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

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            <s xml:id="echoid-s9442" xml:space="preserve">
              <pb o="309" file="321" n="321" rhead=""/>
            atque adeo reliquus C, grad. </s>
            <s xml:id="echoid-s9443" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9444" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9445" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9446" xml:space="preserve">Hoc modo primo loco inuenitur
              <lb/>
            tertium latus, deinde vero anguli:</s>
            <s xml:id="echoid-s9447" xml:space="preserve">cũ alijs vijs inuenti ſint prius anguli, quam
              <lb/>
            tertium latus.</s>
            <s xml:id="echoid-s9448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9449" xml:space="preserve">SINT iam duo latera AB, BC, circa rectum angulum data, vt AB, palm.
              <lb/>
            </s>
            <s xml:id="echoid-s9450" xml:space="preserve">
              <note position="right" xlink:label="note-321-01" xlink:href="note-321-01a" xml:space="preserve">Quando
                <lb/>
              duo latera
                <lb/>
              circa angu
                <lb/>
              lum rectú
                <lb/>
              data ſunt,</note>
            5. </s>
            <s xml:id="echoid-s9451" xml:space="preserve">& </s>
            <s xml:id="echoid-s9452" xml:space="preserve">BC, palm. </s>
            <s xml:id="echoid-s9453" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9454" xml:space="preserve">Oportet ex his tertium latus AC, & </s>
            <s xml:id="echoid-s9455" xml:space="preserve">acutos angulos in-
              <lb/>
            uenire. </s>
            <s xml:id="echoid-s9456" xml:space="preserve">Quoniam, ex demonſtratis in principio linearum tangentium, ſecan-
              <lb/>
            tiumq́ue, poſito AB, ſinu toto, latus BC, tangens eſt anguli A, & </s>
            <s xml:id="echoid-s9457" xml:space="preserve">latus AC,
              <lb/>
            eiuſdem ſecans; </s>
            <s xml:id="echoid-s9458" xml:space="preserve">dicemus. </s>
            <s xml:id="echoid-s9459" xml:space="preserve">Si AB, palm. </s>
            <s xml:id="echoid-s9460" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9461" xml:space="preserve">dat AB,
              <lb/>
              <figure xlink:label="fig-321-01" xlink:href="fig-321-01a" number="169">
                <image file="321-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/321-01"/>
              </figure>
            ſinum totum partium 100000. </s>
            <s xml:id="echoid-s9462" xml:space="preserve">quid dabit BC,
              <lb/>
            palm. </s>
            <s xml:id="echoid-s9463" xml:space="preserve">12? </s>
            <s xml:id="echoid-s9464" xml:space="preserve">reperiemusq́ue tangentem BC, par-
              <lb/>
            tium 240000. </s>
            <s xml:id="echoid-s9465" xml:space="preserve">vt hic manifeſtum eſt.</s>
            <s xml:id="echoid-s9466" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # BC. # # BC.
            <lb/>
          5. # 100000. # 12? # ſit. # 240000.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9467" xml:space="preserve">Ex tabula ergo tangentium dabitur angulus A,
              <lb/>
            grad.</s>
            <s xml:id="echoid-s9468" xml:space="preserve">67. </s>
            <s xml:id="echoid-s9469" xml:space="preserve">Min.</s>
            <s xml:id="echoid-s9470" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9471" xml:space="preserve">ac proinde reliquus angulus C, grad. </s>
            <s xml:id="echoid-s9472" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9473" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9474" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9475" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s9476" xml:space="preserve">
              <lb/>
            AC, ſecans anguli A, dabitur ex tabula ſecantium, partium 260035. </s>
            <s xml:id="echoid-s9477" xml:space="preserve">Rurſus
              <lb/>
            ergo dicemus. </s>
            <s xml:id="echoid-s9478" xml:space="preserve">Si AB, ſinus totus partium 100000. </s>
            <s xml:id="echoid-s9479" xml:space="preserve">dat AB, palm. </s>
            <s xml:id="echoid-s9480" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9481" xml:space="preserve">Vel, ſit an-
              <lb/>
            gens BC, inuenta partium 240000. </s>
            <s xml:id="echoid-s9482" xml:space="preserve">dat BC, palm. </s>
            <s xml:id="echoid-s9483" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9484" xml:space="preserve">quid dabit AC, ſecans
              <lb/>
            partium 260035? </s>
            <s xml:id="echoid-s9485" xml:space="preserve">inueniemusq́ue AC, palm. </s>
            <s xml:id="echoid-s9486" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9487" xml:space="preserve">ferè vt hic vides.</s>
            <s xml:id="echoid-s9488" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB.
            <lb/>
          100000. # 5.
            <lb/>
          BC. # BC.} # AC. # # AC.
            <lb/>
          240000. # 12. # 260035? # ſit. # 13.
