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 |< < (314) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div820" type="section" level="1" n="460">
          <p>
            <s xml:id="echoid-s9780" xml:space="preserve">
              <pb o="314" file="326" n="326" rhead=""/>
            quadrato rectæ EG, æqualia ſunt, ſi ea in vnam ſummam colligamus, fiet qua-
              <lb/>
            dratum rectæ EG, 2698720744. </s>
            <s xml:id="echoid-s9781" xml:space="preserve">cuius radix quadrata dabit EG, partium
              <lb/>
            51949. </s>
            <s xml:id="echoid-s9782" xml:space="preserve">Cum autem, poſito ſinu toto EG, recta HG, ſinus ſit anguli HEG,
              <lb/>
            vt in ſinuum defin. </s>
            <s xml:id="echoid-s9783" xml:space="preserve">diximus, dicemus rurſum. </s>
            <s xml:id="echoid-s9784" xml:space="preserve">Si EG, inuenta partium 51949.
              <lb/>
            </s>
            <s xml:id="echoid-s9785" xml:space="preserve">dat EG, ſinum totum partium 100000. </s>
            <s xml:id="echoid-s9786" xml:space="preserve">quid dabit HG, inuenta partium
              <lb/>
            30210? </s>
            <s xml:id="echoid-s9787" xml:space="preserve">inueniemusque HG, ſinum anguli HEG, partiũ 58153. </s>
            <s xml:id="echoid-s9788" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s9789" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          EG. # EG. # HG. # # HG.
            <lb/>
          51949. # 100000. # 30210? # ſit. # 58153.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9790" xml:space="preserve">Ex ſinuum ergo tabula dabitur angulus HEG, ſiue arcus AF, grad. </s>
            <s xml:id="echoid-s9791" xml:space="preserve">35. </s>
            <s xml:id="echoid-s9792" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s9793" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9794" xml:space="preserve">qui additus ſemiſsi AB, grad. </s>
            <s xml:id="echoid-s9795" xml:space="preserve">65. </s>
            <s xml:id="echoid-s9796" xml:space="preserve">exhibebit maiorem arcum BF, ideoq́ue
              <lb/>
            & </s>
            <s xml:id="echoid-s9797" xml:space="preserve">angulum BEF, grad. </s>
            <s xml:id="echoid-s9798" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9799" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9800" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9801" xml:space="preserve">ablatus vero ex ſemiſſe AD, reliquum
              <lb/>
            faciet arcum minorem FD, atque adeo & </s>
            <s xml:id="echoid-s9802" xml:space="preserve">angulum FED, grad. </s>
            <s xml:id="echoid-s9803" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9804" xml:space="preserve">Min.</s>
            <s xml:id="echoid-s9805" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9806" xml:space="preserve">
              <lb/>
            vt prius.</s>
            <s xml:id="echoid-s9807" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9808" xml:space="preserve">QVOCIRCA, quando aggregatum duorum arcuum, vel angulo-
              <lb/>
              <note position="left" xlink:label="note-326-02" xlink:href="note-326-02a" xml:space="preserve">Praxis.</note>
            rum minus eſt, quam grad. </s>
            <s xml:id="echoid-s9809" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9810" xml:space="preserve">Si fiat, vt ſemiſſis aggregati terminorum
              <lb/>
            proportionis datæ ad ſinum ſemiſſis aggregatiarcuum, angulorumve, ita
              <lb/>
            differentia inter ſemiſſem aggregati terminorum datæ proportionis, & </s>
            <s xml:id="echoid-s9811" xml:space="preserve">
              <lb/>
            alterutrum terminorum, ad aliud, inuenietur numerus; </s>
            <s xml:id="echoid-s9812" xml:space="preserve">cuius quadr atum
              <lb/>
            ſi adiungatur quadrato ſinus complementi ſemiſſis aggregati arcuum, ſeu
              <lb/>
            angulorum; </s>
            <s xml:id="echoid-s9813" xml:space="preserve">Et tandem fiat, vt compoſiti buius numeri radix quadrata
              <lb/>
            ad ſinum totum, it a numerus per auream regulam nuper inuẽtus ad aliud,
              <lb/>
            producetur ſinus anguli, ſiue arcus, quo vter angulus, arcusve quæſitus
              <lb/>
            ab eorundem aggregati ſemiſſe differt. </s>
            <s xml:id="echoid-s9814" xml:space="preserve">Additus ergo arcus, ſiue angulus
              <lb/>
            buius ſinus inuenti ad ſemiſſem aggregati dati, dabit maiorem arcum, vel
              <lb/>
            angulum; </s>
            <s xml:id="echoid-s9815" xml:space="preserve">ablatus vero ex eadem ſemiſſe relinquet minorem arcum, ſiu@
              <lb/>
            angulum. </s>
            <s xml:id="echoid-s9816" xml:space="preserve">Sed priores duæ viæ longe ſunt expeditiores; </s>
            <s xml:id="echoid-s9817" xml:space="preserve">vt perſpicuum eſt</s>
          </p>
          <p>
