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

Table of Notes

< >
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
< >
page |< < (317) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div833" type="section" level="1" n="462">
          <pb o="317" file="329" n="329" rhead=""/>
          <p>
            <s xml:id="echoid-s9966" xml:space="preserve">ALITER ſine tangentibus per ſolos ſinus. </s>
            <s xml:id="echoid-s9967" xml:space="preserve">Iisdem poſitis, quoniam, per
              <lb/>
              <note position="right" xlink:label="note-329-01" xlink:href="note-329-01a" xml:space="preserve">Aliter ſine
                <lb/>
              tãgẽtibus.</note>
            ea, quæ in ſinuum deſin. </s>
            <s xml:id="echoid-s9968" xml:space="preserve">oſtendimus, poſito ſinu toto ED, recta HD, ſinus
              <lb/>
            eſt anguli HED, nimirum ſ@miſsis differentiæ arcuum, vel angulorum datæ,
              <lb/>
            hoc eſt, grad. </s>
            <s xml:id="echoid-s9969" xml:space="preserve">30. </s>
            <s xml:id="echoid-s9970" xml:space="preserve">& </s>
            <s xml:id="echoid-s9971" xml:space="preserve">HE, ſinus anguli HDE, grad. </s>
            <s xml:id="echoid-s9972" xml:space="preserve">60. </s>
            <s xml:id="echoid-s9973" xml:space="preserve">vt pote complementi
              <lb/>
            anguli HED; </s>
            <s xml:id="echoid-s9974" xml:space="preserve">dabitur ex ſinuum tabula, HD, partium 50000. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">& </s>
            <s xml:id="echoid-s9976" xml:space="preserve">EH, par-
              <lb/>
            tium 86603. </s>
            <s xml:id="echoid-s9977" xml:space="preserve">Iam vero ſi dicamus. </s>
            <s xml:id="echoid-s9978" xml:space="preserve">Si HD, ſemiſsis differentiæ terminorum
              <lb/>
            proportionis datæ, nimirum 3. </s>
            <s xml:id="echoid-s9979" xml:space="preserve">dat HD, ſinum @0000. </s>
            <s xml:id="echoid-s9980" xml:space="preserve">vtpote ſinum ſemiſsis
              <lb/>
            differentiæ arcuũ, angulorum ve datæ, quid dabit HG, aggregatũ ex ſemiſſe
              <lb/>
            differentiæ terminorum proportionis, & </s>
            <s xml:id="echoid-s9981" xml:space="preserve">conſequente eiuſdem proportionis,
              <lb/>
            nempe 8? </s>
            <s xml:id="echoid-s9982" xml:space="preserve">inueniemus HG, eſſe 133333. </s>
            <s xml:id="echoid-s9983" xml:space="preserve">reſpectu ſinus totius ED, vt hic vides.</s>
            <s xml:id="echoid-s9984" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          HD. # HD. # HG. # # HG.
            <lb/>
          3. # 50000. # 8? # ſit. # 133333.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9985" xml:space="preserve">Igitur, cum quadrata rectarum EH, HG, nempe 7499906404. </s>
            <s xml:id="echoid-s9986" xml:space="preserve">17777688889.
              <lb/>
            </s>
            <s xml:id="echoid-s9987" xml:space="preserve">æqualia ſint quadrato rectæ EG, fiet quadratum rectæ EG, 25277595293. </s>
            <s xml:id="echoid-s9988" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-329-03" xlink:href="note-329-03a" xml:space="preserve">47.primi.</note>
            cuius radix quadrata indicabit rectam EG, eſſe 158989. </s>
            <s xml:id="echoid-s9989" xml:space="preserve">reſpectu ſinus totius
              <lb/>
            ED. </s>
            <s xml:id="echoid-s9990" xml:space="preserve">Cum autem, vt in noſtris ſinubus diximus, poſito ſinutoto EG, recta
              <lb/>
            HG, ſit ſinus anguli HEG; </s>
            <s xml:id="echoid-s9991" xml:space="preserve">dicemus rurſum. </s>
            <s xml:id="echoid-s9992" xml:space="preserve">Si EG, inuenta partiũ 158989.
              <lb/>
            </s>
            <s xml:id="echoid-s9993" xml:space="preserve">dat EG, ſinum totum partium 100000. </s>
            <s xml:id="echoid-s9994" xml:space="preserve">quid dabit HG, inuenta partium
              <lb/>
            133333? </s>
            <s xml:id="echoid-s9995" xml:space="preserve">reperiemusq́; </s>
            <s xml:id="echoid-s9996" xml:space="preserve">HG, ſinum anguli HEG, partiũ 83863. </s>
            <s xml:id="echoid-s9997" xml:space="preserve">vt hic apparet.</s>
            <s xml:id="echoid-s9998" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          EG. # EG. # HG. # # HG.
