml:space="preserve">_CH,_ ſt ſinus verſus arcus _FC:_ </s>
            <s xml:id="echoid-s3808" xml:space="preserve">qui quidem duo ſinus ve ſi diametrum _AC,_
              <lb/>
            conſtituũt. </s>
            <s xml:id="echoid-s3809" xml:space="preserve">V bi vides ſinum verſum _CH,_ arcus _FC,_ quadrantem ſuperantis maiorem
              <lb/>
              <note position="right" xlink:label="note-115-05" xlink:href="note-115-05a" xml:space="preserve">Duo angu-
                <lb/>
              li duobꝰ re
                <lb/>
              ctis ęquales
                <lb/>
              eundẽ ſinũ
                <lb/>
              habent, ſed
                <lb/>
              ſinus ver-
                <lb/>
              ſos differẽ-
                <lb/>
              tes, vtpote
                <lb/>
              ꝗ totã dia-
                <lb/>
              metrũ cõfi
                <lb/>
              ciant.</note>
            eſſe ſemidiametro, ſeu ſinu toto _CE._</s>
            <s xml:id="echoid-s3810" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3811" xml:space="preserve">_SIC_ etiam duo anguli duobus rectis æquales eundem ſinum babent tam rectum,
              <lb/>
            quam complementi. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Vt patet in angulis _AEF, FEC,_ quorum vtriuſque ſinus re-
              <lb/>
            ctus eſt _FH;_ </s>
            <s xml:id="echoid-s3813" xml:space="preserve">ſinus autem complementi _FK:_ </s>
            <s xml:id="echoid-s3814" xml:space="preserve">propterea quòd arcubus _AF, FC,_ inſi-
              <lb/>
            ſtunt, quorum vtriuſque ſinus rectus eſt _FH,_ complementi autem ſinus _FK,_ vt dictum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s3815" xml:space="preserve">Sinus tamen verſi eorundem angulorum ijdem non ſunt, ſed _AH,_ ſinus verſus eſt
              <lb/>
            anguli _AEF,_ nempe arcus _AF; </s>
            <s xml:id="echoid-s3816" xml:space="preserve">& </s>
            <s xml:id="echoid-s3817" xml:space="preserve">HC,_ eſt ſinus verſus anguli _FEC,_ puta arcus
              <lb/>
            _FC._ </s>
            <s xml:id="echoid-s3818" xml:space="preserve">Conficiunt autem ambo ſinus verſi totam diametrum _AC._</s>
            <s xml:id="echoid-s3819" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3820" xml:space="preserve">_RVRSVM_ ſinus rectus cuiuſuis arcus æqualis eſt ſegmento diametri inter cen-
              <lb/>
              <note position="right" xlink:label="note-115-06" xlink:href="note-115-06a" xml:space="preserve">Sinus tam
                <lb/>
              rectus, ꝗ̃ cõ
                <lb/>
              plementi.
                <lb/>
              cui ſegmen
                <lb/>
              todiametri
                <lb/>
              ſit e qualis.
                <lb/>
              34. primi.
                <lb/>
              28. primi.</note>
            trum, & </s>
            <s xml:id="echoid-s3821" xml:space="preserve">ſinum rectum complementi eiusdem arcus interiecto: </s>
            <s xml:id="echoid-s3822" xml:space="preserve">Sinus autem comple-
              <lb/>
            menti cuiuslibet arcus æqualis eſt ſegmento diametri inter centrum, & </s>
            <s xml:id="echoid-s3823" xml:space="preserve">ſinum rectum
              <lb/>
            eiuſdem arcus poſito. </s>
            <s xml:id="echoid-s3824" xml:space="preserve">Vt _FH,_ ſinus rectus arcus _FA,_ æqualis eſt ſegmento diamet ri
              <lb/>
            _EK: </s>
            <s xml:id="echoid-s3825" xml:space="preserve">& </s>
            <s xml:id="echoid-s3826" xml:space="preserve">FK,_ ſinus complementi eiuſdem arcus _FA,_ æqualis eſt ſegmento diametri _EH;_
              <lb/>
            </s>
            <s xml:id="echoid-s3827" xml:space="preserve">ob parallelogrammum HK: </s>
            <s xml:id="echoid-s3828" xml:space="preserve">ſunt enim tam rectæ _HF, EK,_ quàm rectæ _KF, EH,_
              <lb/>
            parallelæ, propter rectos angulos _H, E, K, F._ </s>
            <s xml:id="echoid-s3829" xml:space="preserve">Hinc fit, ſi ſint duo arcus, quorum vnus
              <lb/>
            alterius ſit complementum, vtriuſuis ſinum rectum æqualem eſſe complemento </s>
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