            <s xml:id="echoid-s9818" xml:space="preserve">DETVR deinde aggregatum arcuum BC, CD, quorum ſinguli ſemicit
              <lb/>
              <note position="left" xlink:label="note-326-03" xlink:href="note-326-03a" xml:space="preserve">Quádo ag-
                <lb/>
              gregatũ ar
                <lb/>
              cuũ, vel an
                <lb/>
              gulorũ ma
                <lb/>
              ius eſt, quá
                <lb/>
              grad.180.</note>
            culo quoq; </s>
            <s xml:id="echoid-s9819" xml:space="preserve">ſint minores, vel angulorum BEC, CED, at aggregatum tam
              <lb/>
            arcuum, quam angulorum ſuperet grad. </s>
            <s xml:id="echoid-s9820" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9821" xml:space="preserve">nempe detur grad. </s>
            <s xml:id="echoid-s9822" xml:space="preserve">230. </s>
            <s xml:id="echoid-s9823" xml:space="preserve">Detut
              <lb/>
            item proportio ſinus arcus BC, vel anguli BEC, ad ſinum arcus CD, vel an-
              <lb/>
            guli CED, eadem, quæ 10. </s>
            <s xml:id="echoid-s9824" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9825" xml:space="preserve">Oportet ex his vtrumq; </s>
            <s xml:id="echoid-s9826" xml:space="preserve">arcum BC, CD, vel
              <lb/>
            vtrumq; </s>
            <s xml:id="echoid-s9827" xml:space="preserve">angulum BEC, CED, elicere. </s>
            <s xml:id="echoid-s9828" xml:space="preserve">Ducta diametro CF, & </s>
            <s xml:id="echoid-s9829" xml:space="preserve">detracto da-
              <lb/>
            to aggregato ex integro circulo, hoc eſt, ex grad. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">360. </s>
            <s xml:id="echoid-s9831" xml:space="preserve">reliquum erit aggrega-
              <lb/>
            tum arcuum BF, FD, vel angulorum BEF, FED, grad. </s>
            <s xml:id="echoid-s9832" xml:space="preserve">130. </s>
            <s xml:id="echoid-s9833" xml:space="preserve">minus, quam
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9834" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9835" xml:space="preserve">Et quoniam arcus BC, BF, eundem ſinuum habent, necnon & </s>
            <s xml:id="echoid-s9836" xml:space="preserve">ar-
              <lb/>
            cus CD, FD, vt in deſin. </s>
            <s xml:id="echoid-s9837" xml:space="preserve">ſinuum diximus, data quoq; </s>
            <s xml:id="echoid-s9838" xml:space="preserve">erit proportio ſinuum
              <lb/>
            arcuum BF, FD, vel angulorum BEF, FED, eadem, quæ 10. </s>
            <s xml:id="echoid-s9839" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9840" xml:space="preserve">Quam
              <lb/>
            ob rem, vt iam demonſtratum eſt, inueniemus arcus BF, FD, vel angulos
              <lb/>
            BEF, FED, grad. </s>
            <s xml:id="echoid-s9841" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9842" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9843" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9844" xml:space="preserve">& </s>
            <s xml:id="echoid-s9845" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9846" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9847" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9848" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9849" xml:space="preserve">qui ex ſemicirculo, hoc
              <lb/>
            eſt, ex grad. </s>
            <s xml:id="echoid-s9850" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9851" xml:space="preserve">ſublati relinquent arcus BC, CD, vel angulos BEC, CED,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9852" xml:space="preserve">79. </s>
            <s xml:id="echoid-s9853" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9854" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9855" xml:space="preserve">& </s>
            <s xml:id="echoid-s9856" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9857" xml:space="preserve">150. </s>
            <s xml:id="echoid-s9858" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9859" xml:space="preserve">34.</s>
            <s xml:id="echoid-s9860" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9861" xml:space="preserve">QVANDO ergo aggregatum duorum arcuum, ſeu angulorum ma-
              <lb/>
              <note position="left" xlink:label="note-326-04" xlink:href="note-326-04a" xml:space="preserve">Praxis.</note>
            ius eſt, quam grad. </s>
            <s xml:id="echoid-s9862" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9863" xml:space="preserve">Si illud ex grad. </s>
            <s xml:id="echoid-s9864" xml:space="preserve">360. </s>
            <s xml:id="echoid-s9865" xml:space="preserve">auferamus, remanebit
              <lb/>
            aggregatum aliorum duorum arcuum, vel angulorum minus, quam grad.</s>
            <s xml:id="echoid-s9866" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum