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

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            <s xml:id="echoid-s9307" xml:space="preserve">
              <pb o="307" file="319" n="319" rhead=""/>
            AB, ad AC, ut 5. </s>
            <s xml:id="echoid-s9308" xml:space="preserve">ad 13. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">Vel ut 38456. </s>
            <s xml:id="echoid-s9310" xml:space="preserve">ad 100000. </s>
            <s xml:id="echoid-s9311" xml:space="preserve">Vel ut 41660. </s>
            <s xml:id="echoid-s9312" xml:space="preserve">ad 108331.
              <lb/>
            </s>
            <s xml:id="echoid-s9313" xml:space="preserve">&</s>
            <s xml:id="echoid-s9314" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9315" xml:space="preserve">In his enim omnibus numeris dicta latera inuenta ſunt. </s>
            <s xml:id="echoid-s9316" xml:space="preserve">Dato ergo uno la-
              <lb/>
            tere, cum uno angulo acuto trianguli rectanguli, &</s>
            <s xml:id="echoid-s9317" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9318" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s9319" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div802" type="section" level="1" n="456">
          <head xml:id="echoid-head488" xml:space="preserve">PROBL. 2. PROPOS. 3.</head>
          <p>
            <s xml:id="echoid-s9320" xml:space="preserve">DATIS duobus lateribus trianguli rectangu
              <lb/>
              <note position="right" xlink:label="note-319-01" xlink:href="note-319-01a" xml:space="preserve">In triã gulo
                <lb/>
              rectãgulo ex
                <lb/>
              duobus late
                <lb/>
              ribus notis,
                <lb/>
              vel ex eorũ
                <lb/>
              proportione
                <lb/>
              nota, vna cũ
                <lb/>
              vno latere
                <lb/>
              quocunque,
                <lb/>
              reliqua in-
                <lb/>
              quiruntur.</note>
            li, duos angulos acutos efficere notos, vna cum
              <lb/>
            tertio latere. </s>
            <s xml:id="echoid-s9321" xml:space="preserve">Item data proportione duorum late-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s9322" xml:space="preserve">inſuper vno latere dato quocunque, duos
              <lb/>
            angulos acutos, vna cum reliquis duobus lateri-
              <lb/>
            bus cognoſcere.</s>
            <s xml:id="echoid-s9323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9324" xml:space="preserve">IN triangulo ABC, cuius angulus B, rectus, ſit primum latus AC, recto
              <lb/>
              <note position="right" xlink:label="note-319-02" xlink:href="note-319-02a" xml:space="preserve">Quando la-
                <lb/>
              tus angulo
                <lb/>
              recto oppoſi
                <lb/>
              tum, cũ vno
                <lb/>
              latere circa
                <lb/>
              angulum r@
                <lb/>
              ctum datur.</note>
            angulo oppoſitum, & </s>
            <s xml:id="echoid-s9325" xml:space="preserve">inſuper latus AB, circa angulum rectum datum, nem-
              <lb/>
            pe AC, palm. </s>
            <s xml:id="echoid-s9326" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9327" xml:space="preserve">& </s>
            <s xml:id="echoid-s9328" xml:space="preserve">AB, palm. </s>
            <s xml:id="echoid-s9329" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9330" xml:space="preserve">Oportet ex his & </s>
            <s xml:id="echoid-s9331" xml:space="preserve">angulos A, C, & </s>
            <s xml:id="echoid-s9332" xml:space="preserve">latus ter-
              <lb/>
            tium BC, explorare. </s>
            <s xml:id="echoid-s9333" xml:space="preserve">Quoniam, poſito ſinu toto AC, latus AB, eſt ſinus an-
              <lb/>
            guli C, dicemus. </s>
            <s xml:id="echoid-s9334" xml:space="preserve">Si AC, palm. </s>
            <s xml:id="echoid-s9335" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9336" xml:space="preserve">dat AC, ſinum totum partiũ 100000. </s>
            <s xml:id="echoid-s9337" xml:space="preserve">quid
              <lb/>
            dabit AB, palm. </s>
            <s xml:id="echoid-s9338" xml:space="preserve">5? </s>
            <s xml:id="echoid-s9339" xml:space="preserve">inueniemusq́ue
              <lb/>
              <figure xlink:label="fig-319-01" xlink:href="fig-319-01a" number="168">
                <image file="319-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/319-01"/>
              </figure>
            ſinum AB, partium 38461. </s>
            <s xml:id="echoid-s9340" xml:space="preserve">ut hic
              <lb/>
            uides.</s>
            <s xml:id="echoid-s9341" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # AB. # # AB.
            <lb/>
          13. # 100000. # 5? # fit # 38461.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9342" xml:space="preserve">Ex tabula ergo ſinuum dabitur an-
              <lb/>
            gulus C, grad. </s>
            <s xml:id="echoid-s9343" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9344" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9345" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9346" xml:space="preserve">ac pro-
              <lb/>
            inde reliquus angulus A, grad. </s>
            <s xml:id="echoid-s9347" xml:space="preserve">67.
              <lb/>
            </s>
            <s xml:id="echoid-s9348" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9349" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9350" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s9351" xml:space="preserve">huius anguli A,
              <lb/>
            ſinus, nempe BC, dabitur partium
              <lb/>
            92310. </s>
            <s xml:id="echoid-s9352" xml:space="preserve">ex eadem tabula ſinuum. </s>
            <s xml:id="echoid-s9353" xml:space="preserve">Dicemus ergo rurſum. </s>
            <s xml:id="echoid-s9354" xml:space="preserve">Si ſinus totus AC, par
              <lb/>
            tium 100000. </s>
            <s xml:id="echoid-s9355" xml:space="preserve">dat AC, palm. </s>
            <s xml:id="echoid-s9356" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9357" xml:space="preserve">Vel ſi ſinus AB, inuentus partium 38461. </s>
            <s xml:id="echoid-s9358" xml:space="preserve">
              <lb/>
            dat AB, palm. </s>
            <s xml:id="echoid-s9359" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9360" xml:space="preserve">quid dabit ſinus BC, partium 92310? </s>
            <s xml:id="echoid-s9361" xml:space="preserve">reperiemusq́ue BC, eſ-
              <lb/>
            ſe palm. </s>
            <s xml:id="echoid-s9362" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9363" xml:space="preserve">fermè, ut hic apparet.</s>
            <s xml:id="echoid-s9364" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC.
            <lb/>
          100000. # 13.
            <lb/>
          AB. # AB.} # BC. # # BC.
            <lb/>
          38461. # 13. # 5. # 92310? # fit # 12.
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s9365" xml:space="preserve">CVM ergo datur latus angulo recto oppoſitum, cum vno latere cir-
              <lb/>
              <note position="right" xlink:label="note-319-05" xlink:href="note-319-05a" xml:space="preserve">Praxis.</note>
            ca eundem angulum rectum; </s>
            <s xml:id="echoid-s9366" xml:space="preserve">Si fiat, vt datum latus recto angulo oppoſi-
              <lb/>
            tum ad ſinum totum, ita alterum latus datum ad aliud, prodibit ſinus acu
              <lb/>
            ti anguli, qui lateri dato circarectum angulum opponitur. </s>
            <s xml:id="echoid-s9367" xml:space="preserve">Inuento autem,
              <lb/>
            beneficio huius ſinus inuenti, vtro angulo acuto; </s>
            <s xml:id="echoid-s9368" xml:space="preserve">Si iterum fiat, vt </s>
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