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s9489" xml:space="preserve">ITAQVE ſidentur duo latera circa angulum rectum: </s>
            <s xml:id="echoid-s9490" xml:space="preserve">Si fiat, vt
              <lb/>
              <note position="right" xlink:label="note-321-04" xlink:href="note-321-04a" xml:space="preserve">Praxis.</note>
            alterutrum datorum laterum ad ſinum totum, ita alterum latus datum
              <lb/>
            ad aliud, proueniet tangẽs acuti anguli buic alteri dato lateri oppoſiti. </s>
            <s xml:id="echoid-s9491" xml:space="preserve">In-
              <lb/>
            uento ergo, beneficio huius tangentis inuentæ, vtroq; </s>
            <s xml:id="echoid-s9492" xml:space="preserve">angulo acuto, in tabu-
              <lb/>
            la tangentium; </s>
            <s xml:id="echoid-s9493" xml:space="preserve">& </s>
            <s xml:id="echoid-s9494" xml:space="preserve">extabula ſecantium, ſecante anguli acuti, qui alteri
              <lb/>
            buic dato lateri opponitur: </s>
            <s xml:id="echoid-s9495" xml:space="preserve">Sirurſum fiat, vt ſinus totus ad primum la-
              <lb/>
            tus datum; </s>
            <s xml:id="echoid-s9496" xml:space="preserve">Vel vt tangens inuenta ad ſecundum latus datum, ita ſecans
              <lb/>
            accepta ex tabula ſecantium, ad aliud, notum fiet latus tertium recto an-
              <lb/>
            gulo oppoſitum in ijſdem partibus, in quibus duo latera circa angulum
              <lb/>
              <note position="right" xlink:label="note-321-05" xlink:href="note-321-05a" xml:space="preserve">Aliter ſine
                <lb/>
              tãgentibus
                <lb/>
              & Secanti-
                <lb/>
              bus.</note>
            rectum data ſunt.</s>
            <s xml:id="echoid-s9497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9498" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s9499" xml:space="preserve">Sit rurſum AB, palm. </s>
            <s xml:id="echoid-s9500" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9501" xml:space="preserve">& </s>
            <s xml:id="echoid-s9502" xml:space="preserve">BC, palm. </s>
            <s xml:id="echoid-s9503" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9504" xml:space="preserve">Et quoniam qua-
              <lb/>
            drata laterum AB, BC, ſimul æqualia ſunt quadrato lateris AC; </s>
            <s xml:id="echoid-s9505" xml:space="preserve">erit qua-
              <lb/>
              <note position="right" xlink:label="note-321-06" xlink:href="note-321-06a" xml:space="preserve">47.primi.</note>
            dratum lateris AC, palm. </s>
            <s xml:id="echoid-s9506" xml:space="preserve">169. </s>
            <s xml:id="echoid-s9507" xml:space="preserve">cuius radix quadrata dabit latus AC, palm.
              <lb/>
            </s>
            <s xml:id="echoid-s9508" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9509" xml:space="preserve">Quia vero, vt in deſin. </s>
            <s xml:id="echoid-s9510" xml:space="preserve">ſinuum traditum eſt, poſito AC, ſinu toto, latera
              <lb/>
            AB, BC, ſunt ſinus oppoſitorum angulorum: </s>
            <s xml:id="echoid-s9511" xml:space="preserve">Si ſiat, vt latus AC, quod an-
              <lb/>
            gulo recto opponitur, inuẽtum palm. </s>
            <s xml:id="echoid-s9512" xml:space="preserve">13. </s>
            <s xml:id="echoid-s9513" xml:space="preserve">ad AC, ſinum totum partiũ 100000. </s>
            <s xml:id="echoid-s9514" xml:space="preserve">
              <lb/>
            ita alterutrum laterum circa angulum rectum, nempe AB, palm. </s>
            <s xml:id="echoid-s9515" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9516" xml:space="preserve">ad aliud,
              <lb/>
            reperietur ſinus anguli acuti C, qui accepto lateri opponitur, partiũ 38461. </s>
            <s xml:id="echoid-s9517" xml:space="preserve">
              <lb/>
            Ex tabula ergo ſinuum dabitur angulus C, grad. </s>
            <s xml:id="echoid-s9518" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9519" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9520" xml:space="preserve">37. </s>
            <s xml:id="echoid-s9521" xml:space="preserve">ac propterea re-
              <lb/>
            liquus A, grad. </s>
            <s xml:id="echoid-s9522" xml:space="preserve">67. </s>
            <s xml:id="echoid-s9523" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9524" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9525" xml:space="preserve">Hac via primo loco reperitur tertium latus, de-
              <lb/>
            inde vero duo anguli: </s>
            <s xml:id="echoid-s9526" xml:space="preserve">cum tamen alio modo anguli prius inuenti ſint, quam
              <lb/>
            tertium latus.</s>
            <s xml:id="echoid-s9527" xml:space="preserve"/>
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