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

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        <div xml:id="echoid-div784" type="section" level="1" n="454">
          <pb o="305" file="317" n="317" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s9180" xml:space="preserve">_SED_ iam ad inuentionem laterum, atq; </s>
            <s xml:id="echoid-s9181" xml:space="preserve">angulorum in triangulis rectilineis ex
              <lb/>
            quibuſdam datis ac cognitis accedamus; </s>
            <s xml:id="echoid-s9182" xml:space="preserve">qua in re, vt certum ordinem, ac methodum
              <lb/>
            ſeruemus, agemus primo loco de triangulis rectangulis, deinde vero de non rectangu-
              <lb/>
            lis, cum in illis minor, quàm in his, difficultas reperiatur.</s>
            <s xml:id="echoid-s9183" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div793" type="section" level="1" n="455">
          <head xml:id="echoid-head487" xml:space="preserve">PROBL. 1. PROPOSITIO 2.</head>
          <p>
            <s xml:id="echoid-s9184" xml:space="preserve">DATO vno latere, cum vno angulo acuto
              <lb/>
              <note position="right" xlink:label="note-317-01" xlink:href="note-317-01a" xml:space="preserve">In triangu
                <lb/>
              lo rectangu
                <lb/>
              lo ex vno la
                <lb/>
              tere dato,
                <lb/>
              vna cũ an-
                <lb/>
              gulo acuto
                <lb/>
              reliqua in-
                <lb/>
              ueſtigãtur.</note>
            trianguli rectáguli, vel cum proportione duorum
              <lb/>
            angulorum quorumcunq;</s>
            <s xml:id="echoid-s9185" xml:space="preserve">; reliqua duo latera co-
              <lb/>
            gnoſcere, & </s>
            <s xml:id="echoid-s9186" xml:space="preserve">quorumlibet duorum laterum pro-
              <lb/>
            portionem efficere notam.</s>
            <s xml:id="echoid-s9187" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9188" xml:space="preserve">SIT triangulum ABC, cuius angulus B, rectus, ſitq; </s>
            <s xml:id="echoid-s9189" xml:space="preserve">primò latus AC,
              <lb/>
              <note position="right" xlink:label="note-317-02" xlink:href="note-317-02a" xml:space="preserve">Quando la
                <lb/>
              tꝰ recto an-
                <lb/>
              gulo oppo-
                <lb/>
              ſitũ datur,
                <lb/>
              cum acuto
                <lb/>
              angulo.</note>
            recto angulo oppoſitũ datum 13. </s>
            <s xml:id="echoid-s9190" xml:space="preserve">palmorum, vna cum angulo acuto C, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s9191" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9192" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9193" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9194" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s9195" xml:space="preserve">cum angulo acuto A, grad. </s>
            <s xml:id="echoid-s9196" xml:space="preserve">67. </s>
            <s xml:id="echoid-s9197" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9198" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9199" xml:space="preserve">Oportet
              <lb/>
            ex his indagare reliqua latera. </s>
            <s xml:id="echoid-s9200" xml:space="preserve">Quoniam, per ea, quæ in defin. </s>
            <s xml:id="echoid-s9201" xml:space="preserve">Sinuum tra-
              <lb/>
            didimus, poſito ſinu toto AC, latera AB, BC, ſunt ſinus oppoſitorum angulo
              <lb/>
            rum: </s>
            <s xml:id="echoid-s9202" xml:space="preserve">ſunt autem anguli dati; </s>
            <s xml:id="echoid-s9203" xml:space="preserve">noti erunt ſinus di-
              <lb/>
              <figure xlink:label="fig-317-01" xlink:href="fig-317-01a" number="167">
                <image file="317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/317-01"/>
              </figure>
            ctorum angulorum; </s>
            <s xml:id="echoid-s9204" xml:space="preserve">AB, quidem 38456. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">at BC,
              <lb/>
            92310. </s>
            <s xml:id="echoid-s9206" xml:space="preserve">Per regulam ergo auream dicemus. </s>
            <s xml:id="echoid-s9207" xml:space="preserve">Si AC,
              <lb/>
            partium 100000. </s>
            <s xml:id="echoid-s9208" xml:space="preserve">nempe quatenus ſinus totus,
              <lb/>
            dat 13. </s>
            <s xml:id="echoid-s9209" xml:space="preserve">palmos, quid dabit AB, ſinus partium
              <lb/>
            38456. </s>
            <s xml:id="echoid-s9210" xml:space="preserve">& </s>
            <s xml:id="echoid-s9211" xml:space="preserve">quid ſinus BC, partium 92310? </s>
            <s xml:id="echoid-s9212" xml:space="preserve">vt hic
              <lb/>
            vides. </s>
            <s xml:id="echoid-s9213" xml:space="preserve">Inueniemusq́ue latus AB, palm. </s>
            <s xml:id="echoid-s9214" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9215" xml:space="preserve">& </s>
            <s xml:id="echoid-s9216" xml:space="preserve">BC,
              <lb/>
            palm. </s>
            <s xml:id="echoid-s9217" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9218" xml:space="preserve">ferè.</s>
            <s xml:id="echoid-s9219" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # {AB.} # # {AB.
