Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres
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            <s xml:id="echoid-s9368" xml:space="preserve">
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            totus ad datum latus recto angulo oppoſitum; </s>
            <s xml:id="echoid-s9369" xml:space="preserve">vel vt ſinus anguli acuti
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            dato lateri circa rectum angulum oppoſiti ad datum latus circa angulum
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            rectum, ita ſinus alterius anguli acuti ad aliud, cognoſcetur tertium latus
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            in partibus menſuræ, ſec@ndum quam duo latera ſunt data.</s>
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            <s xml:id="echoid-s9371" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s9372" xml:space="preserve">Sit rurſus AC, palm. </s>
            <s xml:id="echoid-s9373" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">& </s>
            <s xml:id="echoid-s9375" xml:space="preserve">AB, palm. </s>
            <s xml:id="echoid-s9376" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9377" xml:space="preserve">Quia igitur, ut ad
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              <note position="left" xlink:label="note-320-01" xlink:href="note-320-01a" xml:space="preserve">Aliter per li
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              neas tangẽ-
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              tes & ſecan-
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              tes.</note>
            initium lincarum tangentium, ac ſecantium oſtendimus, poſito AB, ſinu toto
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            latus AC, ſecans eſt anguli A, & </s>
            <s xml:id="echoid-s9378" xml:space="preserve">BC, tãgens eiuſdem; </s>
            <s xml:id="echoid-s9379" xml:space="preserve">dicemus. </s>
            <s xml:id="echoid-s9380" xml:space="preserve">Si AB, palm.
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            </s>
            <s xml:id="echoid-s9381" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9382" xml:space="preserve">dat AB, ſinum totum partium 100000 quid dabit AC, palm. </s>
            <s xml:id="echoid-s9383" xml:space="preserve">13? </s>
            <s xml:id="echoid-s9384" xml:space="preserve">inuenie-
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            musq́; </s>
            <s xml:id="echoid-s9385" xml:space="preserve">ſecantem AC, partium 260000. </s>
            <s xml:id="echoid-s9386" xml:space="preserve">ut hic patet.</s>
            <s xml:id="echoid-s9387" xml:space="preserve"/>
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          AB. # AB. # AC. # # AC.
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          5. # 100000. # 13? # fit # 260000.
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          </note>
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            <s xml:id="echoid-s9388" xml:space="preserve">Ex tabula ergo Secantium erit angulus A, grad 67. </s>
            <s xml:id="echoid-s9389" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9390" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9391" xml:space="preserve">& </s>
            <s xml:id="echoid-s9392" xml:space="preserve">proinde reli-
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            quus angulus C, grad. </s>
            <s xml:id="echoid-s9393" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9394" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9395" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">tangens anguli A, nempe BC, da-
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            bitur partium 240038. </s>
            <s xml:id="echoid-s9398" xml:space="preserve">ex tangentium tabula. </s>
            <s xml:id="echoid-s9399" xml:space="preserve">Quare rurſum dicemus. </s>
            <s xml:id="echoid-s9400" xml:space="preserve">Si ſinus
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            totus AB, partium 100000. </s>
            <s xml:id="echoid-s9401" xml:space="preserve">dat AB, palm. </s>
            <s xml:id="echoid-s9402" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9403" xml:space="preserve">Vel ſi ſecans AC, inuenta par-
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            tium 260000. </s>
            <s xml:id="echoid-s9404" xml:space="preserve">dat AC, palm. </s>
            <s xml:id="echoid-s9405" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9406" xml:space="preserve">quid dabit tangens BC, partium 240038? </s>
            <s xml:id="echoid-s9407" xml:space="preserve">in-
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            ueniemusque iterum BC, eſſe ferme palm. </s>
            <s xml:id="echoid-s9408" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9409" xml:space="preserve">ut hic conſtat.</s>
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          AB. # AB.
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          100000. # 5.
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          AC. # AC.} # BC. # # BC.
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          260000. # 13. # 240038? # fit. # 12.