            <lb/>
          158989. # 100000. # 133333? # ſit. # 83863.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9999" xml:space="preserve">Hic ſinus in tabula ſinuum monſtratarcum grad. </s>
            <s xml:id="echoid-s10000" xml:space="preserve">57. </s>
            <s xml:id="echoid-s10001" xml:space="preserve">Tantus eſt ergo angulus
              <lb/>
            AEF, ſiue arcus AF; </s>
            <s xml:id="echoid-s10002" xml:space="preserve">cui ſi adijciatur ſemiſsis AB, grad. </s>
            <s xml:id="echoid-s10003" xml:space="preserve">30. </s>
            <s xml:id="echoid-s10004" xml:space="preserve">fiet arcus maior
              <lb/>
            BF, & </s>
            <s xml:id="echoid-s10005" xml:space="preserve">angulus BEF, grad. </s>
            <s xml:id="echoid-s10006" xml:space="preserve">87. </s>
            <s xml:id="echoid-s10007" xml:space="preserve">Sivero ab eodem minuatur ſemiſsis AD,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s10008" xml:space="preserve">30. </s>
            <s xml:id="echoid-s10009" xml:space="preserve">reliquus erit minor arcus DF, & </s>
            <s xml:id="echoid-s10010" xml:space="preserve">angulus DEF, grad. </s>
            <s xml:id="echoid-s10011" xml:space="preserve">27. </s>
            <s xml:id="echoid-s10012" xml:space="preserve">vt prius.</s>
            <s xml:id="echoid-s10013" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10014" xml:space="preserve">SI igitur (quando proportio ſinuum data eſt maioris inæqualitatis)
              <lb/>
              <note position="right" xlink:label="note-329-05" xlink:href="note-329-05a" xml:space="preserve">Praxis.</note>
            fiat, vt ſemiſſis differentiæ terminorum proportionis datæ ad ſinum ſemiſ-
              <lb/>
            ſis differentiæ arcuum, vel angulorum datæ, ita aggregatum ex ſemiſſe
              <lb/>
            differentiæ terminorum proportionis, & </s>
            <s xml:id="echoid-s10015" xml:space="preserve">conſequente eiuſdem proportio-
              <lb/>
            nis, ad aliud, inuenietur numerus; </s>
            <s xml:id="echoid-s10016" xml:space="preserve">cuius quadratum ſi adijciatur quadra-
              <lb/>
            to ſinus compl@menti ſemiſſis differentiæ arcuum, vel angulorum datæ: </s>
            <s xml:id="echoid-s10017" xml:space="preserve">Et
              <lb/>
            tandem fiat, vt compoſiti buius numeriradix quadrata ad ſinum totum,
              <lb/>
            itanumerus per regulam auream nuper inuentus ad aliud, inuenietur ſi-
              <lb/>
            nus anguli, ſiue arcus, cui ſi addatur ſemiſſis differentiæ arcuum, vel an-
              <lb/>
            gulorum datæ, notus fict maior arcus, ſiue angulus: </s>
            <s xml:id="echoid-s10018" xml:space="preserve">Ab eodem vero ſi
              <lb/>
            eadem ſemiſſis detrahatur, remanebit minor arcus, angulusve cognitus.
              <lb/>
            </s>
            <s xml:id="echoid-s10019" xml:space="preserve">Sed prior ratio breuior eſt, vt conſtat.</s>
            <s xml:id="echoid-s10020" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10021" xml:space="preserve">ADHVC aliter tam per tangentes, quam per ſinus. </s>
            <s xml:id="echoid-s10022" xml:space="preserve">Ijſdem poſitis, & </s>
            <s xml:id="echoid-s10023" xml:space="preserve">
              <lb/>
            extenſa recta BE, vſq; </s>
            <s xml:id="echoid-s10024" xml:space="preserve">ad I: </s>
            <s xml:id="echoid-s10025" xml:space="preserve">Quoniam arcus BD, hoc eſt, differentia arcuum
              <lb/>
            BF, DF, datur grad. </s>
            <s xml:id="echoid-s10026" xml:space="preserve">60. </s>
            <s xml:id="echoid-s10027" xml:space="preserve">dabitur reliquus ſemicirculiarcus DI, nimirum ag-
              <lb/>
            gregatum arcuum DF, FI, grad. </s>
            <s xml:id="echoid-s10028" xml:space="preserve">120. </s>
            <s xml:id="echoid-s10029" xml:space="preserve">Datur autem & </s>
            <s xml:id="echoid-s10030" xml:space="preserve">proportio ſinus arcus
              <lb/>
            BF, hoc eſt, arcus FI, (cum arcus BF, FI, eundem ſinum habeant, vt in de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s10031" xml:space="preserve">ſinuum diximus.) </s>
            <s xml:id="echoid-s10032" xml:space="preserve">ad ſinum arcus DF, eadem, quæ 11. </s>
            <s xml:id="echoid-s10033" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s10034" xml:space="preserve">Quare, vt de-
              <lb/>
            monſtratum eſt, vterq; </s>
            <s xml:id="echoid-s10035" xml:space="preserve">arcus IF, DF, cognoſcetur, quorum DF, eſt minor
              <lb/>
              <note position="right" xlink:label="note-329-06" xlink:href="note-329-06a" xml:space="preserve">6.huius.</note>
            propoſitorum arcuum: </s>
            <s xml:id="echoid-s10036" xml:space="preserve">at FI, complementum maioris BF, vſq; </s>
            <s xml:id="echoid-s10037" xml:space="preserve">ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum