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

Table of figures

< >
< >
page |< < (489) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1422" type="section" level="1" n="631">
          <p>
            <s xml:id="echoid-s17704" xml:space="preserve">
              <pb o="489" file="501" n="501" rhead=""/>
            lorum ſubducatur, reliquus erit arcus, vel angulus minor.</s>
            <s xml:id="echoid-s17705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17706" xml:space="preserve">SI vero proportio ſinus maioris arcus, vel anguli, ad ſinum minoris eſt
              <lb/>
            minoris inæqualitatis; </s>
            <s xml:id="echoid-s17707" xml:space="preserve">inuertantur eius termini, vt fiat proportio maioris in-
              <lb/>
            æqualitatis; </s>
            <s xml:id="echoid-s17708" xml:space="preserve">atque ex hac, & </s>
            <s xml:id="echoid-s17709" xml:space="preserve">data differentia arcuum, ſeu angulorum inue-
              <lb/>
            niantur duo arcus, vel anguli, vt dictum eſt. </s>
            <s xml:id="echoid-s17710" xml:space="preserve">Nam maior eotum ex ſemicircu-
              <lb/>
            lo ſublatus dabit minorem arcum, ſeu angulum quæſitum; </s>
            <s xml:id="echoid-s17711" xml:space="preserve">minor vero ſubdu-
              <lb/>
            ctus ex ſemicirculo offeret maiorem.</s>
            <s xml:id="echoid-s17712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1424" type="section" level="1" n="632">
          <head xml:id="echoid-head667" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17713" xml:space="preserve">QVANDO ſinus maioris arcus, vel anguli ad ſinũ minoris habet pro-
              <lb/>
              <note position="right" xlink:label="note-501-01" xlink:href="note-501-01a" xml:space="preserve">Propoſ. 7.
                <lb/>
              triang re-
                <lb/>
              ctil.</note>
            portionem maioris inæqualitatis; </s>
            <s xml:id="echoid-s17714" xml:space="preserve">inquirantur ex data illa proportione maio-
              <lb/>
            ris inæqualitatis, & </s>
            <s xml:id="echoid-s17715" xml:space="preserve">ex arcu, ſeu angulo, qui poſt detractionem datæ differen-
              <lb/>
            tiæ ex ſemicirculo relinquitur, tanquam ex aggregato duorum arcuum, ſiue
              <lb/>
            angulorum, duo arcus, ſiue anguli huius aggregati, vt in problemate 6. </s>
            <s xml:id="echoid-s17716" xml:space="preserve">præ-
              <lb/>
            cepimus. </s>
            <s xml:id="echoid-s17717" xml:space="preserve">Nam maior arcus, ſeu angulus inuentus, ſi ex ſemicirculo aufera-
              <lb/>
            tur, dabit maiorem arcum ſiue angulum quæſitum: </s>
            <s xml:id="echoid-s17718" xml:space="preserve">Minor autem inuentus
              <lb/>
            erit minor quæſitus.</s>
            <s xml:id="echoid-s17719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17720" xml:space="preserve">QVANDO autem proportio data eſt minoris inæqualitatis; </s>
            <s xml:id="echoid-s17721" xml:space="preserve">inuertan-
              <lb/>
            tur eius termini, vt fiat proportio maioris inæqualitatis: </s>
            <s xml:id="echoid-s17722" xml:space="preserve">atque ex hac, & </s>
            <s xml:id="echoid-s17723" xml:space="preserve">da-
              <lb/>
            ta differentia arcuum, ſeu angulorum, inueſtigentur duo arcus, ſiue anguli,
              <lb/>
            vt iam dictum eſt. </s>
            <s xml:id="echoid-s17724" xml:space="preserve">Maior enim eorum ex ſemicirculo ſubtractus dabit arcum,
              <lb/>
            ſeu angulum quæſitum minorem; </s>
            <s xml:id="echoid-s17725" xml:space="preserve">Minor vero maiorem.</s>
            <s xml:id="echoid-s17726" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1426" type="section" level="1" n="633">
          <head xml:id="echoid-head668" xml:space="preserve">Aliter per ſolos ſinus.</head>
          <p style="it">
            <s xml:id="echoid-s17727" xml:space="preserve">SI data proportio ſinus maioris arcus, ſiue anguli ad ſinum minoris eſt maioris in-
              <lb/>
              <note position="right" xlink:label="note-501-02" xlink:href="note-501-02a" xml:space="preserve">Propoſ. 7.
                <lb/>
              trtrang. re-
                <lb/>
              ctil.</note>
            æqualitatis; </s>
            <s xml:id="echoid-s17728" xml:space="preserve">fiat, vt ſemiſsis differentiæ terminorum proportionis datæ ad ſinum ſe-
              <lb/>
            miſsis datæ differentiæ arcuum, vel angulorum, ita aggregatum ex ſemiſſe differen
              <lb/>
            tiæ terminorum proportionis, & </s>
            <s xml:id="echoid-s17729" xml:space="preserve">conſequẽte termino eiuſdem proportionis, ad aliud,
              <lb/>
            inuenieturq́; </s>
            <s xml:id="echoid-s17730" xml:space="preserve">quartus quidam numerus; </s>
            <s xml:id="echoid-s17731" xml:space="preserve">cuius quadratum ſi adijciatur quadrato ſi-
              <lb/>
            nus complementi ſemiſsis differentiæ arcuum, ſeu angulorum datæ: </s>
            <s xml:id="echoid-s17732" xml:space="preserve">Et rurſum fiat,
              <lb/>
            vt radix quadrata aggregati dictorum duorum quadratorum ad ſinum totum, ita
              <lb/>
            numerus ille quartus inuentus ad aliud, reperietur ſinus arcus, ſiue anguli, cui ſi
              <lb/>
            addatur ſemißis datæ differentiæ arcuum, ſeu angulorum, notus fiet maior arcus, ſi-
              <lb/>
            ue angulus: </s>
            <s xml:id="echoid-s17733" xml:space="preserve">ab eodem vero ſi eadem ſemiſsis detrahatur, reliquus erit minor.</s>
            <s xml:id="echoid-s17734" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17735" xml:space="preserve">QVOD ſi data proportio ſit minoris inæqualitatis, agẽdũ erit, vt ſupra diximus.</s>
            <s xml:id="echoid-s17736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17737" xml:space="preserve">IAM vero ſi forte proportio data ſit æqualitatis, detrahatur differentia
              <lb/>
            data arcuum, ſiue angulorum ex ſemicirculo. </s>
            <s xml:id="echoid-s17738" xml:space="preserve">Nam reſidui ſemiſsis erit minor
              <lb/>
            arcus, ſeu angulus quæſitus: </s>
            <s xml:id="echoid-s17739" xml:space="preserve">eadem vero ſemiſsis ad datam differentiam adie-
              <lb/>
            cta dabit maiorem.</s>
            <s xml:id="echoid-s17740" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quærũtur
            <lb/>
          caſus lineæ
            <lb/>
          perpẽdicu-
            <lb/>
          laris.</note>
        </div>
        <div xml:id="echoid-div1428" type="section" level="1" n="634">
          <head xml:id="echoid-head669" xml:space="preserve">9. SI ab vno angulo trianguli cuiuſvis dato-
            <lb/>
          rum laterum ad latus oppoſitum perpendicu
            <lb/>
          laris demittatur, quãta ſit recta inter perpen-
            <lb/>
          dicularem, & vtrum vis reliquorum angulo-
            <lb/>
          rum, inuenire.</head>
        </div>
      </text>
    </echo>
Impressum