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          </note>
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            <s xml:id="echoid-s9411" xml:space="preserve">IGITVR quando latus recto angulo oppoſitum datur, cum vno
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              <note position="left" xlink:label="note-320-04" xlink:href="note-320-04a" xml:space="preserve">Praxis.</note>
            latere circa angulum rectum; </s>
            <s xml:id="echoid-s9412" xml:space="preserve">Si fiat, vt datum latus circa angulum re-
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            ctum ad ſinum totum, ita datum latus angulo recto oppoſitum ad aliud,
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            prodibit ſecans anguli acuti ſub datis lateribus comprehenſi. </s>
            <s xml:id="echoid-s9413" xml:space="preserve">Inuento er-
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            go, beneficio huius ſecantis repertæ, vtroque angulo acuto, & </s>
            <s xml:id="echoid-s9414" xml:space="preserve">tangente acu
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            ti anguli ſub datis lateribus comprehenſi, ex tarigentiũ tabula; </s>
            <s xml:id="echoid-s9415" xml:space="preserve">S@ iterum
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            fiat, vt ſinus totus ad datum latus circa angulum rectum; </s>
            <s xml:id="echoid-s9416" xml:space="preserve">Vel vt ſecans
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            acuti anguli ſub datis lateribus comprehenſi ad latus datum recto angu-
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            lo oppoſitum, ita tangens acuti anguli ſub lateribus datis comprehenſi ad
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            aliud, notum fiet tertium latus in partibus menſuræ, ſecundum quam ſunt
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            data duo latera. </s>
            <s xml:id="echoid-s9417" xml:space="preserve">Verum ſatius eſt per ſolos ſinus operari, cum tangentes
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            lineæ, at que ſecantes nihil compendij afferant, ſintque per ſinus inuentæ.</s>
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            <s xml:id="echoid-s9419" xml:space="preserve">ADHVC aliter. </s>
            <s xml:id="echoid-s9420" xml:space="preserve">Ponatur rurſum AC, palm. </s>
            <s xml:id="echoid-s9421" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9422" xml:space="preserve">& </s>
            <s xml:id="echoid-s9423" xml:space="preserve">AB, palm. </s>
            <s xml:id="echoid-s9424" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9425" xml:space="preserve">Quoniã
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            ergo quadratum rectæ AC, duobus quadratis rectarum AB, BC, æquale
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              <note position="left" xlink:label="note-320-05" xlink:href="note-320-05a" xml:space="preserve">47. primi.</note>
            eſi; </s>
            <s xml:id="echoid-s9426" xml:space="preserve">ſi auferatur quadratum lateris AB, quod eſt 25. </s>
            <s xml:id="echoid-s9427" xml:space="preserve">ex quadrato lateris AC,
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            quod eſt 169 relinquetur quadratũ lateris BC, nempe 144. </s>
            <s xml:id="echoid-s9428" xml:space="preserve">cuius radix qua-
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            diata 12. </s>
            <s xml:id="echoid-s9429" xml:space="preserve">dabit latus BC, palm.</s>
            <s xml:id="echoid-s9430" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9431" xml:space="preserve">Et quia, poſito AC, ſinu toto, latera AB,
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            BC, ſunt ſinus angulorum oppoſitorum, ut in defin. </s>
            <s xml:id="echoid-s9432" xml:space="preserve">ſinuum explicauimus:
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            </s>
            <s xml:id="echoid-s9433" xml:space="preserve">Sifiat, ut latus AC, angulo recto oppoſitum palmorum 13. </s>
            <s xml:id="echoid-s9434" xml:space="preserve">ad AC, ſinum
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            totum partium 100000. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">ita alterutrum laterum circa angulum rectum, nempe
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            BC, palm. </s>
            <s xml:id="echoid-s9436" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9437" xml:space="preserve">ad aliud, prodibit ſinus anguli acuti A, ſumpto lateri oppoſiti
              <lb/>
            partium 92308. </s>
            <s xml:id="echoid-s9438" xml:space="preserve">Ex ſinuum ergo tabula dabitur angulus A, grad. </s>
            <s xml:id="echoid-s9439" xml:space="preserve">67. </s>
            <s xml:id="echoid-s9440" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9441" xml:space="preserve">23.</s>
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