            <lb/>
          100000. # 13. # 38456? # funt # 5
            <lb/>
          # # BC. # # BC.
            <lb/>
          # # 92310? # # 12
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s9220" xml:space="preserve">IT AQVE quando latus recto angulo oppoſitum datur cum angu-
              <lb/>
              <note position="right" xlink:label="note-317-04" xlink:href="note-317-04a" xml:space="preserve">Praxis.</note>
            lo vno acuto, ac proinde cum altero etiam acuto: </s>
            <s xml:id="echoid-s9221" xml:space="preserve">Sifiat, vt ſinus totus ad
              <lb/>
            latus datum recto angulo oppoſitum, ita ſinus vtriusque anguli acuti
              <lb/>
            ſeorſum ad aliud, reperientur latera eiſdem angulis oppoſita in partibus
              <lb/>
            menſuræ, ſecundum quam datum est latus angulo recto oppoſitum.</s>
            <s xml:id="echoid-s9222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9223" xml:space="preserve">
              <emph style="sc">DEINDe</emph>
            datum ſit vnum ex lateribus circa angulum rectum, vt BC,
              <lb/>
              <note position="right" xlink:label="note-317-05" xlink:href="note-317-05a" xml:space="preserve">Quãdo la-
                <lb/>
              tus vnum
                <lb/>
              circa angu
                <lb/>
              lum rectũ
                <lb/>
              datur, cum
                <lb/>
              acuto an-
                <lb/>
              gulo.</note>
            palmorum 12. </s>
            <s xml:id="echoid-s9224" xml:space="preserve">cum angulo C, grad. </s>
            <s xml:id="echoid-s9225" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9226" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9227" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9228" xml:space="preserve">& </s>
            <s xml:id="echoid-s9229" xml:space="preserve">proinde cum angulo etiam
              <lb/>
            A, grad. </s>
            <s xml:id="echoid-s9230" xml:space="preserve">67. </s>
            <s xml:id="echoid-s9231" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9232" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9233" xml:space="preserve">Oportet ex his reliqua latera inueſtigare. </s>
            <s xml:id="echoid-s9234" xml:space="preserve">Quoniam per
              <lb/>
            ea, quæ in lineis tangentibus, atque ſecantibus ad initium oſtendimus, poſito
              <lb/>
            ſinu toto BC, latus AB, eſt tangens anguli C, & </s>
            <s xml:id="echoid-s9235" xml:space="preserve">latus AC, ciuſdem ſecans,
              <lb/>
            dabitur tangẽs AB, partium 41660. </s>
            <s xml:id="echoid-s9236" xml:space="preserve">& </s>
            <s xml:id="echoid-s9237" xml:space="preserve">ſecans AC, partium 108331. </s>
            <s xml:id="echoid-s9238" xml:space="preserve">Quare </s>
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